1 00:00:11,110 --> 00:00:16,510 OK, so in this lecture, we will be looking at another Gargash model, this time with more lag's. 2 00:00:17,230 --> 00:00:22,570 So you can see that I've set P to eight and cute's of five, although you can feel free to choose other 3 00:00:22,570 --> 00:00:23,690 values if you like. 4 00:00:24,340 --> 00:00:29,740 Again, we're going to use the T distribution since we've seen that it works well with only one extra 5 00:00:29,740 --> 00:00:30,520 parameter. 6 00:00:35,620 --> 00:00:37,570 The next step is to call a Fed function. 7 00:00:43,560 --> 00:00:45,250 The next step is to call summary. 8 00:00:50,370 --> 00:00:56,670 So as you can see, the log likelihood has improved slightly as an exercise, if you've forgotten what 9 00:00:56,670 --> 00:01:01,040 the previous values were, print them out in this notebook to check them yourself. 10 00:01:03,850 --> 00:01:08,890 Now, interestingly, when we look at the large coefficients, we see that many of them do not have 11 00:01:08,890 --> 00:01:10,420 significant P values. 12 00:01:14,980 --> 00:01:20,620 So you might assume that because I regard SPQR model has a better log likelihood that this is our best 13 00:01:20,620 --> 00:01:21,320 choice. 14 00:01:21,880 --> 00:01:25,480 However, recall that statisticians prefer to use the AIC. 15 00:01:26,290 --> 00:01:30,490 So the next step is to check the AIC for each of our models. 16 00:01:35,160 --> 00:01:41,940 So as you can see, the arch one is by far the worst gurche one, one normal was a significant improvement, 17 00:01:42,180 --> 00:01:45,630 but one one t improves the AIC even more. 18 00:01:46,290 --> 00:01:51,360 In this case, we would reject the Garchik five, since that gives us a worse EIC. 19 00:01:55,320 --> 00:02:01,780 The next step is to save the condition of volatility in our data frame DRV, to also plot the guards 20 00:02:01,810 --> 00:02:04,410 Bhiku against the guards one on one TE. 21 00:02:10,450 --> 00:02:12,850 So as you can see, they are very close. 22 00:02:17,220 --> 00:02:22,230 The next step is to create a forecast again, we'll start at the same date as before. 23 00:02:28,140 --> 00:02:33,390 The next step is to store the forecast using the column name Garchik you forecast. 24 00:02:38,400 --> 00:02:43,680 The next step is to plot the forecast against our best models so far, the March one won T. 25 00:02:50,600 --> 00:02:56,420 OK, so as you can see, they're essentially indistinguishable, so just in terms of this, there would 26 00:02:56,420 --> 00:02:58,910 be no advantage to using the guards PKU. 27 00:03:02,370 --> 00:03:07,440 The next step is to plot the forecast for the test set, which you may have noticed we haven't yet done, 28 00:03:08,400 --> 00:03:12,900 we'll do this using the Q only because it's the last model we created. 29 00:03:13,680 --> 00:03:18,780 So we'll start by creating trainer and test 3x the same way we've done in the past. 30 00:03:23,980 --> 00:03:28,460 The next step is to store the train predictions using the conditional volatility. 31 00:03:29,350 --> 00:03:34,480 We'll also store the test predictions using the square root of the variance of the forecasts. 32 00:03:39,320 --> 00:03:42,890 The final step will be to plot our train and test predictions. 33 00:03:47,790 --> 00:03:53,790 So as expected for the test set, the forecast of the variance simply converges to the unconditional 34 00:03:53,790 --> 00:03:54,320 value. 35 00:03:54,930 --> 00:03:58,590 The actual long term variance, of course, does not follow this pattern. 36 00:03:59,340 --> 00:04:04,170 However, the prediction seems to be somewhere in the middle below the highest values, but above the 37 00:04:04,170 --> 00:04:05,220 lowest values. 38 00:04:05,760 --> 00:04:11,580 As mentioned in the previous lectures, we don't expect any model to predict random volatility fluctuations 39 00:04:11,790 --> 00:04:13,080 several years ahead. 40 00:04:13,260 --> 00:04:15,020 It simply wouldn't make sense.