1 00:00:11,100 --> 00:00:15,840 OK, so in this lecture, we are going to continue looking at our Gaja notebook. 2 00:00:16,500 --> 00:00:21,220 The next step is to consider a full Gargash model, specifically the guards one one. 3 00:00:21,990 --> 00:00:27,120 This happens to be the most popular Gargash due to the fact that it fits Financial Times series quite 4 00:00:27,120 --> 00:00:29,250 well, while also being very simple. 5 00:00:30,520 --> 00:00:34,570 As you recall, statisticians tend to prefer parsimonious models. 6 00:00:35,190 --> 00:00:40,710 So we'll start by calling the arch model function, specifying the model type as gargash and setting 7 00:00:40,710 --> 00:00:41,580 both incudes. 8 00:00:41,580 --> 00:00:47,250 One note that the last three arguments are not really necessary, since currently these are the default 9 00:00:47,250 --> 00:00:48,090 values. 10 00:00:52,660 --> 00:00:54,550 The next step is to call a function. 11 00:01:00,060 --> 00:01:02,190 The next step is to call the summary function. 12 00:01:06,610 --> 00:01:08,560 OK, so notice a few things. 13 00:01:09,190 --> 00:01:14,020 Firstly, notice that the log likelihood and the AIC are much better than before. 14 00:01:14,560 --> 00:01:17,320 This is a sign that this model is a much better fit. 15 00:01:19,580 --> 00:01:25,040 The next thing to notice is that the Beetle one coefficient has a very small P value indicating that 16 00:01:25,040 --> 00:01:26,450 it is very significant. 17 00:01:27,080 --> 00:01:29,930 This makes sense given the improvement in the likelihood. 18 00:01:33,640 --> 00:01:39,430 The next step is to store the conditional volatility in the data data frame under the column name Gaja 19 00:01:39,430 --> 00:01:45,970 one one, we'll also plot this against the one and against the original scaled time series. 20 00:01:50,790 --> 00:01:56,520 OK, so this may be a bit hard to see, but basically you can tell that the model is able to match the 21 00:01:56,520 --> 00:01:59,300 higher values as well as the lower values. 22 00:02:03,350 --> 00:02:09,830 The next step is to make a forecast using the same start date as before, as you recall, we chose this 23 00:02:09,830 --> 00:02:13,000 start date because the value was very high on this date. 24 00:02:13,460 --> 00:02:16,660 So we expect to see the forecasts converge downwards. 25 00:02:21,520 --> 00:02:26,560 The next step is to store the variance forecast using essentially the same code as before. 26 00:02:30,640 --> 00:02:34,720 The next step is to compute the absolute value of the scale time series. 27 00:02:35,470 --> 00:02:41,140 Note that the Time series itself is on the same scale as the volatility, while the Square of the Time 28 00:02:41,140 --> 00:02:43,610 series is on the same scale as the variance. 29 00:02:44,020 --> 00:02:48,300 So either of these is fine, but you just have to pick which one you want to use. 30 00:02:49,540 --> 00:02:55,780 The next step is to plot the scale time series with the one forecast and the large one one forecast. 31 00:03:01,530 --> 00:03:04,020 So there are two things you should notice about this. 32 00:03:04,680 --> 00:03:09,150 Firstly, notice that the garden model matches the actual data much more closely. 33 00:03:09,660 --> 00:03:13,350 The arch one seems to not be able to reach those high values. 34 00:03:14,280 --> 00:03:19,020 Secondly, notice how quickly the arch one converges compared to the Ghazwan one. 35 00:03:19,800 --> 00:03:23,220 That is to say, the arch model is much more persistent. 36 00:03:28,560 --> 00:03:34,290 So, as you recall, one possible option when we create the garbage is what kind of distribution to 37 00:03:34,290 --> 00:03:36,300 use by default. 38 00:03:36,330 --> 00:03:41,610 This is the normal, but we've heard that the student t distribution may be a better fit for financial 39 00:03:41,610 --> 00:03:42,450 returns. 40 00:03:43,110 --> 00:03:49,380 So the next step is to create another Ghazwan one, but this time using the T distribution instead of 41 00:03:49,380 --> 00:03:50,250 the default. 42 00:03:55,450 --> 00:03:58,420 As before, the next step is to call modeled that fit. 43 00:04:03,840 --> 00:04:06,080 And again, we're going to look at the model summary. 44 00:04:11,400 --> 00:04:16,290 So as you can see, the log likelihood has again improved, as has the AC. 45 00:04:21,090 --> 00:04:24,820 Notice also that all of the search parameters are still significant. 46 00:04:25,560 --> 00:04:31,980 And also notice that there is one more parameter under distribution since, as you recall, the T distribution 47 00:04:31,980 --> 00:04:35,280 has a parameter called NU, which is the degrees of freedom. 48 00:04:35,970 --> 00:04:38,160 This also has a significant P value. 49 00:04:42,520 --> 00:04:49,060 OK, so the next step is, again, to store the condition of volatility and to plot the results, this 50 00:04:49,060 --> 00:04:53,230 time we're going to plot the Garden one Wante against the March one, one normal. 51 00:04:59,080 --> 00:05:04,240 OK, so you can see that the results look essentially the same, although you may be able to see the 52 00:05:04,240 --> 00:05:06,430 differences more clearly if you zoom in. 53 00:05:10,090 --> 00:05:12,250 The next step is to compute the forecast. 54 00:05:18,310 --> 00:05:22,270 The next step is to store the forecast for the same dates as before. 55 00:05:27,740 --> 00:05:31,760 The next step is to plot the forecasts for both Gargash models we've created. 56 00:05:37,870 --> 00:05:43,360 So what we can see from this is that the new model seems to reach an even higher value and it seems 57 00:05:43,360 --> 00:05:46,570 to have even more persistence than the one one normal.