1 00:00:11,060 --> 00:00:16,160 In this video, we will continue looking at our Varma Notebook for predicting temperatures. 2 00:00:17,000 --> 00:00:23,510 To recap, what we've done so far is loaded in our data, which wasn't in the T by D format we expected. 3 00:00:23,690 --> 00:00:29,480 So we did some work to convert it into that format and we plotted the data to see what it looks like. 4 00:00:29,810 --> 00:00:33,070 The next step is to split our data into train and test. 5 00:00:33,080 --> 00:00:37,010 So I've chosen n test equals 12, which represents one year. 6 00:00:41,230 --> 00:00:43,360 The next step is to scale our data. 7 00:00:43,690 --> 00:00:48,820 As you recall, the temperatures are not on the same scale and they're also pretty large Fahrenheit 8 00:00:48,820 --> 00:00:49,840 values. 9 00:00:50,380 --> 00:00:56,260 So you can see that I've used a fit transform on the train set and transform on the test at the new 10 00:00:56,260 --> 00:00:56,500 scale. 11 00:00:56,500 --> 00:01:01,120 Two columns are given a new name, which is the old name pre with scaled. 12 00:01:04,840 --> 00:01:07,210 The next step is to scale the other column. 13 00:01:11,640 --> 00:01:16,200 The next step is to create a train idea and test out X, which you've seen before. 14 00:01:16,620 --> 00:01:22,200 As you recall, we use these to index the original data frame for both the train and test sets. 15 00:01:26,260 --> 00:01:30,760 The next step is to also put the scale data back into the original data frame. 16 00:01:31,240 --> 00:01:34,270 As you recall, train and test are just copies. 17 00:01:38,940 --> 00:01:41,580 The next step is to plot the scaled columns. 18 00:01:46,960 --> 00:01:50,740 So as you can see, the two time series are now on the same scale. 19 00:01:53,240 --> 00:01:56,540 The next step is to plot the arc of the first column. 20 00:02:00,930 --> 00:02:05,760 As you recall, we can use these to guide our choice for the number of legs in our model. 21 00:02:06,300 --> 00:02:12,210 Notice how the ACF has a strong seasonal pattern due to the fact that the Time series itself has a strong 22 00:02:12,210 --> 00:02:13,350 seasonal pattern. 23 00:02:16,330 --> 00:02:18,550 The next step is to plot the ICF. 24 00:02:22,810 --> 00:02:27,940 So we see a similar pattern, except that the lags closer to zero are more significant. 25 00:02:31,340 --> 00:02:34,700 The next step is to plot the ACF for the second column. 26 00:02:39,130 --> 00:02:41,830 So again, there is a strong seasonal pattern. 27 00:02:44,350 --> 00:02:47,920 The next step is to plot the passage of the second column. 28 00:02:52,060 --> 00:02:54,310 So again, we see a similar pattern. 29 00:02:57,780 --> 00:03:02,100 The next step is to create a var max object and fit it to the Time series. 30 00:03:02,700 --> 00:03:07,860 Note that because this is going to take some time, I've used datetime to measure the duration. 31 00:03:09,060 --> 00:03:13,950 Also notice that I've picked P equals ten and Q equals ten for no particular reason. 32 00:03:14,310 --> 00:03:16,740 Feel free to try other values if you like. 33 00:03:23,320 --> 00:03:23,650 Okay. 34 00:03:23,680 --> 00:03:28,660 So you'll see that when you use a queue other than zero, you'll get this estimation warning saying 35 00:03:28,660 --> 00:03:33,610 that the estimation of parameters has ID issues. 36 00:03:33,640 --> 00:03:36,310 This is because the solution is not unique. 37 00:03:36,670 --> 00:03:41,920 What you'll also notice is that due to the training methods used behind the scenes, fitting a Varma 38 00:03:41,920 --> 00:03:44,920 model takes much longer than a pure VAR model. 39 00:03:45,820 --> 00:03:48,670 In any case, we'll continue using Varma for now. 40 00:03:49,990 --> 00:03:52,360 So make note of how long this took to train. 41 00:03:55,200 --> 00:04:01,140 The next step is to call the get forecast function to get the forecast for pn test time steps. 42 00:04:04,890 --> 00:04:08,220 The next step is to demonstrate that the results objects. 43 00:04:08,220 --> 00:04:09,270 We got back from fitting. 44 00:04:09,270 --> 00:04:15,090 The model already contains the in sample predictions in an attribute called fitted values. 45 00:04:18,250 --> 00:04:20,830 As you can see, it returns a series. 46 00:04:23,390 --> 00:04:28,190 The next step is to store the predictions in the original joint part DataFrame. 47 00:04:28,610 --> 00:04:34,640 So we use train for the end sample predictions, assigning it to be the fitted values we use. 48 00:04:34,640 --> 00:04:40,640 Test X for the out of sample predictions, assigning it to be the predicted mean of the forecast. 49 00:04:44,720 --> 00:04:48,800 The next step is to plot our predictions along with the original TIME series. 50 00:04:49,040 --> 00:04:53,810 Note that we only plot the last 100 values to keep the plot a reasonable size. 51 00:04:59,080 --> 00:05:03,070 So as you can see, both the train and test predictions look pretty good. 52 00:05:06,170 --> 00:05:09,770 The next step is to perform all the same steps for the other city. 53 00:05:10,010 --> 00:05:13,910 So again, we store the sample and out of sample predictions. 54 00:05:13,940 --> 00:05:19,640 Note that this uses the same objects we had before, since they store the predictions for both cities. 55 00:05:23,700 --> 00:05:26,070 The next step is to plot our predictions. 56 00:05:30,570 --> 00:05:30,740 Okay. 57 00:05:31,010 --> 00:05:35,000 So as you can see, our predictions for the second city look pretty similar. 58 00:05:38,720 --> 00:05:41,720 The next step is to check the R squared of our model. 59 00:05:42,260 --> 00:05:46,640 Basically, we can just index the data frame where we stored the predictions. 60 00:05:50,070 --> 00:05:50,460 Okay. 61 00:05:50,460 --> 00:05:53,070 So the r squared for oakland looks pretty good. 62 00:05:55,590 --> 00:05:58,380 The next step is to check the R squared for Stockholm. 63 00:06:02,140 --> 00:06:04,720 So again, the R squared looks pretty good. 64 00:06:05,680 --> 00:06:11,350 Now, of course, how good these predictions really are doesn't depend on these values in isolation. 65 00:06:11,650 --> 00:06:15,670 Instead, what we should really do is compare to a baseline. 66 00:06:16,150 --> 00:06:21,940 So the reason I chose to use Varma first is because after years of getting to know my students online, 67 00:06:21,940 --> 00:06:24,220 I believe this is what they would want to try. 68 00:06:24,610 --> 00:06:28,150 Of course, we've already seen a few disadvantages of Varma. 69 00:06:28,540 --> 00:06:33,040 One issue is that Varma processes are generally not identifiable. 70 00:06:33,400 --> 00:06:36,460 Another problem is that they take longer to train. 71 00:06:36,850 --> 00:06:42,220 So in the coming lecture, we'll explore alternative options and also compare their performance.