1 00:00:11,030 --> 00:00:11,450 Okay. 2 00:00:11,450 --> 00:00:15,950 So in this lecture we are going to continue our econometrics example with Varma. 3 00:00:18,700 --> 00:00:23,860 The next step is to define which columns we care about, which are GDP growth and term spread. 4 00:00:24,490 --> 00:00:28,840 If you decide to difference the term spread, you could change this to use that column instead. 5 00:00:32,690 --> 00:00:35,660 The next step is to get rid of the first row of the data. 6 00:00:36,410 --> 00:00:40,690 Since we use different thing on GDPR, the first row will have missing values. 7 00:00:43,910 --> 00:00:46,730 The next step is to split our data into train and test. 8 00:00:47,120 --> 00:00:51,590 I've chosen an testicles 12, but you can feel free to try other values if you like. 9 00:00:55,190 --> 00:00:58,060 The next step is to declare train ATX ancestry checks. 10 00:00:58,280 --> 00:00:59,450 As we've done before. 11 00:01:03,330 --> 00:01:06,360 The next step is through scalar data using the standard scalar. 12 00:01:06,930 --> 00:01:10,850 Note that we are overwriting the old values which we won't be using anyway. 13 00:01:15,420 --> 00:01:20,400 The next step is to also overwrite the old values in Def one since we don't need them anymore. 14 00:01:24,370 --> 00:01:27,250 The next step is to plot the achieve of GDP growth. 15 00:01:32,050 --> 00:01:32,440 Okay. 16 00:01:32,440 --> 00:01:37,180 So based on GDP growth alone, the ECF seems to suggest a small Q value. 17 00:01:37,930 --> 00:01:43,120 By the way, note that these plots are not exactly what you need in order to determine PACU. 18 00:01:43,420 --> 00:01:45,520 Since they do not consider cross terms. 19 00:01:46,150 --> 00:01:48,580 So we're only using these as a very rough guide. 20 00:01:48,820 --> 00:01:50,230 Just to give you some idea. 21 00:01:51,220 --> 00:01:56,710 In practice, the easiest way to do model selection is just to do a grid search and pick the best value 22 00:01:56,920 --> 00:01:58,780 based on the criteria you care about. 23 00:02:02,300 --> 00:02:04,280 The next step is to check the PKF. 24 00:02:08,510 --> 00:02:12,410 So again, the piece have seems to suggest a small p value as well. 25 00:02:15,490 --> 00:02:18,340 The next step is to pull out the ACF for the term spread. 26 00:02:22,580 --> 00:02:27,500 Note that the act suggests that the signal has a cyclical pattern, which is what we observed. 27 00:02:31,310 --> 00:02:33,350 The next step is to check the passive. 28 00:02:37,740 --> 00:02:42,180 So this time a note that quite a few legs are significant, up to a pretty high order. 29 00:02:45,090 --> 00:02:45,480 Okay. 30 00:02:45,480 --> 00:02:47,700 So the next step is to check for stationery. 31 00:02:48,120 --> 00:02:49,830 So we'll start with GDP growth. 32 00:02:52,770 --> 00:02:53,160 Okay. 33 00:02:53,160 --> 00:02:56,640 So recall that the p value is the second element in this tuple. 34 00:02:57,180 --> 00:03:00,900 Since it's very small, we can conclude that this time series is stationary. 35 00:03:04,160 --> 00:03:07,340 The next step is to perform the ADF tests on the term spread. 36 00:03:10,830 --> 00:03:14,310 So again, we get a small p value, but not as small as before. 37 00:03:15,030 --> 00:03:19,800 However, even with the 1% significance threshold, we would consider this stationary. 38 00:03:20,250 --> 00:03:21,810 So it's probably not necessary. 39 00:03:21,810 --> 00:03:22,710 It's a difference. 40 00:03:25,640 --> 00:03:27,500 The next step is to set P and Q. 41 00:03:28,100 --> 00:03:30,800 Note that I've chosen these values somewhat arbitrarily. 42 00:03:31,190 --> 00:03:36,440 I've chosen a high value for P since the PSA for the term spread suggests that a large P. 43 00:03:39,730 --> 00:03:43,300 The next step is to fit our VMAX model, which is the same as before. 44 00:03:49,740 --> 00:03:55,050 So notice that this model trains a bit faster than before, but still not what we would consider fast. 45 00:03:58,610 --> 00:04:03,590 The next step is to call get forecast to get the forecasts for and test timestamps. 46 00:04:07,040 --> 00:04:11,720 The next step is to store the train and test predictions in our DataFrame and to plot the results. 47 00:04:12,290 --> 00:04:15,590 Since this code is the same as before, I won't explain it again. 48 00:04:20,210 --> 00:04:20,600 Okay. 49 00:04:20,600 --> 00:04:25,880 So notice that both the train and test fit are not particularly good, at least compared to the previous 50 00:04:25,880 --> 00:04:26,630 example. 51 00:04:27,260 --> 00:04:31,700 It seems to have the most trouble predicting the extreme values even in the train set. 52 00:04:32,480 --> 00:04:36,170 This makes sense since we've seen the same kind of behavior in stock prices. 53 00:04:36,950 --> 00:04:41,870 However, note that the prediction does seem to go in the same direction as the true value. 54 00:04:43,040 --> 00:04:48,860 One way to check whether or not this forecast is useful is to compare it with the naive forecast that 55 00:04:48,860 --> 00:04:51,890 is comparing it with predicting the last known train value. 56 00:04:52,460 --> 00:04:56,840 In this case, without actually plugging in numbers, it would seem that our model is better. 57 00:04:59,570 --> 00:05:02,450 The next step is to plot the predictions for the term spread. 58 00:05:03,020 --> 00:05:06,320 Since this is the same code as before, I won't explain it again. 59 00:05:10,810 --> 00:05:15,940 So in this case, notice that the train predictions are pretty good, but may maybe lagging by one step. 60 00:05:16,480 --> 00:05:22,660 This kind of behavior is typical when you have a trend with noise, but note that for the test predictions 61 00:05:22,870 --> 00:05:24,430 we still see a similar thing. 62 00:05:25,270 --> 00:05:30,850 However, this is not a case of lagging behind by one step because remember that the model doesn't know 63 00:05:30,850 --> 00:05:32,470 anything about the values in the tests. 64 00:05:33,520 --> 00:05:38,260 In this case, the model really is forecasting this curve, only having seen the train set. 65 00:05:38,920 --> 00:05:43,600 So it's interesting that the model is able to capture the pattern despite it being off by a step or 66 00:05:43,600 --> 00:05:44,090 two. 67 00:05:47,150 --> 00:05:52,280 In the next block, we're going to compute the R squared for both the train and test set for each column. 68 00:05:56,500 --> 00:05:56,880 Okay. 69 00:05:56,890 --> 00:06:02,290 So as expected, the trainer squared for GDP growth is pretty low and the tests are squared is even 70 00:06:02,290 --> 00:06:02,800 lower. 71 00:06:03,790 --> 00:06:08,650 However, note that it is above zero, meaning that it's still better than predicting the average test 72 00:06:08,650 --> 00:06:11,320 value for the term spread. 73 00:06:11,410 --> 00:06:16,270 The trainer scored is high, which makes sense because of the strong correlation with lags we saw in 74 00:06:16,270 --> 00:06:17,140 the ECF. 75 00:06:17,740 --> 00:06:19,930 However, the test R-squared is low. 76 00:06:23,090 --> 00:06:26,570 The next step is to try some other models such as Var and a Remo. 77 00:06:27,080 --> 00:06:29,210 So we'll start with creating a var object. 78 00:06:33,430 --> 00:06:36,010 The next step is to call the select order function. 79 00:06:38,930 --> 00:06:45,620 We can see that if we were to use the AIC, we would select a league order of ten, which is 2.5 years. 80 00:06:47,810 --> 00:06:49,520 The next step is to fit our model. 81 00:06:52,980 --> 00:06:56,550 The next step is to get the flag order of our model, which we know is ten. 82 00:06:57,600 --> 00:07:03,060 Recall that we need this value in order to select the right number of rows for the prior time series. 83 00:07:06,390 --> 00:07:12,300 The next step is to grab the prior time series from the train set and then we call forecast to predict 84 00:07:12,300 --> 00:07:14,010 and test the time steps ahead. 85 00:07:17,820 --> 00:07:20,850 The next step is to store and plot our predictions for GDP. 86 00:07:25,350 --> 00:07:30,720 So from my point of view, it's difficult to tell whether this is better or worse than what we had before. 87 00:07:31,080 --> 00:07:32,990 But it doesn't look particularly bad. 88 00:07:35,580 --> 00:07:38,730 The next step is to store and plot our predictions for term spread. 89 00:07:42,990 --> 00:07:46,710 So in this case, we can see that our forecast is much worse than before. 90 00:07:47,280 --> 00:07:51,900 When we look at the end sample predictions, we can tell that they definitely just lag the previous 91 00:07:51,900 --> 00:07:52,440 value. 92 00:07:55,260 --> 00:07:59,730 The next step is to compute the R squared for the GDP for both train and test. 93 00:08:02,790 --> 00:08:07,260 So for the VAR model, we see that for both train and test the r squared is worse. 94 00:08:07,710 --> 00:08:11,290 This means that var does not be varma, at least for GDP. 95 00:08:11,310 --> 00:08:13,290 With the hyper parameters we used. 96 00:08:16,040 --> 00:08:20,420 The next step is to compute the R squared for the term spread for both train and test. 97 00:08:23,720 --> 00:08:27,620 So again, we see that for both train and test, the R squared is worse. 98 00:08:28,280 --> 00:08:32,770 Again, we can conclude that Varma is better than var, at least for the orders we selected. 99 00:08:36,460 --> 00:08:39,880 The final step in this lecture is to check our remote baseline. 100 00:08:40,450 --> 00:08:44,230 Since this code is essentially the same as before, I won't explain it again. 101 00:08:44,980 --> 00:08:48,010 Note that we are using the same PNG Q as our Varma model. 102 00:08:48,160 --> 00:08:49,570 For a more fair comparison. 103 00:08:55,780 --> 00:08:59,140 So this time we see that Arima does not outperform Varma. 104 00:08:59,950 --> 00:09:04,960 The R squared is worse for both train and test for both GDP and term spread. 105 00:09:06,040 --> 00:09:11,050 In this case, we've seen that Varma is useful and that there could be some predictive value in looking 106 00:09:11,050 --> 00:09:12,730 across the two time series.