1 00:00:11,110 --> 00:00:16,300 So in this lecture, we are going to go over a topic that is typically taught in a module on Varma, 2 00:00:16,720 --> 00:00:22,870 which is Granger causality, earlier in this course, we were exposed to various hypothesis tests. 3 00:00:23,350 --> 00:00:30,100 This is another the Granger causality test is a statistical test that checks whether one time series 4 00:00:30,100 --> 00:00:33,550 is useful in forecasting another time series. 5 00:00:34,510 --> 00:00:40,900 Now, one important thing to note about the Granger causality test is it's actually not a test for causality. 6 00:00:41,590 --> 00:00:48,310 When we use the term causality, we typically mean that one thing causes another thing, and this concept 7 00:00:48,310 --> 00:00:52,480 can get pretty philosophical in this case, despite its name. 8 00:00:52,690 --> 00:00:55,450 We are actually not talking about true causality. 9 00:00:56,140 --> 00:00:58,750 Instead, we take a more mechanical perspective. 10 00:00:59,410 --> 00:01:05,500 Granger causal simply means that one time series can be used in forecasting a different time series. 11 00:01:06,310 --> 00:01:11,080 A predictive relationship does not necessarily imply a causal relationship. 12 00:01:15,880 --> 00:01:17,470 Let's now look at some details. 13 00:01:18,340 --> 00:01:25,630 Suppose that we have two stationary time Series X of T and Y of T, suppose that we build in auto regressive 14 00:01:25,630 --> 00:01:27,040 model for Y of T. 15 00:01:27,940 --> 00:01:33,880 Now suppose that we build another auto regressive model to predict Y of T, but instead of only using 16 00:01:33,880 --> 00:01:38,170 past values of Y of T, we also use arbitrary legs from X of T. 17 00:01:39,020 --> 00:01:44,680 As you can see, you can pick a very specific lags like X of T minus three and X of T minus seven and 18 00:01:44,680 --> 00:01:45,370 so forth. 19 00:01:45,940 --> 00:01:49,570 So this method allows you to test only the legs you choose. 20 00:01:50,530 --> 00:01:56,770 Now what this test essentially does is it checks whether or not the coefficients on the legs of X are 21 00:01:56,770 --> 00:01:58,360 statistically significant. 22 00:01:59,410 --> 00:02:04,090 If they are, then we conclude that X of T Granger causes Y of T. 23 00:02:08,890 --> 00:02:14,770 As a reminder, recall that in regression analysis, it's always possible to test whether the coefficients 24 00:02:14,770 --> 00:02:17,680 of your model are statistically significant. 25 00:02:18,700 --> 00:02:24,280 Intuitively, what we mean by significant is that the coefficient is far away from zero. 26 00:02:25,300 --> 00:02:31,120 If it is far away enough from zero, then we have more confidence that it truly has an effect on the 27 00:02:31,120 --> 00:02:33,250 dependent variable or the target. 28 00:02:34,330 --> 00:02:39,850 In this lecture, we're essentially doing this, but with VAR models instead of generic linear regression. 29 00:02:44,540 --> 00:02:50,180 Note that there is also a multivariate version of the Granger causality test, but this is not available 30 00:02:50,180 --> 00:02:51,710 in the Stats Model's package. 31 00:02:52,670 --> 00:02:55,370 This looks at a VAR model, as we've seen in this section. 32 00:02:56,330 --> 00:03:03,560 Essentially, if we find that a subscript TAO at Roget column, I for any title has an absolute value, 33 00:03:03,560 --> 00:03:10,340 which is significantly larger than zero, then we can say that the time Series Y so by Granger causes 34 00:03:10,340 --> 00:03:11,840 the time Series Y Sub J. 35 00:03:12,620 --> 00:03:14,030 This should be pretty intuitive. 36 00:03:14,720 --> 00:03:21,140 Basically, it means that the coefficient from a lag of Y has an influence on the current value of YJ. 37 00:03:22,640 --> 00:03:26,000 So hopefully this helps to connect this topic to the rest of this section. 38 00:03:26,420 --> 00:03:31,730 But again, a note that the multivariate version is not included in the stats modest package. 39 00:03:36,380 --> 00:03:40,610 Now, let's get to the practical question, which is how do you do this in Python? 40 00:03:41,510 --> 00:03:46,130 Suppose that we have a buy very at time series, which occupy two columns of a data frame. 41 00:03:46,850 --> 00:03:52,490 We can then pass this through the method Granger causality tests, and this will produce a p value for 42 00:03:52,490 --> 00:03:56,120 every leg you want to test for using various different tests. 43 00:03:56,870 --> 00:04:01,730 Now, in order to understand what these specific tests are and how they work, you would need to take 44 00:04:01,730 --> 00:04:04,100 a graduate course on mathematical statistics. 45 00:04:04,490 --> 00:04:06,980 So that's definitely outside the scope of this course. 46 00:04:08,150 --> 00:04:13,880 These tests will typically produce similar results anyway, so the main thing in your work is to remain 47 00:04:13,880 --> 00:04:14,690 consistent. 48 00:04:15,680 --> 00:04:20,780 As always, you will choose a significance threshold beforehand, and any p value smaller than this 49 00:04:20,780 --> 00:04:23,000 threshold will be deemed significant.