1 00:00:11,080 --> 00:00:17,060 OK, so for this code, the main idea is not to focus on every line, but to focus on what is different. 2 00:00:17,650 --> 00:00:20,860 You'll notice that most of this is the same as what we had before. 3 00:00:23,520 --> 00:00:28,950 So when we build our supervised data set, notice that we now use the difference in log passengers, 4 00:00:29,610 --> 00:00:33,660 also notice that we start from index one instead of taking the full array. 5 00:00:34,380 --> 00:00:38,640 This is because due to taking the first difference, the first value is zero. 6 00:00:49,680 --> 00:00:55,660 The next thing to notice is that R squared is much lower than before with a stationary time series. 7 00:00:55,800 --> 00:01:00,990 We can't simply predicts the previous value, which you've seen leads to a higher squared in particular 8 00:01:00,990 --> 00:01:01,710 cases. 9 00:01:04,050 --> 00:01:09,150 The next thing to notice is that for the train index, we now said the first big plus one values to 10 00:01:09,150 --> 00:01:09,780 false. 11 00:01:10,260 --> 00:01:12,210 Previously this was just big T. 12 00:01:16,390 --> 00:01:22,330 The next step is to compute the previous values, which we need to d difference our predictions for 13 00:01:22,330 --> 00:01:26,890 one step predictions, we can do this simply by shifting the log passengers up by one. 14 00:01:30,610 --> 00:01:35,650 For multistep predictions, we have to keep in mind that we only know the values from the train set, 15 00:01:36,280 --> 00:01:39,970 so we take the last value from the train set and we call that last train. 16 00:01:43,610 --> 00:01:49,190 OK, so let's see how to do the One-Step forecast for the train set, we take the shifted values in 17 00:01:49,190 --> 00:01:51,940 the train and add them to our predictions. 18 00:01:52,400 --> 00:01:57,200 You should recognize this from the equations we saw earlier for the test set. 19 00:01:57,210 --> 00:01:58,220 We do the same thing. 20 00:01:58,910 --> 00:02:02,180 Notice that this only applies to the ones that forecast. 21 00:02:10,420 --> 00:02:15,850 So you can see that the results look pretty good, much better than before, we now do not have a problem 22 00:02:15,850 --> 00:02:16,810 reaching the peak. 23 00:02:20,310 --> 00:02:23,870 The next step is to look at the incremental multistep forecast. 24 00:02:24,660 --> 00:02:27,810 Now, the loop to make the incremental predictions is the same. 25 00:02:28,320 --> 00:02:29,780 This gives us our deltas. 26 00:02:30,450 --> 00:02:33,270 The part that's different is what we do with these deltas. 27 00:02:38,350 --> 00:02:43,270 So this time it's a multi-step forecast, so the last known value comes from the train. 28 00:02:44,560 --> 00:02:49,270 So we take the last train value and add it to the cumulative some of the deltas. 29 00:02:56,340 --> 00:02:59,660 So we see that the multistep prediction is also pretty good. 30 00:03:03,650 --> 00:03:08,870 OK, so again, most of this stuff like the code to build the data set is the same as before. 31 00:03:20,860 --> 00:03:25,660 Notice again that the R-squared is lower because we're trying to predict a time series where there isn't 32 00:03:25,660 --> 00:03:27,640 a lot of correlation in the values. 33 00:03:31,000 --> 00:03:37,120 OK, so again, the forecast is the last train value, plus the cumulative some of the predictions. 34 00:03:44,680 --> 00:03:49,190 So we again see that the forecast is pretty good, but it's hard to tell from this plot. 35 00:03:49,210 --> 00:03:50,320 Which one is best? 36 00:03:56,110 --> 00:04:01,090 So when we look at the map, we see that the multipotent forecast achieves the best value. 37 00:04:05,080 --> 00:04:11,260 OK, so the next part is, again, to test different models, so this function follows exactly the same 38 00:04:11,260 --> 00:04:11,770 pattern. 39 00:04:12,280 --> 00:04:17,440 The only difference, again, is that we use our new calculations to difference the predictions. 40 00:04:24,330 --> 00:04:26,760 OK, so let's try the support vector machine. 41 00:04:31,740 --> 00:04:34,430 So the support vector machine doesn't do too well. 42 00:04:37,500 --> 00:04:39,660 The next step is to try the random forest. 43 00:04:45,230 --> 00:04:48,890 So this does pretty well, it seems to be on par with linear regression. 44 00:04:51,920 --> 00:04:54,810 The next step is to look at the multi output forecast. 45 00:04:55,490 --> 00:04:58,150 So, again, there's nothing really different about this function. 46 00:05:03,050 --> 00:05:07,520 Now, recall that the support vector machine does not support having multiple outputs. 47 00:05:08,360 --> 00:05:14,100 However, this does not stop us from simply creating our own SVM that can handle multiple outputs. 48 00:05:14,540 --> 00:05:19,340 It simply means we're going to create a separate support vector machine, one for each time step of 49 00:05:19,340 --> 00:05:20,270 the forecast. 50 00:05:24,010 --> 00:05:30,100 So here you can see I've created my own class called SVR wrapper in the constructor, we take in the 51 00:05:30,100 --> 00:05:37,420 forecast horizon and generic keyword arguments, which will be passed on to the SVR constructor inside 52 00:05:37,420 --> 00:05:38,250 the constructor. 53 00:05:38,260 --> 00:05:44,740 We simply save the forecast horizon and we instantiate multiple SVR objects, one for each time step 54 00:05:45,850 --> 00:05:47,200 inside the fit function. 55 00:05:47,230 --> 00:05:51,490 We simply call fit for each SVR, for each column of the target matrix. 56 00:05:51,970 --> 00:05:57,060 Inside the predicts function, we simply call predict for each SVR and then stack the result. 57 00:05:57,730 --> 00:05:59,230 Notice that we use each stack. 58 00:05:59,230 --> 00:06:05,710 Since each output is an end length vector, the result will be a new array of size n by the forecast 59 00:06:05,710 --> 00:06:06,370 horizon. 60 00:06:11,520 --> 00:06:15,600 OK, so in the next block, we're going to test our custom SVR rapper. 61 00:06:19,870 --> 00:06:22,190 Notice how it still does not perform too well. 62 00:06:22,570 --> 00:06:27,700 It seems like this is simply not a good model for this Time series, but note that you can still tune 63 00:06:27,700 --> 00:06:28,780 the hyper parameters. 64 00:06:35,620 --> 00:06:42,040 OK, so we see that the random forest does very well notice how much better it performs when we do different 65 00:06:42,040 --> 00:06:42,370 saying.