1 00:00:11,090 --> 00:00:17,050 In this lecture, we are going to apply everything we learned about Arima and apply that to stock prices. 2 00:00:17,750 --> 00:00:22,220 So this goes back to the fundamental question we asked at the beginning of this section. 3 00:00:22,880 --> 00:00:27,470 If we make use of time series analysis, can we predict stock prices? 4 00:00:27,950 --> 00:00:33,800 After all, stock prices are a time series, just like airline passengers, just like sales data and 5 00:00:33,800 --> 00:00:34,520 so forth. 6 00:00:35,150 --> 00:00:39,020 I think by the end of this section, we've come to learn a few basic facts. 7 00:00:39,770 --> 00:00:44,940 Firstly, that Arima is a pretty well accepted staple of time series forecasting. 8 00:00:45,680 --> 00:00:51,500 Secondly, is that a more modern approach to finding the best Arima orders would be to use auto arima 9 00:00:51,680 --> 00:00:53,760 rather than trying to pick the orders manually. 10 00:00:54,470 --> 00:00:59,390 So this lecture is all about taking everything that we learned and applying that to stock prices. 11 00:01:00,020 --> 00:01:05,700 As a side note, I want to mention that this lecture contains no new code, which you haven't seen before. 12 00:01:06,230 --> 00:01:11,660 So if you feel like exercising what you've learned, you already know what we're going to do if you 13 00:01:11,660 --> 00:01:13,190 want to try to do it all on your own. 14 00:01:13,340 --> 00:01:14,930 That would be highly encouraged. 15 00:01:16,240 --> 00:01:20,050 OK, so let's start by downloading the S&P 500 at CSFI. 16 00:01:22,870 --> 00:01:29,530 Next, let's install PMed Yarema, unfortunately, because this library doesn't come with Google CoLab, 17 00:01:29,650 --> 00:01:32,230 you're going to need to install it manually each time. 18 00:01:35,860 --> 00:01:41,110 Next, we're going to import PMed Yarema as well as pandas, lumpia matplotlib. 19 00:01:47,150 --> 00:01:52,190 Next, we're going to use Pedigree's GSV to load in our data as a data frame. 20 00:01:57,220 --> 00:02:01,570 Next, we're going to check the head to remind ourselves what the data looks like. 21 00:02:07,730 --> 00:02:12,860 Next, we're going to filter out Google's closed prices and assign this to a variable named GOOG. 22 00:02:14,430 --> 00:02:18,840 Note that you also have the option of filling the log prices instead for this lecture. 23 00:02:18,870 --> 00:02:23,070 We're going to work with the nonlawyers prices, but you're encouraged to try both on your own. 24 00:02:25,420 --> 00:02:30,570 Next, we're going to apply Google's closed prices so that we know what auto Auriemma is trying to model. 25 00:02:36,340 --> 00:02:43,010 Next, we're going to split our data into train and test set, we'll use 30 days as the forecast horizon. 26 00:02:46,180 --> 00:02:52,390 Next, let's call the function auto arima note that we pass in seasonal equals false sense. 27 00:02:52,390 --> 00:02:56,680 If we pass in a seasonal equals true, then we have to pass in the seasonal period. 28 00:02:56,830 --> 00:02:58,960 And of course, it's not clear what that is. 29 00:02:59,620 --> 00:03:01,300 OK, so let's run this. 30 00:03:16,010 --> 00:03:17,870 Next, let's run a model summary. 31 00:03:22,680 --> 00:03:26,820 OK, so we see that the best model found is in a rhema three one zero. 32 00:03:27,330 --> 00:03:28,680 So does that make sense? 33 00:03:29,280 --> 00:03:34,230 The difference in order makes a lot of sense, because as you've seen, returns are pretty stationary. 34 00:03:34,890 --> 00:03:40,020 Although the first difference of the raw price is not exactly the return, we can imagine that they 35 00:03:40,020 --> 00:03:41,760 are related to. 36 00:03:41,760 --> 00:03:45,130 Be sure you might want to plot the first difference and check it yourself. 37 00:03:46,500 --> 00:03:50,460 The next thing we see is that the auto regressive component has order three. 38 00:03:50,910 --> 00:03:52,220 That kind of makes sense. 39 00:03:52,620 --> 00:03:57,380 It says that the last three days of data might be useful in predicting the next return. 40 00:04:00,760 --> 00:04:03,700 OK, so let's look at Model yet Perens. 41 00:04:05,150 --> 00:04:09,960 This provides some interesting information about the model, but not much we didn't already know. 42 00:04:10,610 --> 00:04:14,950 The important part of this is that it gives us a nice way to retrieve the order of the model. 43 00:04:15,530 --> 00:04:20,350 As you recall, we need to know this, since it affects which days we can make predictions for. 44 00:04:20,870 --> 00:04:26,420 For example, if this is equal to one, then we can make a prediction on day one, because defensing 45 00:04:26,420 --> 00:04:28,790 always makes the first row and any value. 46 00:04:32,720 --> 00:04:35,920 OK, so next, we're going to write a function called plot result. 47 00:04:36,530 --> 00:04:39,990 This function is very similar to the ones we wrote for the previous scripts. 48 00:04:40,700 --> 00:04:47,060 Basically, the point is to plot the data itself, the fit it values for the sample data, the forecast 49 00:04:47,060 --> 00:04:49,990 for the out of sample data and the confidence balance. 50 00:04:50,630 --> 00:04:57,320 So as input into this function, we take in a trained model the full data, the train data and the test 51 00:04:57,320 --> 00:04:57,800 data. 52 00:04:58,610 --> 00:05:00,080 The full data is just the data. 53 00:05:00,080 --> 00:05:02,510 Before we split the data into train and test. 54 00:05:03,800 --> 00:05:08,730 The first thing we do in this function is to make use of the jet programs function we just looked at. 55 00:05:09,290 --> 00:05:10,450 This is a dictionary. 56 00:05:10,700 --> 00:05:15,600 So first we look at the key order, which gives us the order of the fitted Arima. 57 00:05:16,400 --> 00:05:20,540 Next, we grab the second component, which gives us back the difference in order. 58 00:05:20,640 --> 00:05:26,670 The next we call model predict in sample to get the train predictions. 59 00:05:27,260 --> 00:05:34,760 Note that the starting value is the next we call model to predict to get the out of sample predictions 60 00:05:34,790 --> 00:05:36,680 along with the confidence balance. 61 00:05:37,850 --> 00:05:39,880 Next, we call our plotting functions. 62 00:05:40,430 --> 00:05:42,030 First we plot the full data. 63 00:05:42,260 --> 00:05:44,000 This will be given the label data. 64 00:05:44,900 --> 00:05:46,760 Next, we plot the trend predictions. 65 00:05:47,000 --> 00:05:48,710 This will be given the label fitted. 66 00:05:49,370 --> 00:05:51,290 Next, we plot the test predictions. 67 00:05:51,710 --> 00:05:53,810 This will be given the label forecast. 68 00:05:54,410 --> 00:05:58,400 Next, we call the function to fill between to draw the confidence bounce. 69 00:05:59,090 --> 00:06:02,210 Lastly, we call a legend to show the legend. 70 00:06:04,140 --> 00:06:05,220 So let's run this. 71 00:06:07,790 --> 00:06:10,370 And let's test that our plot result function. 72 00:06:14,390 --> 00:06:17,790 So as you can see, the fitted model looks pretty good. 73 00:06:18,410 --> 00:06:21,590 Of course, you shouldn't trust a plow like this because it's very small. 74 00:06:22,330 --> 00:06:27,800 Unfortunately, it's too small to see whether or not our forecast is good, which is the part we actually 75 00:06:27,800 --> 00:06:28,410 care about. 76 00:06:33,710 --> 00:06:39,170 So next, we're going to write a function called a plot test, the point of this function is only to 77 00:06:39,170 --> 00:06:40,460 plot the test period. 78 00:06:41,030 --> 00:06:46,010 By seeing it up close, we'll get a better idea of how well our model actually performs. 79 00:06:46,610 --> 00:06:52,430 So in this function, we only take in at two arguments, a fit model and the test data frame. 80 00:06:54,060 --> 00:06:59,280 Inside the function we call model predict to get the predictions and the confidence bounce. 81 00:07:00,030 --> 00:07:05,310 Next, we plot the true test data along with the forecast and then the confidence bounce. 82 00:07:05,850 --> 00:07:10,190 Actually, this is the same code from earlier, so hopefully you're comfortable with it by now. 83 00:07:16,660 --> 00:07:19,390 Next, we test out our new functional a test. 84 00:07:23,060 --> 00:07:24,080 So what do we see? 85 00:07:24,920 --> 00:07:28,150 Well, we see that our forecast is not actually that good. 86 00:07:28,820 --> 00:07:31,260 Remember, this is over 30 trading days. 87 00:07:32,150 --> 00:07:36,390 One nice thing about this is that it does seem to capture that average quite well. 88 00:07:37,070 --> 00:07:42,550 In addition, the true price always seems to stay within the confidence bounds for the most part. 89 00:07:44,060 --> 00:07:48,770 Of course, it's worth asking whether a model like this could actually predict what will happen over 90 00:07:48,770 --> 00:07:50,510 the next 30 trading days. 91 00:07:51,410 --> 00:07:54,470 Elon Musk goes on Twitter and starts making crazy tweets. 92 00:07:54,680 --> 00:07:57,830 I don't think models like this will be able to predict that. 93 00:08:05,210 --> 00:08:10,940 OK, so as you know, one important question we have to ask at this point is, do these models perform 94 00:08:10,940 --> 00:08:12,980 better than the new forecast? 95 00:08:13,460 --> 00:08:15,090 Is using these models worth it? 96 00:08:15,860 --> 00:08:19,160 So let's define the arm as a function which you've seen before. 97 00:08:22,080 --> 00:08:28,950 Next, let's print out the pharmacy for our Arima model and for the naive forecast note that for the 98 00:08:28,950 --> 00:08:34,590 naive forecast, the train prediction can simply be a single value, which is the final value of the 99 00:08:34,590 --> 00:08:35,530 train series. 100 00:08:36,030 --> 00:08:42,420 This is because series and LEMPIRAS broadcast during subtraction so you can subtract a scalar from an 101 00:08:42,420 --> 00:08:43,680 array or vice versa. 102 00:08:45,240 --> 00:08:45,600 All right. 103 00:08:45,600 --> 00:08:46,740 So what do we see? 104 00:08:48,090 --> 00:08:53,250 Well, we see that although we've done a lot of hard work to train this model, it is, in fact the 105 00:08:53,250 --> 00:08:55,350 naive forecast that wins. 106 00:08:59,600 --> 00:09:03,260 OK, so next, we're going to do the same thing for Apple stocks. 107 00:09:08,450 --> 00:09:14,720 OK, so note that for Apple, there was a big dip in the price over the last period, it's worth asking 108 00:09:14,720 --> 00:09:19,430 yourself, is such a drastic event predictable by NRMA model? 109 00:09:20,480 --> 00:09:25,730 Remember that these models tend to follow patterns if there's a trend, it follows the trend. 110 00:09:25,910 --> 00:09:28,600 If they're seasonality, it follows the seasonality. 111 00:09:29,240 --> 00:09:34,850 But I think intuition, it tells us that models like these do not predict anomalous events. 112 00:09:35,180 --> 00:09:40,600 For example, a stock like this rising upwards very quickly and then dropping off all of a sudden. 113 00:09:41,060 --> 00:09:42,350 That's not really a pattern. 114 00:09:42,380 --> 00:09:44,210 That's more like the opposite of a pattern. 115 00:09:45,260 --> 00:09:49,250 OK, so next, we're going to split our data into train and test. 116 00:09:53,060 --> 00:09:57,630 Next, we're going to call Otto Arima again, note that seasonal is false. 117 00:09:58,160 --> 00:09:59,240 So let's run this. 118 00:10:13,070 --> 00:10:15,050 OK, so here's the model summary. 119 00:10:18,980 --> 00:10:24,710 Again, the fact that the difference in order is one is not surprising, what is kind of surprising 120 00:10:24,710 --> 00:10:27,580 is that this model is very different from the previous model. 121 00:10:28,070 --> 00:10:31,100 Here we have P equals two and two equals two. 122 00:10:31,520 --> 00:10:34,520 Earlier we had a P equals three and Q equals zero. 123 00:10:40,620 --> 00:10:42,900 Next, we're going to call a function of plot result. 124 00:10:46,870 --> 00:10:52,780 So as you can see, even with this tiny plot, it's obvious that the true data goes way outside the 125 00:10:52,780 --> 00:10:53,850 confidence bounds. 126 00:10:54,440 --> 00:10:57,820 However, I think this makes sense in terms of the model we're using. 127 00:10:58,540 --> 00:11:01,730 The model seems to just want to carry on the existing trend. 128 00:11:02,320 --> 00:11:08,080 Philosophically, I think that's what most models would do in the context of pattern recognition and 129 00:11:08,080 --> 00:11:08,920 machine learning. 130 00:11:09,070 --> 00:11:10,330 That makes total sense. 131 00:11:16,730 --> 00:11:22,250 OK, so next, let's call the function a plot test so we can see the forecast period of close up. 132 00:11:27,550 --> 00:11:31,100 All right, and we see that, in fact, the prediction is pretty far off. 133 00:11:31,810 --> 00:11:35,380 However, note that in the short term, the prediction is not that bad. 134 00:11:35,950 --> 00:11:40,530 Over the first few days, the true values stay within the confidence bounce for the most part. 135 00:11:45,270 --> 00:11:50,220 Now, of course, we still have to check the root mean squared error against the naive forecast. 136 00:11:53,450 --> 00:11:57,170 Again, the Niyi forecast performs better than the Arima. 137 00:12:01,520 --> 00:12:07,520 Next, we're going to do the same exercise, but for the IBM stock prices, again, let's start by plotting 138 00:12:07,520 --> 00:12:08,140 the data. 139 00:12:14,460 --> 00:12:17,040 Next, let's split the data into train and test. 140 00:12:20,970 --> 00:12:22,950 Next, let's call Auto Arima. 141 00:12:29,530 --> 00:12:31,490 Next, let's check model summary. 142 00:12:35,390 --> 00:12:41,220 OK, so what do we see, in fact, for IBM, the best fitting model is a random walk. 143 00:12:41,660 --> 00:12:42,590 What does this mean? 144 00:12:43,280 --> 00:12:49,970 It means that IBM stock returns are completely unpredictable, given lagged values or lagged errors. 145 00:12:54,280 --> 00:12:55,930 Next, let's call Plott result. 146 00:12:58,610 --> 00:13:00,750 OK, so nothing out of the ordinary. 147 00:13:01,220 --> 00:13:05,210 It does look like the confidence bounce and close the true values in the forecast. 148 00:13:09,870 --> 00:13:11,610 Next, let's call playtest. 149 00:13:14,160 --> 00:13:19,770 Again, we see that the confidence balance and close the true values, in fact, this prediction doesn't 150 00:13:19,770 --> 00:13:25,110 look that bad, the actual price crisis through the prediction line multiple times. 151 00:13:28,600 --> 00:13:33,130 So what happens when we check the root mean square error against the naive forecast? 152 00:13:35,890 --> 00:13:40,900 Well, we see that they are the same since this is a random walk model with no drift. 153 00:13:41,230 --> 00:13:46,090 The forecast is just the last known value and it's the same as the naive forecast. 154 00:13:49,220 --> 00:13:53,930 OK, so next, let's try Starbucks again, let's start by looking at the plot. 155 00:13:59,190 --> 00:14:02,010 Next, let's split the data into train and test. 156 00:14:05,760 --> 00:14:07,950 Next, let's call Otto Arima. 157 00:14:15,770 --> 00:14:17,810 Next, let's check the model summary. 158 00:14:22,420 --> 00:14:29,650 OK, so here is another random walk, a rhema zero one zero note, however, that this is a random walk 159 00:14:29,650 --> 00:14:33,930 with Dreft since the model fits with a non-zero intercept term. 160 00:14:37,520 --> 00:14:39,320 Next, let's check Resul. 161 00:14:42,250 --> 00:14:45,550 OK, so it's a bit hard to see what's going on during the forecast. 162 00:14:49,860 --> 00:14:51,960 Next, let's check playtest. 163 00:14:56,070 --> 00:15:01,770 All right, so this doesn't look too bad, it's decently accurate for the first few values and then 164 00:15:01,770 --> 00:15:07,440 it overestimates the price when the price drops, although most of the time the price does stay within 165 00:15:07,440 --> 00:15:08,670 the confidence bounds. 166 00:15:09,330 --> 00:15:13,410 So the lesson is, don't ignore the negative side of your confidence balance. 167 00:15:13,770 --> 00:15:17,700 Those values are perfectly achievable and they result in a loss of money. 168 00:15:22,720 --> 00:15:25,270 So what happens when we check the root mean square error? 169 00:15:29,240 --> 00:15:35,240 Well, although we detected that this was a random walk with a non-zero drift, it turns out that assuming 170 00:15:35,240 --> 00:15:40,450 a random walk with zero drift would have been better, the naive forecast wins again.