1 00:00:00,000 --> 00:00:11,200 Welcome to the Cannabis Data Science Meetup Group. 2 00:00:11,200 --> 00:00:12,760 Happy to have you here. 3 00:00:12,760 --> 00:00:14,600 So got a lot to talk about. 4 00:00:14,600 --> 00:00:23,240 So last week we were at MJ Biz, so we didn't have too much material to actually sit down 5 00:00:23,240 --> 00:00:26,000 and work on, so we're going to make it up today. 6 00:00:26,000 --> 00:00:29,800 And even launched a new event, Saturday Statistics. 7 00:00:29,800 --> 00:00:36,440 So you're welcome to join us on Saturdays and then we'll get a little bit more in-depth 8 00:00:36,440 --> 00:00:43,600 about the actual statistics behind what we're doing. 9 00:00:43,600 --> 00:00:49,120 And so we'll do a statistics lesson, supplement that with some cannabis data, and we'll have 10 00:00:49,120 --> 00:00:57,480 a nice fun time of it. 11 00:00:57,480 --> 00:01:02,580 So here's just the standard group for today. 12 00:01:02,580 --> 00:01:12,000 And then you're welcome to find the Saturday morning statistics, which will be a fun time. 13 00:01:12,000 --> 00:01:17,880 So essentially each Saturday I'll make sure that we walk away at the end of the day having 14 00:01:17,880 --> 00:01:21,640 created a beautiful visualization. 15 00:01:21,640 --> 00:01:29,440 And so I heard somewhere that the one in control of the data and the visualization is often 16 00:01:29,440 --> 00:01:31,860 the one in control of the decision. 17 00:01:31,860 --> 00:01:39,200 So if you're able to create some beautiful charts at your organization, then it'll take 18 00:01:39,200 --> 00:01:41,040 you a long way. 19 00:01:41,040 --> 00:01:46,520 So I'll try to make that worthwhile for you. 20 00:01:46,520 --> 00:01:48,720 All right. 21 00:01:48,720 --> 00:01:58,600 So for today, I thought we could dust off a little work we've done in the past and apply 22 00:01:58,600 --> 00:02:04,240 it to the Massachusetts market because that's a market that still have interesting. 23 00:02:04,240 --> 00:02:10,360 So it's still an up and coming market despite there being some established players since 24 00:02:10,360 --> 00:02:13,160 the industry has been around since 2018. 25 00:02:13,160 --> 00:02:18,960 However, it is one of the more strictly regulated markets. 26 00:02:18,960 --> 00:02:27,320 So it is taking certain players longer than expected to get up and running. 27 00:02:27,320 --> 00:02:32,900 So one thing we're going to look at are prices, right? 28 00:02:32,900 --> 00:02:43,140 So in the past, we looked at prices in Oregon and we tried to estimate the output and prices 29 00:02:43,140 --> 00:02:44,140 in Oregon. 30 00:02:44,140 --> 00:02:52,960 And so remember, we were looking at inflation and we can simply define inflation as the 31 00:02:52,960 --> 00:03:02,840 change in prices from the day to yesterday divided by yesterday's prices. 32 00:03:02,840 --> 00:03:07,560 So we'll be interested in inflation as well as output. 33 00:03:07,560 --> 00:03:22,560 So before we dived, well, I guess just a bit of the cannabis information. 34 00:03:22,560 --> 00:03:33,400 So prices dropping precipitously here in Oregon has been a challenge for the producers and 35 00:03:33,400 --> 00:03:36,280 perhaps retailers in Oregon. 36 00:03:36,280 --> 00:03:39,160 Because it's incredibly competitive. 37 00:03:39,160 --> 00:03:41,560 It's really hard to make a profit. 38 00:03:41,560 --> 00:03:49,300 So many people that may have been profitable at a $40 per gram price point may no longer 39 00:03:49,300 --> 00:03:50,720 be profitable. 40 00:03:50,720 --> 00:04:09,680 So I think we may have. 41 00:04:09,680 --> 00:04:10,680 Welcome. 42 00:04:10,680 --> 00:04:11,680 Happy to have you. 43 00:04:11,680 --> 00:04:17,960 So right now we're talking about prices in Oregon. 44 00:04:17,960 --> 00:04:33,120 So let's see. 45 00:04:33,120 --> 00:04:39,240 And we'll maybe do introductions here at the end since we have already dived in or perhaps 46 00:04:39,240 --> 00:04:43,640 we'll take a break in the middle. 47 00:04:43,640 --> 00:04:48,320 So let's just try to. 48 00:04:48,320 --> 00:04:51,360 Hi, Cheyenne. 49 00:04:51,360 --> 00:04:53,080 It's good to have you here. 50 00:04:53,080 --> 00:04:57,240 So I'll try to stay unfocused since I'm already presenting here. 51 00:04:57,240 --> 00:05:01,000 Okay, let's try this one more time. 52 00:05:01,000 --> 00:05:03,840 Pardon the interruptions. 53 00:05:03,840 --> 00:05:09,240 So long story short, we've got historical data in Oregon. 54 00:05:09,240 --> 00:05:11,360 We saw the price point fall. 55 00:05:11,360 --> 00:05:15,280 This made it difficult for producers. 56 00:05:15,280 --> 00:05:18,560 Some producers are still making a good go of it. 57 00:05:18,560 --> 00:05:25,060 We're interested in what may happen in Massachusetts. 58 00:05:25,060 --> 00:05:28,880 So we're going to use some economic models. 59 00:05:28,880 --> 00:05:33,280 As we found out last time with our theoretical models, we were having a hard time getting 60 00:05:33,280 --> 00:05:41,840 them to fit in Massachusetts due to the sporadic nature of the data and the small number of 61 00:05:41,840 --> 00:05:45,880 observations and perhaps the flimsy theory. 62 00:05:45,880 --> 00:05:50,840 So we're going to go with an a theoretical approach this time. 63 00:05:50,840 --> 00:05:56,380 And we're going to introduce a variable, the interest rate. 64 00:05:56,380 --> 00:06:04,280 So we talked about the dynamic here when we talked about Oregon, how the central bank 65 00:06:04,280 --> 00:06:14,040 will try to set interest rates to ultimately keep inflation under control and try to maximize 66 00:06:14,040 --> 00:06:18,640 output. 67 00:06:18,640 --> 00:06:25,160 So you can actually model these economic variables in a system of equations. 68 00:06:25,160 --> 00:06:27,960 And so these are simultaneous equations. 69 00:06:27,960 --> 00:06:30,800 So these are all happening at the same time. 70 00:06:30,800 --> 00:06:34,360 So you've got output y. 71 00:06:34,360 --> 00:06:45,040 And so output today is dependent on output from the past, any given historical periods, 72 00:06:45,040 --> 00:06:46,040 t minus j. 73 00:06:46,040 --> 00:06:52,160 So t minus 1, t minus 2, t minus 3, what have you. 74 00:06:52,160 --> 00:06:56,280 Output today is dependent on inflation in the past. 75 00:06:56,280 --> 00:07:02,560 And then output today is also dependent on the interest rates in the past. 76 00:07:02,560 --> 00:07:12,000 Because investors needed to, well, the producers needed to invest in capital equipment. 77 00:07:12,000 --> 00:07:16,480 And the investors needed to supply a certain amount of capital. 78 00:07:16,480 --> 00:07:22,520 So that's a whole market of its own, the capital market. 79 00:07:22,520 --> 00:07:30,120 Inflation, so what's happening with prices, but governs what's going to happen with output. 80 00:07:30,120 --> 00:07:34,440 So we know that from our economic theory. 81 00:07:34,440 --> 00:07:39,320 And now we've introduced a third player, the central bank. 82 00:07:39,320 --> 00:07:46,440 And so the central bank, they're going to be making their decisions based on past output. 83 00:07:46,440 --> 00:07:50,920 Past inflation, as well as past interest rates. 84 00:07:50,920 --> 00:07:57,080 So you have these simultaneous equations that are happening. 85 00:07:57,080 --> 00:08:03,760 Luckily, we can estimate these because these are nice linear equations. 86 00:08:03,760 --> 00:08:08,240 And we have each of these data points. 87 00:08:08,240 --> 00:08:11,920 So why are we picking this model? 88 00:08:11,920 --> 00:08:16,320 Well, for starters, it's a theoretical model. 89 00:08:16,320 --> 00:08:17,800 It's theoretical. 90 00:08:17,800 --> 00:08:29,640 So we're not imposing any production function assumptions or any assumptions of that sort, 91 00:08:29,640 --> 00:08:31,640 like we have done in previous weeks. 92 00:08:31,640 --> 00:08:37,800 So if you look at the recordings from the prior weeks, we attempted to estimate production 93 00:08:37,800 --> 00:08:40,120 functions in Massachusetts. 94 00:08:40,120 --> 00:08:46,560 As Heather can attest, we were having trouble estimating those models well. 95 00:08:46,560 --> 00:08:53,120 So can we use those models for predicting the future? 96 00:08:53,120 --> 00:08:59,160 You know, perhaps, but they may not be the best predictors. 97 00:08:59,160 --> 00:09:05,800 So what's cool about the VARS is they're flexible. 98 00:09:05,800 --> 00:09:10,040 They can really fit many different data points, as I'll show you here in a bit. 99 00:09:10,040 --> 00:09:12,720 They can fit any frequency. 100 00:09:12,720 --> 00:09:17,680 So we were seeing that, oh, you know, we may have daily, we may have weekly, we may have 101 00:09:17,680 --> 00:09:20,980 monthly, we may even have quarterly data. 102 00:09:20,980 --> 00:09:26,440 So the frequency of the data matters. 103 00:09:26,440 --> 00:09:29,120 Bitfall of the VAR. 104 00:09:29,120 --> 00:09:34,520 If you look here, we have many different variables. 105 00:09:34,520 --> 00:09:42,120 As we were talking about, every variable introduces possibilities for measurement error or what 106 00:09:42,120 --> 00:09:43,240 have you. 107 00:09:43,240 --> 00:09:52,000 And so the top of those concerns, you also have each variable, each way at your degrees 108 00:09:52,000 --> 00:09:53,840 of freedom. 109 00:09:53,840 --> 00:09:57,560 So on that each variable rate to each parameter, right? 110 00:09:57,560 --> 00:10:00,520 So we're going to be estimating all of these parameters. 111 00:10:00,520 --> 00:10:07,240 So our degrees of freedom is going to go down rapidly. 112 00:10:07,240 --> 00:10:13,680 So you have to be careful, because if you're limited to your number of observations, which 113 00:10:13,680 --> 00:10:20,000 we are, it can be difficult to fit a VAR model. 114 00:10:20,000 --> 00:10:26,800 And so you may overfit, which once again can lead to bad forecasts. 115 00:10:26,800 --> 00:10:33,640 So we're going to hedge this. 116 00:10:33,640 --> 00:10:36,840 This is how you can write the VAR. 117 00:10:36,840 --> 00:10:41,640 So this is just a simplified manner. 118 00:10:41,640 --> 00:10:42,640 Let's get to the forecasting. 119 00:10:42,640 --> 00:10:45,440 That's the more interesting part. 120 00:10:45,440 --> 00:10:52,120 So it's easy to forecast with a VAR, right? 121 00:10:52,120 --> 00:10:56,920 And so the first equation is the model we'll be estimating, right? 122 00:10:56,920 --> 00:11:05,000 Where output, inflation, and the interest rate, those all depend on yesterday's values. 123 00:11:05,000 --> 00:11:13,840 Well, given yesterday's values, you can, and you've estimated your parameters, then you 124 00:11:13,840 --> 00:11:18,160 can simply play that one period forward. 125 00:11:18,160 --> 00:11:24,480 So you can just plug in today's values with the parameters you estimated, and you can 126 00:11:24,480 --> 00:11:26,920 get the next period's values. 127 00:11:26,920 --> 00:11:34,360 You can then plug in next period's values with your parameters and get the period after. 128 00:11:34,360 --> 00:11:44,200 So you can do this subsequently, and you can get forecasts for end periods into the future. 129 00:11:44,200 --> 00:11:55,680 So we can predict output, inflation, and interest rate however long we want into the future. 130 00:11:55,680 --> 00:12:03,040 Keep in mind the confidence of our forecasts is going to be increasing the further we go 131 00:12:03,040 --> 00:12:09,680 into the future, but we can still do powerful things, right? 132 00:12:09,680 --> 00:12:17,600 So this is how people can say, oh, what may sales be in 2030, right? 133 00:12:17,600 --> 00:12:18,920 We could play that out. 134 00:12:18,920 --> 00:12:23,280 It could be wildly inaccurate, but we can play that out. 135 00:12:23,280 --> 00:12:25,600 What will sales be like in 2022? 136 00:12:25,600 --> 00:12:26,600 We can play that out. 137 00:12:26,600 --> 00:12:30,000 It will be slightly more accurate than 2030. 138 00:12:30,000 --> 00:12:33,660 Or what would sales be like next month, right? 139 00:12:33,660 --> 00:12:43,980 And then that's going to have the least, the smallest confidence interval. 140 00:12:43,980 --> 00:12:54,320 So we can be a bit more certain about that one, but there's still going to be uncertainty. 141 00:12:54,320 --> 00:13:03,400 And so I want to hit on what a professor boiled down to me as the 10 Commandments of Forecasting. 142 00:13:03,400 --> 00:13:04,400 Right? 143 00:13:04,400 --> 00:13:09,120 And so we'll just go over these real quick since we're about to be doing forecasting. 144 00:13:09,120 --> 00:13:14,000 And I want to have these in everyone's mind, and then we'll go over them at the end just 145 00:13:14,000 --> 00:13:17,080 to make sure that we hit each point. 146 00:13:17,080 --> 00:13:23,100 So we first and foremost need to know what we're forecasting. 147 00:13:23,100 --> 00:13:29,040 That's going to be sales in Massachusetts, right? 148 00:13:29,040 --> 00:13:35,880 Because we want to have an estimate for what sales may be in 2021. 149 00:13:35,880 --> 00:13:41,320 And then we may like to know what sales may be like next year in 2022. 150 00:13:41,320 --> 00:13:49,680 So we can maybe say, making prediction about how much sales may increase or perhaps decrease 151 00:13:49,680 --> 00:13:51,160 next year. 152 00:13:51,160 --> 00:13:52,380 Right? 153 00:13:52,380 --> 00:14:01,920 And then we could perhaps make forecasts all the way to 2025 or 2030 or what have you, 154 00:14:01,920 --> 00:14:08,640 because you're seeing some large analytics firms making predictions that far into the 155 00:14:08,640 --> 00:14:09,640 future. 156 00:14:09,640 --> 00:14:15,280 And like I'd said in the past, I'm not a big fan of the black box approach, because we've 157 00:14:15,280 --> 00:14:18,680 seen how many assumptions are made along the way. 158 00:14:18,680 --> 00:14:24,400 So we're going to make a clear box for forecasting. 159 00:14:24,400 --> 00:14:25,400 Right? 160 00:14:25,400 --> 00:14:31,080 So you can at least look into it and see what gears are turning. 161 00:14:31,080 --> 00:14:34,440 What are the inputs and what are the outputs? 162 00:14:34,440 --> 00:14:35,960 And it's not a black box. 163 00:14:35,960 --> 00:14:41,660 So we're making a nice transparent box right now where you can see the forecasting model. 164 00:14:41,660 --> 00:14:43,760 You can see where you get your data from. 165 00:14:43,760 --> 00:14:49,800 You can see how things are operated and you can see how forecasts are made. 166 00:14:49,800 --> 00:14:58,320 And you can get in there and tinker yourself if you're not satisfied with how we made forecasts 167 00:14:58,320 --> 00:15:02,880 and improve upon what we've done to make even better forecasts. 168 00:15:02,880 --> 00:15:05,640 So that's what we're doing here. 169 00:15:05,640 --> 00:15:10,200 So that's step one. 170 00:15:10,200 --> 00:15:17,760 And really step two, right, the purpose of this is to have a nice transparent mechanism 171 00:15:17,760 --> 00:15:23,400 for forecasting that people can use to have better insights for the future so they can 172 00:15:23,400 --> 00:15:27,640 understand the market better. 173 00:15:27,640 --> 00:15:29,680 The cost of forecasting. 174 00:15:29,680 --> 00:15:36,540 This is where we need to emphasize that there's measurement error and our predictions could 175 00:15:36,540 --> 00:15:43,600 be inaccurate, right, because we don't want people putting too much stake in our forecasts, 176 00:15:43,600 --> 00:15:44,600 right? 177 00:15:44,600 --> 00:15:50,560 Because if you're a producer and you think the market is going to grow by X percent and 178 00:15:50,560 --> 00:15:57,160 the market doesn't grow by X percent, well, you need to have accounted for that in your 179 00:15:57,160 --> 00:15:59,680 business model, right? 180 00:15:59,680 --> 00:16:03,900 Because if you put too much stake into the forecast, sales don't grow as much as you 181 00:16:03,900 --> 00:16:06,440 expect. 182 00:16:06,440 --> 00:16:08,920 You may wind up in the red. 183 00:16:08,920 --> 00:16:27,600 So sometimes it's better to, you know, be a bit more, you know. 184 00:16:27,600 --> 00:16:36,080 Sometimes it's a bit prudent to plan based on the lower ends of the forecast and often 185 00:16:36,080 --> 00:16:42,760 than other times, maybe when you're predicting risk, it may be more prudent to operate in 186 00:16:42,760 --> 00:16:45,880 the upper bounds of the forecast. 187 00:16:45,880 --> 00:16:53,720 So you have to know, you know, is your risk asymmetric or symmetric? 188 00:16:53,720 --> 00:16:59,760 So three is a tricky point and we'll we'll dance around this as we we go through our 189 00:16:59,760 --> 00:17:00,760 estimation. 190 00:17:00,760 --> 00:17:07,760 Four, we've hit on this, so this is the rationalize the forecast horizon. 191 00:17:07,760 --> 00:17:11,200 So what's useful to forecast? 192 00:17:11,200 --> 00:17:17,160 So at the moment, I figured we may as well forecast to the end of the year. 193 00:17:17,160 --> 00:17:22,240 So that way we can go ahead and get an early estimate of the year total. 194 00:17:22,240 --> 00:17:25,240 So slightly valuable. 195 00:17:25,240 --> 00:17:29,000 And then I figured we may as well estimate sales next year. 196 00:17:29,000 --> 00:17:38,160 So that way we can start to to predict to what extent sales may rise or fall. 197 00:17:38,160 --> 00:17:40,400 So I think that would be useful. 198 00:17:40,400 --> 00:17:49,120 And then it perhaps would be useful to forecast through 2025, 2030, just for the fun of things, 199 00:17:49,120 --> 00:17:51,800 just to see how much things may grow. 200 00:17:51,800 --> 00:18:01,360 But I think the utility diminishes in that horizon. 201 00:18:01,360 --> 00:18:02,360 Understand our variables. 202 00:18:02,360 --> 00:18:03,360 Right. 203 00:18:03,360 --> 00:18:07,240 So these are we're going to dive into the deeper here in a second. 204 00:18:07,240 --> 00:18:13,360 But these are the variables that are available to us that match our economic theory and that 205 00:18:13,360 --> 00:18:16,280 fit into our model. 206 00:18:16,280 --> 00:18:18,760 Which forecasting model are we going to use? 207 00:18:18,760 --> 00:18:24,520 We talked about this where we were trying the theoretical approach, not working very 208 00:18:24,520 --> 00:18:25,520 well for us. 209 00:18:25,520 --> 00:18:30,000 We're going to try the a theoretical VAR approach. 210 00:18:30,000 --> 00:18:33,240 Of course, we need to present our results. 211 00:18:33,240 --> 00:18:34,240 Right. 212 00:18:34,240 --> 00:18:39,080 A nice time series visualization would be wonderful. 213 00:18:39,080 --> 00:18:41,360 You need to know how to decipher the results. 214 00:18:41,360 --> 00:18:42,360 Right. 215 00:18:42,360 --> 00:18:46,440 So that's when we're talking about, OK, if sales are going to increase, right, it would 216 00:18:46,440 --> 00:18:51,480 be nice to know about what percentage they're going to increase. 217 00:18:51,480 --> 00:18:56,360 And then these are the two most important points, in my opinion. 218 00:18:56,360 --> 00:18:58,920 One use recursive methods. 219 00:18:58,920 --> 00:19:11,560 So this is essentially what I mean by I boil this down to revisiting the model. 220 00:19:11,560 --> 00:19:12,560 Right. 221 00:19:12,560 --> 00:19:19,520 So we're going to forecast this period and then we can then forecast next period when 222 00:19:19,520 --> 00:19:21,520 the data comes in. 223 00:19:21,520 --> 00:19:28,600 So, you know, just keep iterating. 224 00:19:28,600 --> 00:19:37,240 And then we as we iterate, we may we may find flaws in the model. 225 00:19:37,240 --> 00:19:44,560 And it's OK for us to improve our model over time. 226 00:19:44,560 --> 00:19:49,680 So that's the main thing is we want to revisit our forecasts. 227 00:19:49,680 --> 00:19:55,760 So we want to forecast and then next month we want to come back, check our forecasts 228 00:19:55,760 --> 00:20:04,020 with the actual and use the actual and try to forecast the next month even better. 229 00:20:04,020 --> 00:20:11,560 So just so that's the recursion where each month you come back, you see. 230 00:20:11,560 --> 00:20:16,120 You measure your forecasting error. 231 00:20:16,120 --> 00:20:23,120 And then you use the new actual data to try to create a better a better model and reduce 232 00:20:23,120 --> 00:20:27,560 your forecast error for the next time. 233 00:20:27,560 --> 00:20:35,680 So I think let's get our hands on the data at this point. 234 00:20:35,680 --> 00:20:41,640 So all right. 235 00:20:41,640 --> 00:20:52,040 So just going to use a handful of standard packages here as well as two utility functions 236 00:20:52,040 --> 00:20:59,360 I've written that just help help us clean and clean the data. 237 00:20:59,360 --> 00:21:04,240 Using Python, but you're welcome to use your favorite programming language. 238 00:21:04,240 --> 00:21:08,480 OK. 239 00:21:08,480 --> 00:21:09,480 First things. 240 00:21:09,480 --> 00:21:10,480 Hold on. 241 00:21:10,480 --> 00:21:15,920 We may have a new attendee. 242 00:21:15,920 --> 00:21:24,120 All right. 243 00:21:24,120 --> 00:21:26,640 Awesome to have you, Eric. 244 00:21:26,640 --> 00:21:34,160 Just just wanted to point out that it was a little much for me to get everything ready 245 00:21:34,160 --> 00:21:36,960 for last Saturday for Saturday's statistics. 246 00:21:36,960 --> 00:21:39,360 So I apologize if you were looking for that. 247 00:21:39,360 --> 00:21:42,880 However, I have created the event. 248 00:21:42,880 --> 00:21:49,600 And so this coming Saturday will finally kick off with Saturday's statistics. 249 00:21:49,600 --> 00:21:56,880 And the goal of Saturday's statistics is to walk away with one beautiful visualization 250 00:21:56,880 --> 00:21:59,320 at the end of the day. 251 00:21:59,320 --> 00:22:07,640 Because that's sort of what we're going to emphasize here is how much you can persuade 252 00:22:07,640 --> 00:22:15,160 informed and even entertain people with a nice visualization. 253 00:22:15,160 --> 00:22:26,800 So for today, we're just going to get our hands dirty trying to actually do some forecasting. 254 00:22:26,800 --> 00:22:29,840 So we may make some visualizations. 255 00:22:29,840 --> 00:22:31,840 They may not be beautiful. 256 00:22:31,840 --> 00:22:38,040 But that's why you can tune in on Saturday. 257 00:22:38,040 --> 00:22:42,000 But without further ado, let's get the data. 258 00:22:42,000 --> 00:22:49,760 So I may go over the getting the data quickly, because we've done this a bit more in depth 259 00:22:49,760 --> 00:22:51,240 in prior weeks. 260 00:22:51,240 --> 00:23:01,800 But long story short, at least for Massachusetts, you can get quite rich data through the first 261 00:23:01,800 --> 00:23:02,800 week. 262 00:23:02,800 --> 00:23:06,560 So we're going to start with the Socrata API. 263 00:23:06,560 --> 00:23:12,160 So here we're going to be grabbing the average prices. 264 00:23:12,160 --> 00:23:16,200 This is a monthly series. 265 00:23:16,200 --> 00:23:22,880 And we're also going to be grabbing sales totals. 266 00:23:22,880 --> 00:23:30,200 And this is a daily series that we'll be aggregating into a monthly series. 267 00:23:30,200 --> 00:23:33,880 Data from the Federal Reserve. 268 00:23:33,880 --> 00:23:41,880 So we're going to grab the federal funds rate, which is essentially what economists refer 269 00:23:41,880 --> 00:23:49,040 to when they are talking about the interest rate. 270 00:23:49,040 --> 00:23:55,840 So this is the interest rate the banks pay, and thus it affects all the other interest 271 00:23:55,840 --> 00:23:59,960 rates. 272 00:23:59,960 --> 00:24:13,840 So we're going to get these data points and clean them to a certain extent. 273 00:24:13,840 --> 00:24:18,080 So for example, we need to calculate sales. 274 00:24:18,080 --> 00:24:24,460 So sales total is a cumulative series. 275 00:24:24,460 --> 00:24:27,440 So we need to take the difference of that. 276 00:24:27,440 --> 00:24:33,240 There are also these outliers that aren't rational. 277 00:24:33,240 --> 00:24:39,320 So these are negative sales and sales greater than, I believe this is 10 million in one 278 00:24:39,320 --> 00:24:40,320 day. 279 00:24:40,320 --> 00:24:45,480 And so these appear to be outliers to me. 280 00:24:45,480 --> 00:24:50,480 And so coding them is zero. 281 00:24:50,480 --> 00:24:54,840 And so this is where we're starting to get into how the sausage is made, right? 282 00:24:54,840 --> 00:25:03,440 Because if you're using a black box approach, you wouldn't see these adjustments, or they 283 00:25:03,440 --> 00:25:06,720 may be in a tiny little footnote. 284 00:25:06,720 --> 00:25:14,120 And here we're being quite transparent that, yes, we're dealing with these outliers. 285 00:25:14,120 --> 00:25:16,040 My coding them is zero. 286 00:25:16,040 --> 00:25:23,480 If you have a better approach, then by all means, either fix it or send me an email or 287 00:25:23,480 --> 00:25:24,480 what have you. 288 00:25:24,480 --> 00:25:25,480 Then we'll get it fixed. 289 00:25:25,480 --> 00:25:39,640 And long story short, we can get the sales data here. 290 00:25:39,640 --> 00:25:49,040 And this was throwing us a curveball in prior weeks. 291 00:25:49,040 --> 00:25:54,920 And I finally got an answer at MJBizCon. 292 00:25:54,920 --> 00:26:01,640 And it was real funny because I think I was one of the only people to actually know this 293 00:26:01,640 --> 00:26:02,640 answer. 294 00:26:02,640 --> 00:26:06,800 So there was one of the seminars was this cannabis data game show. 295 00:26:06,800 --> 00:26:12,760 And you had some of the top data scientists from the top analytics companies. 296 00:26:12,760 --> 00:26:15,680 And they were just asking them trivia questions. 297 00:26:15,680 --> 00:26:24,280 And one of the questions was how much cannabis was sold in Massachusetts in April of 2020? 298 00:26:24,280 --> 00:26:27,560 And I had a sneaking suspicion that I knew the answer. 299 00:26:27,560 --> 00:26:31,520 And I guessed it was zero. 300 00:26:31,520 --> 00:26:35,640 And now we know for a fact it is in fact zero. 301 00:26:35,640 --> 00:26:40,800 So these data points here aren't missing. 302 00:26:40,800 --> 00:26:51,240 They in fact suspended sales of cannabis in Massachusetts from I want to say, what was 303 00:26:51,240 --> 00:27:07,280 it like March 24th or so through May 24th or so. 304 00:27:07,280 --> 00:27:09,200 I won't take up too much time with it now. 305 00:27:09,200 --> 00:27:13,240 You can drill down here and get the specific dates. 306 00:27:13,240 --> 00:27:18,800 But long story short, they did actually suspend sales during that period, which I think is 307 00:27:18,800 --> 00:27:20,640 real interesting. 308 00:27:20,640 --> 00:27:25,200 So now it's real interesting for a couple of factors. 309 00:27:25,200 --> 00:27:31,960 One, it's unfortunate because, well, it's unfortunate to maybe the producers or what 310 00:27:31,960 --> 00:27:38,840 have you because it may be fortunate for the people of Massachusetts, who knows. 311 00:27:38,840 --> 00:27:42,960 You saw a spike in most states, right? 312 00:27:42,960 --> 00:27:50,080 So most people went into a buying frenzy. 313 00:27:50,080 --> 00:27:56,480 But then again, economic theory suggests that people may just smooth out their consumption. 314 00:27:56,480 --> 00:28:02,760 So just because they went into a buying frenzy on one date, they may just reduce their consumption 315 00:28:02,760 --> 00:28:04,960 at a later date. 316 00:28:04,960 --> 00:28:11,160 But what have you, Massachusetts suspended sales. 317 00:28:11,160 --> 00:28:20,120 So we're kind of given essentially what you would call a shock, right? 318 00:28:20,120 --> 00:28:28,120 So here you're given this industry and this would be a production shock, right? 319 00:28:28,120 --> 00:28:39,000 Because you're going along, going along, and then we're just going to put a large negative 320 00:28:39,000 --> 00:28:42,680 production shock, the pandemic. 321 00:28:42,680 --> 00:28:51,680 And in this case, Massachusetts, it knocked sales to zero for this set period. 322 00:28:51,680 --> 00:29:00,680 So that's essentially a production shock and we can measure, okay, what effect did that 323 00:29:00,680 --> 00:29:05,360 have on prices? 324 00:29:05,360 --> 00:29:10,720 And also the interest rate, but the interest rate, we may go ahead and make the assumption 325 00:29:10,720 --> 00:29:19,520 that the interest rate's not really determined by output and prices of cannabis in Massachusetts, 326 00:29:19,520 --> 00:29:20,800 which it probably really isn't. 327 00:29:20,800 --> 00:29:30,800 I mean, maybe to a minor, minor degree, but that really depends on much larger scale factors. 328 00:29:30,800 --> 00:29:33,520 But that matters more for identification. 329 00:29:33,520 --> 00:29:44,560 And so long story short, if you're particularly interested in the theory behind VARs, so vector 330 00:29:44,560 --> 00:29:49,200 autoregressions, which we'll get to here in a minute, I'll recommend that you check out 331 00:29:49,200 --> 00:29:50,200 my website. 332 00:29:50,200 --> 00:29:53,960 So this is just keeganskeet.com. 333 00:29:53,960 --> 00:30:02,760 If you go to the PDFs and macroeconomics, I've got a real good section here about these vector 334 00:30:02,760 --> 00:30:03,760 autoregressions. 335 00:30:03,760 --> 00:30:09,600 And so here you'll get all the sources and more in depth about how we're actually estimating 336 00:30:09,600 --> 00:30:11,480 these. 337 00:30:11,480 --> 00:30:17,800 And if you really want to get into the weeds behind the statistics about what assumptions 338 00:30:17,800 --> 00:30:26,360 need to be made in a statistical sense, then I'll let you read into that, get into the 339 00:30:26,360 --> 00:30:29,560 weeds if you wish. 340 00:30:29,560 --> 00:30:34,400 But long story short, we'll estimate the model. 341 00:30:34,400 --> 00:30:38,320 We're not going to get into the weeds yet, perhaps on Saturday. 342 00:30:38,320 --> 00:30:42,720 But for today, we're just going to run through this. 343 00:30:42,720 --> 00:30:47,760 So long story short, we're interested in this production shock and how that's going to 344 00:30:47,760 --> 00:30:50,120 affect prices. 345 00:30:50,120 --> 00:30:55,960 So we can go ahead and create our monthly series here. 346 00:30:55,960 --> 00:31:04,360 And so here we're just aggregating sales. 347 00:31:04,360 --> 00:31:15,520 As you see, in April of 2020, sales dropped to zero. 348 00:31:15,520 --> 00:31:18,440 And then they carry along their way. 349 00:31:18,440 --> 00:31:27,560 And so it's going to be interesting to see if we can't disentangle what effect this shock 350 00:31:27,560 --> 00:31:28,880 may have had. 351 00:31:28,880 --> 00:31:40,000 And then the whole grand scheme is what's cool about these VARs is you can simulate 352 00:31:40,000 --> 00:31:54,680 production shocks, or you can simulate price shocks or interest rate shocks to figure out 353 00:31:54,680 --> 00:31:56,960 what would happen in the future. 354 00:31:56,960 --> 00:32:09,280 So you basically just add a large positive or negative shock to yt. 355 00:32:09,280 --> 00:32:13,200 And then you sort of let that play out in your forecasts. 356 00:32:13,200 --> 00:32:18,100 And you compare that to your forecasts without the shock. 357 00:32:18,100 --> 00:32:25,000 And so you can kind of estimate the effect of the shock. 358 00:32:25,000 --> 00:32:26,720 So I think this is interesting. 359 00:32:26,720 --> 00:32:32,760 And so that's going to require a bit more explanation with statistics. 360 00:32:32,760 --> 00:32:36,320 So this is either something we'll do on Saturday or perhaps next week. 361 00:32:36,320 --> 00:32:43,280 I kind of may say this for next week, because I think the shocks are something that a lot 362 00:32:43,280 --> 00:32:45,780 of people would benefit from understanding. 363 00:32:45,780 --> 00:32:53,840 Because that's sort of seeing things through their logical conclusions. 364 00:32:53,840 --> 00:33:00,560 And I think that's really what's cool about the VARs is you estimate the model. 365 00:33:00,560 --> 00:33:03,680 You use the model to predict the future. 366 00:33:03,680 --> 00:33:09,960 And then you say, OK, what would happen if something changed in the present? 367 00:33:09,960 --> 00:33:14,040 How would that change things in the future? 368 00:33:14,040 --> 00:33:19,800 So that's really quite sophisticated analysis. 369 00:33:19,800 --> 00:33:23,480 And that's sort of what we're moving towards. 370 00:33:23,480 --> 00:33:33,040 And I've gotten near to doing it in the wild, estimating production shocks. 371 00:33:33,040 --> 00:33:36,560 Not quite, but close. 372 00:33:36,560 --> 00:33:46,320 So I think it is something that people can do for companies once you have a nice handle 373 00:33:46,320 --> 00:33:50,320 on all the other statistics. 374 00:33:50,320 --> 00:33:56,640 But first things first, forecasting. 375 00:33:56,640 --> 00:34:02,160 So we've got our sales going along. 376 00:34:02,160 --> 00:34:07,920 Now we can get prices, right? 377 00:34:07,920 --> 00:34:10,600 What do the prices look like? 378 00:34:10,600 --> 00:34:15,760 Well, isn't that interesting? 379 00:34:15,760 --> 00:34:22,840 Of course, prices go to zero if sales. 380 00:34:22,840 --> 00:34:31,320 Well, actually, look, prices didn't necessarily go to zero. 381 00:34:31,320 --> 00:34:44,320 So I think I may want to think about this data point here for a second. 382 00:34:44,320 --> 00:34:51,240 Great, because if there was no sales, you would expect prices to go to. 383 00:34:51,240 --> 00:34:54,440 So these are supposed to be off. 384 00:34:54,440 --> 00:34:56,440 So you'd expect prices to go to zero. 385 00:34:56,440 --> 00:35:00,640 Long story short. 386 00:35:00,640 --> 00:35:05,160 What I would expect is, OK, you've got the production shock. 387 00:35:05,160 --> 00:35:12,880 And so one would expect that in all the periods following April of 2020, that that shock would 388 00:35:12,880 --> 00:35:19,360 have sort of a ripple effect on prices throughout time. 389 00:35:19,360 --> 00:35:27,440 And it seems that here it's an immediate effect. 390 00:35:27,440 --> 00:35:32,440 If we look at our model, right? 391 00:35:32,440 --> 00:35:41,880 So inflation, which is prices, right? 392 00:35:41,880 --> 00:35:45,840 Inflation rate change in price. 393 00:35:45,840 --> 00:35:50,320 So that's dependent on output from yesterday. 394 00:35:50,320 --> 00:35:58,940 So we would expect rate that if output all of a sudden takes a hit, then that's going 395 00:35:58,940 --> 00:36:03,480 to affect prices into the future. 396 00:36:03,480 --> 00:36:09,400 Thus, it's going to affect inflation into the future. 397 00:36:09,400 --> 00:36:17,440 And if inflation is going to be changing, well, that's going to have the the that's 398 00:36:17,440 --> 00:36:22,480 why it's a system of equations, right, because if prices change, then that's going to change 399 00:36:22,480 --> 00:36:27,880 inflation, which is then rate outputs dependent on inflation. 400 00:36:27,880 --> 00:36:32,000 And then rate, the interest rate is dependent rates. 401 00:36:32,000 --> 00:36:38,360 So these are all sort of interdependent on each other. 402 00:36:38,360 --> 00:36:43,960 So that's why we're about to estimate these as a system of equations here. 403 00:36:43,960 --> 00:36:47,200 So we've got our prices. 404 00:36:47,200 --> 00:36:58,040 We're going to go ahead and grab the federal funds rate, which we're going to assume. 405 00:36:58,040 --> 00:37:05,880 You know, we're basically really essentially going to make the assumption rate that inflation 406 00:37:05,880 --> 00:37:12,360 depends on the interest rate and output depends on the interest rate. 407 00:37:12,360 --> 00:37:16,000 But the interest rate doesn't necessarily. 408 00:37:16,000 --> 00:37:24,760 So this is more of an abstract assumption in order to identify your VAR. 409 00:37:24,760 --> 00:37:31,880 But long story short, I'll let you get into the weeds of this. 410 00:37:31,880 --> 00:37:39,320 But check it out, page 96 of Keeganskee.com, macroeconomics. 411 00:37:39,320 --> 00:37:49,640 So it's worth your read because sort of assumptions like this are important because, well, if 412 00:37:49,640 --> 00:37:56,440 you don't correctly identify your VAR with these assumptions, then your output, then 413 00:37:56,440 --> 00:38:08,360 your parameters are biased because these variables, you know, they are dependent on the errors, 414 00:38:08,360 --> 00:38:11,440 right? 415 00:38:11,440 --> 00:38:17,280 Each equation, because it's dependent on the others, it's not independent of the error. 416 00:38:17,280 --> 00:38:32,480 Long story short, you do have to make assumptions in order not to have biased estimators. 417 00:38:32,480 --> 00:38:40,200 But what we're going to see is the VARs are interestingly effective at prediction. 418 00:38:40,200 --> 00:38:53,960 So we may have biased parameters, but we're going to do the Ten Commandments of Forecasting, 419 00:38:53,960 --> 00:38:54,960 right? 420 00:38:54,960 --> 00:39:01,100 So we may have biased parameters, but we're going to compare our forecasts with the actuals 421 00:39:01,100 --> 00:39:03,960 on a month by month basis. 422 00:39:03,960 --> 00:39:11,540 So we can at least judge our bias, right? 423 00:39:11,540 --> 00:39:23,760 So if we can maybe look at our forecasts, right, and we may be consistently over forecasting 424 00:39:23,760 --> 00:39:29,420 or we may be consistently under forecasting. 425 00:39:29,420 --> 00:39:35,040 So that's why it's going to be really important to use these recursive measures, right, because 426 00:39:35,040 --> 00:39:38,900 we'll want to measure our forecasting error from month to month to month. 427 00:39:38,900 --> 00:39:46,300 So that way if we make a forecast and we know, okay, in the past our forecasts have been 428 00:39:46,300 --> 00:39:53,900 under or over, you know, you can kind of take that into consideration. 429 00:39:53,900 --> 00:40:02,400 So it's an imperfect science, but like we say, having a measure is better than no measure, 430 00:40:02,400 --> 00:40:07,280 but definitely hedge the measure with all the assumptions and biases that are built 431 00:40:07,280 --> 00:40:08,280 in. 432 00:40:08,280 --> 00:40:12,960 So that's the best I can tell you. 433 00:40:12,960 --> 00:40:21,880 But we're going to go through the process anyway, so that way you can see the imperfect 434 00:40:21,880 --> 00:40:24,960 nature of forecasting. 435 00:40:24,960 --> 00:40:29,960 If anyone ever asks you to do it, and then you can actually do it for them, and then, 436 00:40:29,960 --> 00:40:40,080 you know, please hedge to them what they need to take into consideration. 437 00:40:40,080 --> 00:40:46,180 So without further ado, hopefully it scared you off enough that you know, you're not going 438 00:40:46,180 --> 00:40:55,440 to replace your life's fortune in these forecasts here. 439 00:40:55,440 --> 00:41:03,120 Okay, so first things first, we actually need to calculate inflation. 440 00:41:03,120 --> 00:41:17,120 And so we were given the prices, so we can actually calculate inflation here. 441 00:41:17,120 --> 00:41:26,440 Okay, just a heads up, in most industries, you would not expect a negative inflation, 442 00:41:26,440 --> 00:41:28,320 so that would be deflation. 443 00:41:28,320 --> 00:41:39,920 Okay, you would expect an increasing or decreasing rate of inflation, but the market wouldn't 444 00:41:39,920 --> 00:41:43,360 be stable unless there is a little bit of inflation. 445 00:41:43,360 --> 00:41:48,840 We talked about this in the past, where as soon as you experience deflation, it's essentially 446 00:41:48,840 --> 00:41:55,360 a race to the bottom, because everybody's just going to be waiting until the future 447 00:41:55,360 --> 00:41:59,440 to make their purchases, right? 448 00:41:59,440 --> 00:42:03,320 And if everybody's waiting for the future to make their purchases, well, outputs just 449 00:42:03,320 --> 00:42:05,760 going to keep coming down and down. 450 00:42:05,760 --> 00:42:11,880 So you don't want to get caught in a deflationary spiral. 451 00:42:11,880 --> 00:42:16,560 You don't want inflation to be out of control either. 452 00:42:16,560 --> 00:42:35,040 So what policymakers are looking for is a steady rate of change of inflation. 453 00:42:35,040 --> 00:42:47,240 So we can maybe rate, so what would the rate of change of inflation be? 454 00:42:47,240 --> 00:43:01,640 Well, just the change of inflation would just be inflation diff. 455 00:43:01,640 --> 00:43:12,600 So right, so anyways, you'd want that to be fairly constant. 456 00:43:12,600 --> 00:43:22,000 As you can see, we've got a big change in inflation happening in August of 2020. 457 00:43:22,000 --> 00:43:26,640 And even actually not even so much, see, it's more the subsequent months, right? 458 00:43:26,640 --> 00:43:32,720 And this is where we were talking about how things are going to play out after various 459 00:43:32,720 --> 00:43:33,960 months, right? 460 00:43:33,960 --> 00:43:36,080 Because it's more, right? 461 00:43:36,080 --> 00:43:44,040 You've got a, yes, you've got a dip in August of 2020, but then the way inflation is calculated, 462 00:43:44,040 --> 00:43:45,920 the change in prices, right? 463 00:43:45,920 --> 00:43:51,520 You've got a big change in May, and then all of a sudden you've got a big change in June, 464 00:43:51,520 --> 00:43:52,520 July. 465 00:43:52,520 --> 00:43:55,200 So it's still white, right? 466 00:43:55,200 --> 00:43:58,800 So this is why you have sort of this ripple effect. 467 00:43:58,800 --> 00:44:09,440 So it's not just like the shock is isolated to one month. 468 00:44:09,440 --> 00:44:16,880 So now we're just going to just look at all of our variables over the same time period 469 00:44:16,880 --> 00:44:19,880 here, right? 470 00:44:19,880 --> 00:44:36,400 So we're basically given inflation rate from December of 2018 through September of 2021. 471 00:44:36,400 --> 00:44:44,440 So we'll just look at all our variables through this time period here. 472 00:44:44,440 --> 00:44:50,240 Awesome. 473 00:44:50,240 --> 00:44:51,440 Oh yeah, that's right. 474 00:44:51,440 --> 00:44:58,440 We're just looking at inflation, not prices. 475 00:44:58,440 --> 00:45:05,320 So now we're going to estimate the system of equations. 476 00:45:05,320 --> 00:45:11,440 So we've got output, inflation, and the interest rate. 477 00:45:11,440 --> 00:45:15,960 And we need to estimate these simultaneously. 478 00:45:15,960 --> 00:45:25,360 And you can actually simply just do this through ordinary least squares. 479 00:45:25,360 --> 00:45:36,600 So this is why we wrote our model here as in matrix form. 480 00:45:36,600 --> 00:45:48,160 So we're just going to estimate our model through ordinary least squares. 481 00:45:48,160 --> 00:45:57,980 So this is where we get into the art of forecasting, right? 482 00:45:57,980 --> 00:46:07,280 So we're given that rate or VOR depends on variables from prior days. 483 00:46:07,280 --> 00:46:12,360 But how many prior periods, not days, periods, right? 484 00:46:12,360 --> 00:46:14,520 Because we're doing monthly here. 485 00:46:14,520 --> 00:46:18,520 So does it depend on just last month? 486 00:46:18,520 --> 00:46:23,400 Does it depend on last month and two months ago? 487 00:46:23,400 --> 00:46:26,920 Does it depend on the whole quarter? 488 00:46:26,920 --> 00:46:34,720 So this is where we try to fit the best VOR from our in-sample data. 489 00:46:34,720 --> 00:46:40,440 So we'll basically try to fit a series of VORs. 490 00:46:40,440 --> 00:46:44,720 So we'll fit, in this case, a VOR 1 through 6. 491 00:46:44,720 --> 00:46:51,880 So we'll say, OK, sales today depend on sales from the prior month, the prior two months, 492 00:46:51,880 --> 00:46:55,160 three, four, five, six months. 493 00:46:55,160 --> 00:46:57,360 We're going to keep doing this. 494 00:46:57,360 --> 00:47:02,600 Keep in mind, we'll run into overfitting, right? 495 00:47:02,600 --> 00:47:10,320 Because say we're trying to say that each equation depends on observations from up to 496 00:47:10,320 --> 00:47:12,320 six periods ago. 497 00:47:12,320 --> 00:47:24,600 Well, then that's going to be six parameters times three for just one equation times three 498 00:47:24,600 --> 00:47:26,000 seconds. 499 00:47:26,000 --> 00:47:35,880 So that would be, what's that, like 40-some parameters? 500 00:47:35,880 --> 00:47:47,160 So if you have a lot of observations, that will be wonderful. 501 00:47:47,160 --> 00:48:01,680 But we're only given 34 observations here because we only have 34 months of data. 502 00:48:01,680 --> 00:48:06,480 So we're not going to be able to estimate a VOR of six. 503 00:48:06,480 --> 00:48:15,560 So we're basically going to try to fit the best fitting VOR that we can with the data 504 00:48:15,560 --> 00:48:20,160 that we have here. 505 00:48:20,160 --> 00:48:30,000 And it actually, right? 506 00:48:30,000 --> 00:48:35,840 So we use stats model to fit all those and select the best order. 507 00:48:35,840 --> 00:48:43,680 So you use a Bayesian information criterion that penalizes you for adding parameters. 508 00:48:43,680 --> 00:48:51,240 So basically, what we're told is the best model is a VOR one. 509 00:48:51,240 --> 00:49:03,240 I suspect that we weren't even able to fit much above a VOR one given the number of observations 510 00:49:03,240 --> 00:49:04,600 we have. 511 00:49:04,600 --> 00:49:09,520 But so this is where, once again, you kind of have to hedge, right? 512 00:49:09,520 --> 00:49:17,720 Because it's like, OK, is the VOR one the best, most accurate model? 513 00:49:17,720 --> 00:49:18,720 Probably not. 514 00:49:18,720 --> 00:49:24,880 But it's the only one that we're really able to fit given our observations. 515 00:49:24,880 --> 00:49:34,640 So once again, we're just going to have to move forward with that, knowing that it's 516 00:49:34,640 --> 00:49:40,840 the best of all of our imperfect options. 517 00:49:40,840 --> 00:49:43,080 So keep that in mind. 518 00:49:43,080 --> 00:49:46,480 And this is where we can get into the recursive nature, right? 519 00:49:46,480 --> 00:49:54,680 Because say in a few months from now, right, or even a year from now or two years from 520 00:49:54,680 --> 00:49:58,240 now, we're going to have more data. 521 00:49:58,240 --> 00:50:06,800 So the more data we get, the more likely we are to be able to fit a higher order VOR model, 522 00:50:06,800 --> 00:50:11,840 which may be a better predictor. 523 00:50:11,840 --> 00:50:13,280 So that's why it's a recursive model. 524 00:50:13,280 --> 00:50:19,200 So each month, we'll see what's the best order VOR that we can fit. 525 00:50:19,200 --> 00:50:26,480 And if we can fit multiple ones, we may want to compare which one actually makes the best 526 00:50:26,480 --> 00:50:29,520 out of sample forecasts. 527 00:50:29,520 --> 00:50:39,160 Because just because you can forecast well in sample, it's out of sample forecasts that 528 00:50:39,160 --> 00:50:41,360 matter, right? 529 00:50:41,360 --> 00:50:45,720 So let's do just that. 530 00:50:45,720 --> 00:50:53,440 So right, we said, OK, we want to go ahead and get forecasts for the rest of this year 531 00:50:53,440 --> 00:50:56,520 plus next year. 532 00:50:56,520 --> 00:50:59,640 So great. 533 00:50:59,640 --> 00:51:00,640 So great. 534 00:51:00,640 --> 00:51:04,320 So our data, right, we go through the end of September. 535 00:51:04,320 --> 00:51:10,800 So we want to get observations for October, November, and December, and then the 12 months 536 00:51:10,800 --> 00:51:12,400 next year. 537 00:51:12,400 --> 00:51:26,760 So our horizon is 15 periods and our lag order is 1. 538 00:51:26,760 --> 00:51:32,440 So right, so right, it's real cool, right, because this is how you forecast with the 539 00:51:32,440 --> 00:51:33,680 VOR, right? 540 00:51:33,680 --> 00:51:39,320 So we've just estimated our parameters. 541 00:51:39,320 --> 00:51:49,680 So I wonder if we can just do this. 542 00:51:49,680 --> 00:51:57,240 OK, well, here are our parameters. 543 00:51:57,240 --> 00:52:04,320 So right, we estimated three equations. 544 00:52:04,320 --> 00:52:09,840 For each equation, we've got a constant and three parameters. 545 00:52:09,840 --> 00:52:21,640 So this is alpha y, beta j, gamma j, delta j, right? 546 00:52:21,640 --> 00:52:34,480 And then here, we've got alpha pi, theta j, theta j, lambda j. 547 00:52:34,480 --> 00:52:39,160 And I don't want to keep going through the Greek alphabet, so I'll leave you with the 548 00:52:39,160 --> 00:52:42,400 idea there. 549 00:52:42,400 --> 00:52:46,440 So we've estimated all our parameters. 550 00:52:46,440 --> 00:52:51,200 And so now, the cool thing is we can just plug and play. 551 00:52:51,200 --> 00:52:55,400 So we've got our parameters, a of l. 552 00:52:55,400 --> 00:53:00,640 And now, we can just plug in the observations from September, right? 553 00:53:00,640 --> 00:53:10,000 We can just plug in September output, September inflation, September interest rates, and we 554 00:53:10,000 --> 00:53:14,200 get October's estimates. 555 00:53:14,200 --> 00:53:22,560 Well, we can then take October's estimates, plug them in, use the same parameters, and 556 00:53:22,560 --> 00:53:25,640 we get November's estimates, right? 557 00:53:25,640 --> 00:53:28,000 And so you see how this plays out. 558 00:53:28,000 --> 00:53:36,200 Plug in November's estimates, use your parameters, December's estimates, so on and so forth. 559 00:53:36,200 --> 00:53:38,600 You can code this up yourself. 560 00:53:38,600 --> 00:53:40,360 I've done so. 561 00:53:40,360 --> 00:53:49,280 Or we can just use stats models here and forecast forward. 562 00:53:49,280 --> 00:53:54,880 Get the same result. 563 00:53:54,880 --> 00:54:00,480 And here are our forecasts. 564 00:54:00,480 --> 00:54:07,880 So we have output, right? 565 00:54:07,880 --> 00:54:15,760 So it dips down to zero, going up, dip down, going up. 566 00:54:15,760 --> 00:54:20,560 And here are our forecasts. 567 00:54:20,560 --> 00:54:28,080 As you can see, and Heather can attest that this has been the case in other weeks, our 568 00:54:28,080 --> 00:54:31,400 confidence is really wide. 569 00:54:31,400 --> 00:54:36,240 We've got, right, we don't have a narrow confidence interval here, right? 570 00:54:36,240 --> 00:54:43,240 So sales could take a dip or they could rise. 571 00:54:43,240 --> 00:54:52,600 So this is where if you were doing your business planning, you would need to acknowledge your 572 00:54:52,600 --> 00:54:54,200 cost of forecasting, right? 573 00:54:54,200 --> 00:54:56,760 So it may not be symmetric, right? 574 00:54:56,760 --> 00:55:04,560 It may be asymmetrically worse for you if sales are lower than expected and higher than 575 00:55:04,560 --> 00:55:07,960 expected. 576 00:55:07,960 --> 00:55:18,680 So you may want to over prepare for this lower period, these lower potential sales, right? 577 00:55:18,680 --> 00:55:26,240 So you may want to do some worst case scenario planning and just say, okay, what if sales 578 00:55:26,240 --> 00:55:32,320 dip way down to this threshold? 579 00:55:32,320 --> 00:55:36,120 We'll actually quantify this here in a second because we have these numbers. 580 00:55:36,120 --> 00:55:43,400 And then you can say, okay, so you need to plan for the rainy day scenario here. 581 00:55:43,400 --> 00:55:47,400 We at least have our estimates here. 582 00:55:47,400 --> 00:55:54,680 This is where we get into our wish for a higher order VAR model. 583 00:55:54,680 --> 00:56:00,960 So as you can see, there's not too much dynamism, if that's a word. 584 00:56:00,960 --> 00:56:07,080 There's not too much dynamics with our forecasts here, right? 585 00:56:07,080 --> 00:56:12,120 And that's because of our plug and play nature here, right? 586 00:56:12,120 --> 00:56:22,440 So if you're just going to plug in today's values to get November's values, right, depending 587 00:56:22,440 --> 00:56:36,120 on your parameters, if you just keep plugging in your forecasts, you may lose the dynamic. 588 00:56:36,120 --> 00:56:41,240 You're going to lose some of the variability and you're just going to get sort of these 589 00:56:41,240 --> 00:56:50,160 steady forecasts, which is not really what we would expect. 590 00:56:50,160 --> 00:56:59,080 And so what I've found is if you're able to estimate and fit a higher order VAR model, 591 00:56:59,080 --> 00:57:07,360 you're going to get a bit more dynamics in your estimates, which tend to reduce your 592 00:57:07,360 --> 00:57:09,560 forecasting error. 593 00:57:09,560 --> 00:57:21,360 So that way, your forecasts tend to fluctuate better with the actuals in my experience. 594 00:57:21,360 --> 00:57:24,960 However, we have to start somewhere. 595 00:57:24,960 --> 00:57:31,080 So we now have a crude forecast of output. 596 00:57:31,080 --> 00:57:36,520 We have a crude forecast of inflation. 597 00:57:36,520 --> 00:57:41,680 And then we even have a crude forecast of the federal funds rate. 598 00:57:41,680 --> 00:57:47,280 We're predicting it's going beneath zero, which we may expect. 599 00:57:47,280 --> 00:57:51,240 As we know, interest rates can't go below zero. 600 00:57:51,240 --> 00:58:00,160 And this is where the Federal Reserve is already undoubtedly doing quantitative easing, right, 601 00:58:00,160 --> 00:58:05,460 to effectively push the interest rate below zero. 602 00:58:05,460 --> 00:58:11,880 So interesting dynamics going on there. 603 00:58:11,880 --> 00:58:21,080 Before we conclude, let's go ahead and save our forecasts here. 604 00:58:21,080 --> 00:58:27,120 Because right, that was the whole point of forecasting, right, is we need to get the 605 00:58:27,120 --> 00:58:35,960 forecasts, so that way we can get a crude forecast for 2021, as well as 2022. 606 00:58:35,960 --> 00:58:39,040 Then we need to compare these to actuals. 607 00:58:39,040 --> 00:58:45,520 And just for the sake of brevity here, I'm just going to do this by hand, and then we 608 00:58:45,520 --> 00:58:47,960 can maybe do it programmatically later. 609 00:58:47,960 --> 00:58:51,160 But remember, the dates here, right. 610 00:58:51,160 --> 00:58:59,920 So this is for October 2021. 611 00:58:59,920 --> 00:59:01,440 Let's see if we can't. 612 00:59:01,440 --> 00:59:06,040 Okay, through December 22. 613 00:59:06,040 --> 00:59:15,680 Let's insert some of these past values. 614 00:59:15,680 --> 00:59:28,360 Because basically I'm just curious what these... 615 00:59:28,360 --> 00:59:29,360 What was it? 616 00:59:29,360 --> 00:59:30,360 Monthly... 617 00:59:30,360 --> 00:59:33,360 What was this? 618 00:59:33,360 --> 00:59:52,040 Sorry, bear with me, because I just want to leave today with the last few estimates here. 619 00:59:52,040 --> 01:00:20,160 That way we can at least leave today with our forecast for 2021 and 2022 real quick. 620 01:00:20,160 --> 01:00:24,880 So let's just put this into Excel real quick. 621 01:00:24,880 --> 01:00:32,400 Okay, so like I said, we're just doing this real quick in bare bones just to have some 622 01:00:32,400 --> 01:00:34,960 tangible forecasts by the end of the day. 623 01:00:34,960 --> 01:01:00,040 But basically 2021 sales forecast, then 2022 sales forecast, and then forecasted change 624 01:01:00,040 --> 01:01:01,520 in sales. 625 01:01:01,520 --> 01:01:08,000 So just bear with me if you can stay an extra five minutes so we can actually walk away 626 01:01:08,000 --> 01:01:09,800 with these two numbers. 627 01:01:09,800 --> 01:01:12,720 But basically we're predicting, right. 628 01:01:12,720 --> 01:01:18,240 And like I said, I would prefer to do this programmatically than just hacking it away 629 01:01:18,240 --> 01:01:24,120 real quick in Excel. 630 01:01:24,120 --> 01:01:32,960 Right, we're just hacking away real quick in Excel just so we can get a number. 631 01:01:32,960 --> 01:01:39,760 So let's put this into millions. 632 01:01:39,760 --> 01:01:41,920 Okay. 633 01:01:41,920 --> 01:01:58,920 So we're estimating above 1 billion in sales. 634 01:01:58,920 --> 01:02:05,800 And let's see what the percent change we're forecasting is going to be. 635 01:02:05,800 --> 01:02:15,680 Okay, so this is interesting here. 636 01:02:15,680 --> 01:02:20,200 So real quick, right. 637 01:02:20,200 --> 01:02:27,240 We've, you know, as you can see, they're not the most dynamic forecasts in the world, but 638 01:02:27,240 --> 01:02:30,360 we wanted to get a number. 639 01:02:30,360 --> 01:02:33,040 And we've got an a number here. 640 01:02:33,040 --> 01:02:34,520 We've gotten a couple. 641 01:02:34,520 --> 01:02:44,920 So we're going to go ahead and estimate that sales in 2021 in Massachusetts are going to 642 01:02:44,920 --> 01:02:51,120 be about 1.1 billion in 2021. 643 01:02:51,120 --> 01:02:57,800 And we're also estimating that they're just going to be a little higher than 1.1 billion 644 01:02:57,800 --> 01:03:00,180 in 2022. 645 01:03:00,180 --> 01:03:08,120 So we're only predicting, you know, a 1.2% increase in sales. 646 01:03:08,120 --> 01:03:19,400 I just from my personal experience, working with other states, I foresee that sales are 647 01:03:19,400 --> 01:03:23,400 going to increase by a lot more than 1.2%. 648 01:03:23,400 --> 01:03:24,440 They may not. 649 01:03:24,440 --> 01:03:31,680 So this is where we're going to want to come back and visit this on a month by month basis. 650 01:03:31,680 --> 01:03:41,240 Because is it the case that this giant hit to production in 2020 is still filtering through 651 01:03:41,240 --> 01:03:44,840 the production? 652 01:03:44,840 --> 01:03:48,900 And is this big hit to inflation? 653 01:03:48,900 --> 01:03:54,960 Is this having lasting effects that may just completely lower overall production? 654 01:03:54,960 --> 01:04:00,280 Because there could have been a whole shift in the production function. 655 01:04:00,280 --> 01:04:12,280 So this is where we'll want to come and on a month by month basis, we all want to come 656 01:04:12,280 --> 01:04:17,520 and look at the actual sales. 657 01:04:17,520 --> 01:04:25,680 And so we already know the actual sales through September 2021. 658 01:04:25,680 --> 01:04:31,520 And now what's cool is, you know, the cannabis data science meetup group, we've now made 659 01:04:31,520 --> 01:04:34,940 forecasts all the way through 2022. 660 01:04:34,940 --> 01:04:39,840 So we can start filling in the actuals month by month. 661 01:04:39,840 --> 01:04:45,880 And we may need to add a whole new series of forecasts. 662 01:04:45,880 --> 01:04:57,920 So next month, we may forecast with a different model if this one has wildly inaccurate forecasts. 663 01:04:57,920 --> 01:05:05,240 And so we can just gradually adapt our model, gradually improve it, and see if we can't 664 01:05:05,240 --> 01:05:08,680 hone in our forecasts. 665 01:05:08,680 --> 01:05:11,200 And so this is what's cool. 666 01:05:11,200 --> 01:05:13,960 So you've now attended the meetup group. 667 01:05:13,960 --> 01:05:19,520 We've gotten real cannabis data through the API. 668 01:05:19,520 --> 01:05:26,720 We've talked about the economic theory, as well as an a theoretical statistical model 669 01:05:26,720 --> 01:05:30,160 that we can use for forecasting. 670 01:05:30,160 --> 01:05:40,240 We've now fit the model, created some visualizations, but help to understand the data. 671 01:05:40,240 --> 01:05:49,120 And we've saved these new data points so that way we can continue to make ongoing analysis. 672 01:05:49,120 --> 01:05:51,960 So that's what's real cool about this. 673 01:05:51,960 --> 01:05:55,680 And it's completely transparent, completely open source. 674 01:05:55,680 --> 01:06:03,380 So right after this meetup, I'll go ahead and commit this to the GitHub repository. 675 01:06:03,380 --> 01:06:06,160 So it is MIT licensed. 676 01:06:06,160 --> 01:06:10,320 So you're welcome to use the code for any reason you see fit. 677 01:06:10,320 --> 01:06:17,760 It would just be awesome if you mentioned the authors, tossing the cannabis data science 678 01:06:17,760 --> 01:06:19,800 group if you wish. 679 01:06:19,800 --> 01:06:24,920 And then you're free to use the code however you see fit. 680 01:06:24,920 --> 01:06:29,000 So you're free to expand upon this. 681 01:06:29,000 --> 01:06:36,080 And just to point you in some avenues for further work. 682 01:06:36,080 --> 01:06:42,040 You can also estimate output with two additional VAR models. 683 01:06:42,040 --> 01:06:47,440 So you could estimate output using unemployment. 684 01:06:47,440 --> 01:06:52,280 You could also estimate output using hours worked. 685 01:06:52,280 --> 01:06:57,480 So perhaps on Saturday, I may show you these models. 686 01:06:57,480 --> 01:07:02,440 And so that way you could prepare two additional forecasts. 687 01:07:02,440 --> 01:07:04,000 And this is what it's all about. 688 01:07:04,000 --> 01:07:08,680 So you could have one forecast with one model. 689 01:07:08,680 --> 01:07:14,260 And then we could add on two more forecasts. 690 01:07:14,260 --> 01:07:19,640 And then we can compare the forecast error from all three models. 691 01:07:19,640 --> 01:07:24,420 And then we can see which model predicts the best. 692 01:07:24,420 --> 01:07:31,600 And then we can have a bit more faith in that model going forward. 693 01:07:31,600 --> 01:07:34,960 So that's the beauty to it. 694 01:07:34,960 --> 01:07:41,000 So until next time, you're welcome to use the code. 695 01:07:41,000 --> 01:07:43,480 Try to make some forecasts of your own. 696 01:07:43,480 --> 01:07:46,680 Feel free to email me if you have any questions. 697 01:07:46,680 --> 01:07:57,360 And then definitely check out Saturday Statistics because we may do even more forecasting. 698 01:07:57,360 --> 01:08:04,000 And we're going to walk away at the end of the day with an even, I wouldn't even call 699 01:08:04,000 --> 01:08:05,660 this a beautiful visualization. 700 01:08:05,660 --> 01:08:10,200 So we're going to walk away at the end of the day with a stunning, stunningly beautiful 701 01:08:10,200 --> 01:08:11,600 visualization. 702 01:08:11,600 --> 01:08:13,600 So that's the objective. 703 01:08:13,600 --> 01:08:21,240 And we'll iron down the forecasting a bit more and build up confidence in that. 704 01:08:21,240 --> 01:08:30,880 So we ran a little long today, but hopefully it was worthwhile for you. 705 01:08:30,880 --> 01:08:37,080 Any questions, comments, thoughts, ideas before we conclude today? 706 01:08:37,080 --> 01:08:39,080 Oh, yes. 707 01:08:39,080 --> 01:08:44,840 OK, here, Shayan has some in the chat here. 708 01:08:44,840 --> 01:08:51,160 So yes, so the confidence interval is a 95% confidence interval right out of the gate. 709 01:08:51,160 --> 01:08:58,400 But for actual applications, that's quite a high confidence level. 710 01:08:58,400 --> 01:09:03,960 I found that if you say you're presenting this to your manager or what have you, I think 711 01:09:03,960 --> 01:09:10,000 it's perfectly OK to reduce your confidence to maybe 80% or so. 712 01:09:10,000 --> 01:09:19,360 It's going to reduce your confidence bars, your confidence interval to make your estimates 713 01:09:19,360 --> 01:09:21,400 appear to be a bit more precise. 714 01:09:21,400 --> 01:09:27,120 Once again, you've got to hedge that you're using only an 80% confidence interval. 715 01:09:27,120 --> 01:09:31,440 Also, this bar does not address seasonality. 716 01:09:31,440 --> 01:09:37,680 So once again, Shayan is a whiz here and knows a lot more about this. 717 01:09:37,680 --> 01:09:41,920 So there's a lot you can add on to these bars. 718 01:09:41,920 --> 01:09:46,120 So we use what's called an ARIMA model. 719 01:09:46,120 --> 01:09:52,960 Shayan notes that you can improve upon this in a manner of ways. 720 01:09:52,960 --> 01:10:01,560 So the ARIMA X model is if you want to add on another explanatory variable. 721 01:10:01,560 --> 01:10:05,960 So I'll explain this real quick. 722 01:10:05,960 --> 01:10:12,240 So we've got our output, our inflation, our interest rate. 723 01:10:12,240 --> 01:10:17,000 Well, let's say we want to add on another variable. 724 01:10:17,000 --> 01:10:24,440 Some variables I love to add on are month effects, because you always know what month 725 01:10:24,440 --> 01:10:26,440 it is. 726 01:10:26,440 --> 01:10:32,920 That's the hard thing about adding on explanatory variables is you also have to predict them. 727 01:10:32,920 --> 01:10:42,440 So say you wanted to add on gas prices, well, that's not really that feasible, because you 728 01:10:42,440 --> 01:10:46,440 don't really know what gas prices are going to be a year from now. 729 01:10:46,440 --> 01:10:51,720 What's cool about the month is you do know what the month is going to be a year from 730 01:10:51,720 --> 01:10:52,720 now. 731 01:10:52,720 --> 01:10:53,720 It'll be October. 732 01:10:53,720 --> 01:11:00,120 So that's a cool way you can add on effects. 733 01:11:00,120 --> 01:11:03,400 You can also add on seasonality effects. 734 01:11:03,400 --> 01:11:07,120 And so this is going to be what's called like your moving averages. 735 01:11:07,120 --> 01:11:08,560 So you can kind of take. 736 01:11:08,560 --> 01:11:18,640 So this is, I don't know the seasonality as well, but you can take into account seasonality. 737 01:11:18,640 --> 01:11:29,040 So long story short is, you know, Shayan pointed out some good additional models that you can 738 01:11:29,040 --> 01:11:31,040 extend upon this analysis with. 739 01:11:31,040 --> 01:11:36,040 And that's exactly what I encourage you to do, because this is the whole idea about the 740 01:11:36,040 --> 01:11:42,040 transparent box is, and this is when you like when you see other people's forecasts, you 741 01:11:42,040 --> 01:11:44,040 know, who knows what model they used? 742 01:11:44,040 --> 01:11:47,040 Are they willing to even say what model they used? 743 01:11:47,040 --> 01:11:50,040 And can it be extended upon? 744 01:11:50,040 --> 01:11:53,040 In this case, we just used an ARIMA model. 745 01:11:53,040 --> 01:11:55,040 It can be extended upon. 746 01:11:55,040 --> 01:11:59,040 And by all means, please try. 747 01:11:59,040 --> 01:12:04,040 And then, you know, you may get better forecasts than we made today. 748 01:12:04,040 --> 01:12:08,040 Excellent, excellent question. 749 01:12:08,040 --> 01:12:10,040 All right. 750 01:12:10,040 --> 01:12:13,040 We ran quite a bit over today. 751 01:12:13,040 --> 01:12:14,040 Excellent. 752 01:12:14,040 --> 01:12:16,040 So definitely be in touch. 753 01:12:16,040 --> 01:12:17,040 So we ran a bit over today. 754 01:12:17,040 --> 01:12:20,040 So I'm going to go ahead and conclude it here. 755 01:12:20,040 --> 01:12:22,040 But I think it was a fun day. 756 01:12:22,040 --> 01:12:28,040 So we finally got our hands back on some data and some statistics. 757 01:12:28,040 --> 01:12:33,040 Like I said, I think the visualizations can still be improved upon and we can still do some more modeling. 758 01:12:33,040 --> 01:12:38,040 So let's let's do let's extend upon that on Saturday. 759 01:12:38,040 --> 01:12:50,040 And then next week, I think it'll be fun to get into the exogenous shocks so we can say, OK, what happens if all of a sudden there's a price shock in Massachusetts? 760 01:12:50,040 --> 01:12:54,040 Or what happens if all of a sudden there's a production shock? 761 01:12:54,040 --> 01:13:05,040 And so you can brainstorm about why there may be various shocks, but why we don't have to worry about we can just do the statistics. 762 01:13:05,040 --> 01:13:13,040 But by all means, bring some good stories as to why there may be some good economic shocks. 763 01:13:13,040 --> 01:13:20,040 And then, like I said, we can do the analyses and then you can take these and apply them how you will. 764 01:13:20,040 --> 01:13:22,040 So we originally did these in Oregon. 765 01:13:22,040 --> 01:13:30,040 And so these analyses could be done in Colorado, where I am now or wherever wherever you see fit. 766 01:13:30,040 --> 01:13:35,040 So please, please take what we've provided here and expand upon it. 767 01:13:35,040 --> 01:13:44,040 So. All right, crew, until next time, stay productive and feel free to reach out. 768 01:13:44,040 --> 01:14:06,040 Kinetics is always here to support you.