1 00:00:11,140 --> 00:00:16,600 So in this lecture, we will be looking at a notebook where we get to explore how to model the volatility 2 00:00:16,810 --> 00:00:17,990 of stock returns. 3 00:00:18,610 --> 00:00:24,340 We'll begin by downloading historical prices for spy, although obviously you can replace this with 4 00:00:24,340 --> 00:00:25,340 whatever you like. 5 00:00:25,360 --> 00:00:27,670 For example, Bitcoin or anything else. 6 00:00:34,310 --> 00:00:38,300 The next step is to update stats models and install Arch at the same time. 7 00:00:45,710 --> 00:00:51,120 The next step is to do our imports, the main import we're going to need is the arch model function, 8 00:00:51,620 --> 00:00:53,310 everything else you've seen before. 9 00:00:53,360 --> 00:00:54,590 Elsewhere in this chorus. 10 00:01:00,870 --> 00:01:04,590 The next step is to load in our data using PDF that reads ESV. 11 00:01:09,070 --> 00:01:13,530 The next step is to call the dot head to remind ourselves what this data looks like. 12 00:01:18,560 --> 00:01:21,640 So we see the open, high, low, close and so forth. 13 00:01:24,900 --> 00:01:29,910 The next step is to compute the log returns, which is the TIME series we're trying to model with Gargash. 14 00:01:34,910 --> 00:01:40,100 The next step is to make a new data frame, which takes in everything except the first row, since that 15 00:01:40,100 --> 00:01:42,470 does not contain any value for the return. 16 00:01:48,030 --> 00:01:51,540 The next step is to plot the longer term so we know what it looks like. 17 00:01:56,530 --> 00:02:02,920 So, as expected, we see a lot of volatility clustering every time the return has a large magnitude, 18 00:02:03,140 --> 00:02:06,040 it's surrounded by other returns of large magnitude. 19 00:02:06,730 --> 00:02:08,860 Notice how these kind of appear like shocks. 20 00:02:09,250 --> 00:02:14,410 There's a really big value and then it tapers off over time, just like the garden model says it should. 21 00:02:17,750 --> 00:02:21,440 OK, so the next step is to compute the square of the log returns. 22 00:02:25,340 --> 00:02:28,580 The next step is to plot the square of the log returns. 23 00:02:33,490 --> 00:02:39,430 So this makes it a bit easier to see that the volatility does, in fact cluster when the returns get 24 00:02:39,430 --> 00:02:42,720 large, they are usually followed by more large returns. 25 00:02:46,380 --> 00:02:50,730 OK, so in the next portion of this notebook, we're going to explore the akef and the. 26 00:02:53,970 --> 00:02:57,730 Let's begin by simply plotting the AKF of the log returns. 27 00:02:58,320 --> 00:03:02,040 We've seen this before, but it helps to remind ourselves what it looks like. 28 00:03:06,300 --> 00:03:11,910 OK, so as expected, there are really no significant correlations, there are a couple of values that 29 00:03:11,910 --> 00:03:14,570 go a little bit outside the significance threshold. 30 00:03:14,790 --> 00:03:18,570 But as you recall, this also happens with actual ID noise as well. 31 00:03:19,470 --> 00:03:24,930 Furthermore, as you recall, with a five percent significance threshold, we do expect to see false 32 00:03:24,930 --> 00:03:28,050 positives five percent of the time by definition. 33 00:03:31,710 --> 00:03:33,360 OK, so the next step is to plot the. 34 00:03:39,260 --> 00:03:42,350 So, again, we see pretty much the same thing as the AKF. 35 00:03:45,860 --> 00:03:48,230 Now, the next part is where things get interesting. 36 00:03:48,770 --> 00:03:52,160 We're now going to plot the AKF of the squared returns. 37 00:03:56,680 --> 00:04:00,220 OK, so as you can see, there are now many significant lags. 38 00:04:00,640 --> 00:04:05,290 This tells us that there is a significant correlation in the Squared series. 39 00:04:09,350 --> 00:04:13,060 The next step is to plot the pickoff of the squared returns. 40 00:04:18,500 --> 00:04:23,990 So, again, we see that there are some very significant legs going far beyond the significance threshold. 41 00:04:28,070 --> 00:04:35,150 So we've seen that the AKF and for the log returns look like a random walk, but the Akef and PKF four 42 00:04:35,150 --> 00:04:37,890 squared returns have significant lags. 43 00:04:38,510 --> 00:04:45,110 Now, by definition, we know that if we were to plot the account for a Gaussian white noise, we would 44 00:04:45,110 --> 00:04:46,040 see the same thing. 45 00:04:46,730 --> 00:04:52,460 But something we have not seen is the akef and the pickoff for the square of Gaussian white noise. 46 00:04:53,060 --> 00:04:58,910 The question we want to answer is, can this be the thing that differentiates stock returns from actual 47 00:04:58,910 --> 00:05:00,150 Gaussian white noise? 48 00:05:00,710 --> 00:05:05,990 So in this next block of code, I've generated 500 points from the standard normal, which gives us 49 00:05:05,990 --> 00:05:07,220 Gaussian white noise. 50 00:05:07,610 --> 00:05:09,370 I've also squared these values. 51 00:05:09,860 --> 00:05:11,340 So let's look at the HCF. 52 00:05:17,440 --> 00:05:23,600 So, as you may have expected, Akef shows essentially no significant legs, we seem to have a couple 53 00:05:23,600 --> 00:05:27,720 of values that peak through slightly, but nothing that goes far outside the blue area. 54 00:05:31,550 --> 00:05:32,690 The next step is to plot the. 55 00:05:38,140 --> 00:05:40,270 So, again, we see pretty much the same thing. 56 00:05:41,260 --> 00:05:42,500 So what have we learned? 57 00:05:43,180 --> 00:05:49,030 We've learned that the dependent's in the square to returns tells us that stock price returns are not 58 00:05:49,030 --> 00:05:52,820 exactly like U.S. and white noise used to produce a random walk. 59 00:05:53,530 --> 00:05:57,260 We've seen that because Gaussian white noise values are truly independent. 60 00:05:57,610 --> 00:06:01,720 There will not be any autocorrelation no matter how you transform the series.