1 00:00:11,090 --> 00:00:17,120 So in this lecture, we will be looking at the syntax for Arche and Gurche with the Python library called 2 00:00:17,120 --> 00:00:22,760 Arche, although there are other libraries in Python that implement Gurche, this seems to be the most 3 00:00:22,760 --> 00:00:23,330 popular. 4 00:00:23,990 --> 00:00:28,790 So this lecture will focus on showing you how to use this library so that when we look at the actual 5 00:00:28,790 --> 00:00:30,840 code, you won't be surprised. 6 00:00:32,180 --> 00:00:38,360 OK, so to begin, unlike most libraries we need on Google CoLab, Arche does not come preinstalled. 7 00:00:38,840 --> 00:00:42,800 However, as with most Python libraries, it's very easy to install. 8 00:00:43,010 --> 00:00:46,640 Simply use PIP install arch as you normally would. 9 00:00:51,340 --> 00:00:53,750 The next step is to consider how we will use our. 10 00:00:54,730 --> 00:00:58,990 Basically, you'll find that it's much more like stat's models compared to typical machine learning 11 00:00:58,990 --> 00:01:00,710 libraries like Cycad Learn. 12 00:01:01,360 --> 00:01:03,160 So the main steps are as follows. 13 00:01:04,090 --> 00:01:10,090 The first step is to create the model during the stage you'll pass in the training data along with model 14 00:01:10,090 --> 00:01:12,380 type of parameters, just like stat's models. 15 00:01:13,000 --> 00:01:18,040 The next step is to call the fifth function, which is not taking any data since you already pass it 16 00:01:18,040 --> 00:01:19,540 in a during the previous step. 17 00:01:20,320 --> 00:01:23,860 The third step is to use your fittin model to make a forecast. 18 00:01:24,460 --> 00:01:29,690 Now this step will require some elaboration, so that will be one of the main topics of this lecture. 19 00:01:30,520 --> 00:01:35,350 So on the next few slides, we're going to expand on each of these three steps and I'll show you the 20 00:01:35,350 --> 00:01:37,150 exact syntax you'll need. 21 00:01:41,840 --> 00:01:47,660 OK, so the first step is to create your model for this, we're going to use a high level function called 22 00:01:47,660 --> 00:01:48,570 arch model. 23 00:01:49,160 --> 00:01:54,230 Note that unlike other libraries, this is not the actual name of the class, but more like a factory 24 00:01:54,230 --> 00:01:57,360 method that returns some object at this point. 25 00:01:57,380 --> 00:02:00,870 We'll look at some, but not all of the possible arguments. 26 00:02:01,760 --> 00:02:03,950 The first argument is the Noise Time series. 27 00:02:03,950 --> 00:02:07,600 You're trying to model, for example, series of log returns. 28 00:02:08,870 --> 00:02:13,720 The next argument is for passing an exogenous data, which we will not use in this course. 29 00:02:14,690 --> 00:02:19,550 The next argument is the mean, which is not a number like it sounds like it might be, but rather a 30 00:02:19,550 --> 00:02:20,120 string. 31 00:02:20,810 --> 00:02:26,740 This string specifies the kind of model you want to use for the mean portion of your time series. 32 00:02:27,380 --> 00:02:33,530 As you recall, we can think of every time series as a model plus a noise model gergis for the noise 33 00:02:33,530 --> 00:02:33,860 part. 34 00:02:33,860 --> 00:02:37,410 While you can really use any technique we've learned about for the mean part. 35 00:02:38,270 --> 00:02:40,470 Now you might ask, what about Arima? 36 00:02:41,210 --> 00:02:47,060 Unfortunately, this library for some reason does not support a rhema as the model, although other 37 00:02:47,060 --> 00:02:51,370 libraries do, for example, are Yuga, which is for the our language. 38 00:02:51,860 --> 00:02:56,570 Since we're not using R in this class, I don't have any plans to cover that at this time. 39 00:02:56,960 --> 00:03:01,520 But you can let me know on the Q&A if that's something you would be interested in seeing. 40 00:03:02,360 --> 00:03:08,720 So the closest thing to a Remo that's included in this library is R x, which is an AP model with the 41 00:03:08,720 --> 00:03:10,900 option of having exoticness inputs. 42 00:03:11,690 --> 00:03:15,830 Now for us, we will be using the default argument, which is constant. 43 00:03:16,280 --> 00:03:21,290 This makes sense since we will be looking at stock returns, which we've seen have no auto regressive 44 00:03:21,290 --> 00:03:21,890 structure. 45 00:03:22,340 --> 00:03:24,890 But feel free to try other options if you like. 46 00:03:26,760 --> 00:03:31,500 The next argument we're going to look at is Volle, which represents the kind of Gargash model you want 47 00:03:31,500 --> 00:03:36,420 to use, the default is Gargash, but the simple arch is another option. 48 00:03:37,080 --> 00:03:41,610 Other advanced options are also possible to choose, for example, eg arch. 49 00:03:43,830 --> 00:03:50,460 The next arguments we're going to discuss are in queue for this library, and you are used as we've 50 00:03:50,460 --> 00:03:52,160 defined them in this course. 51 00:03:52,650 --> 00:03:58,050 So as you recall, although some resources reverse the queue, that won't be the case this time. 52 00:03:59,010 --> 00:04:02,580 Also note that the default values for P and Q are both one. 53 00:04:02,910 --> 00:04:09,000 Since the most common Gurche model is the Ghazwan one, it just so happens that this model tends to 54 00:04:09,150 --> 00:04:10,980 fit financial returns very well. 55 00:04:13,010 --> 00:04:16,350 The final argument I want to discuss is the deceit argument. 56 00:04:17,000 --> 00:04:21,920 Now, this is going to get a bit advanced, but if you've taken courses with me before, you should 57 00:04:21,920 --> 00:04:22,960 find this familiar. 58 00:04:23,690 --> 00:04:29,930 Basically, as you recall, the way that these models are fit is by maximizing some likelihood, of 59 00:04:29,930 --> 00:04:31,980 course, in order to have a likelihood function. 60 00:04:32,180 --> 00:04:34,340 You must have some corresponding distribution. 61 00:04:35,120 --> 00:04:36,530 We've seen that for regression. 62 00:04:36,590 --> 00:04:37,970 This is typically the normal. 63 00:04:38,660 --> 00:04:43,410 However, as you may have learned in the past, financial returns have fat tails. 64 00:04:43,910 --> 00:04:49,310 What we mean by this is financial returns can take on more extreme values than would be predicted by 65 00:04:49,310 --> 00:04:51,740 the normal distribution, which is the default. 66 00:04:52,280 --> 00:04:57,710 If you want to convince yourself of this, try plotting a histogram of stock returns against a fitted 67 00:04:57,710 --> 00:04:58,810 normal distribution. 68 00:04:59,060 --> 00:05:01,520 And you should see that there are large deviations. 69 00:05:02,240 --> 00:05:07,280 Basically, the short story is, although the normal distribution is often the default choice, it's 70 00:05:07,280 --> 00:05:09,880 not actually a good fit for financial returns. 71 00:05:10,430 --> 00:05:14,530 As an example, we often find that the T distribution is a much better fit. 72 00:05:15,230 --> 00:05:19,310 So this this argument allows us to specify a different distribution. 73 00:05:24,020 --> 00:05:30,230 OK, so finally, we are at the second step, which is to actually fit the model, this isn't so interesting 74 00:05:30,230 --> 00:05:32,870 because we can call this function without any arguments. 75 00:05:33,410 --> 00:05:39,050 As with stats models, this returns a result object, which you can then use to forecast and do other 76 00:05:39,050 --> 00:05:39,770 things. 77 00:05:40,910 --> 00:05:45,240 One thing you can do after you fitted your model is you can call the summary function. 78 00:05:45,830 --> 00:05:50,610 So if you've ever done regression analysis, what we get back from this should feel pretty familiar. 79 00:05:51,200 --> 00:05:57,000 Basically, you get to see the final log likelihood, the final I, the model parameters and so forth. 80 00:05:57,440 --> 00:06:02,720 It also does some statistical tests so you can check whether or not the parameters are statistically 81 00:06:02,720 --> 00:06:03,620 significant. 82 00:06:08,230 --> 00:06:14,500 OK, so the interesting part of how we use Gargash is when we make our predictions, let's think about 83 00:06:14,500 --> 00:06:15,490 this for a second. 84 00:06:16,000 --> 00:06:21,690 If we want to make a so-called prediction using Gurche, what is it that we are actually predicting? 85 00:06:22,450 --> 00:06:27,640 You might think it's Epsilon of T, since that's the TIME series we're trying to model, but this actually 86 00:06:27,640 --> 00:06:28,680 doesn't make sense. 87 00:06:33,320 --> 00:06:36,530 OK, so why doesn't it make sense to predict Ypsilanti? 88 00:06:37,340 --> 00:06:39,050 Well, Ypsilanti is Noize. 89 00:06:39,470 --> 00:06:44,720 This would be nearly as random as trying to predict a number sampled from the standard normal or a coin 90 00:06:44,720 --> 00:06:45,120 flip. 91 00:06:45,650 --> 00:06:52,070 In fact, it's pretty much just as hard as predicting a coin flip since, as you recall, ZT is a sample 92 00:06:52,070 --> 00:06:55,070 from the standard normal, which is symmetric around zero. 93 00:06:56,090 --> 00:06:59,060 OK, so it doesn't make sense to predict Ypsilanti. 94 00:07:03,910 --> 00:07:05,950 So what does it make sense to predict? 95 00:07:06,730 --> 00:07:13,080 Well, it makes sense to predict the statistics of Ypsilanti in particular, its mean and its variance. 96 00:07:13,720 --> 00:07:19,090 Note that the median is not so interesting since, as you recall, it's typically zero or in our case, 97 00:07:19,090 --> 00:07:19,660 constant. 98 00:07:20,420 --> 00:07:25,270 What we really care about with Gurche being a model for volatility is the variance. 99 00:07:25,750 --> 00:07:32,380 As you recall, this is Sigma squared T. So when it comes time to forecast, this is really what we 100 00:07:32,380 --> 00:07:35,530 want to forecast, either sigma or sigma squared. 101 00:07:40,290 --> 00:07:45,030 Now, since this lecture has been quite long so far, we're going to take a break and continue in the 102 00:07:45,030 --> 00:07:49,050 next lecture, the next lecture will focus on how to forecast.