1 00:00:11,050 --> 00:00:15,970 In this lecture, we are going to apply the whole winter's exponential smoothing model in code. 2 00:00:16,510 --> 00:00:22,120 This is our final model for this group of models, the culmination of our study of exponential smoothing. 3 00:00:23,230 --> 00:00:28,420 This lecture is going to walk you through a prepared CoLab notebook, although a very good exercise, 4 00:00:28,420 --> 00:00:34,090 which I always recommend is once you know how this is done, to try and recreate it yourself with as 5 00:00:34,090 --> 00:00:35,660 few references as possible. 6 00:00:36,190 --> 00:00:41,890 As always, you can check the lectures, how to code by yourself and how to practice for a more in-depth 7 00:00:41,890 --> 00:00:42,660 discussion. 8 00:00:43,120 --> 00:00:48,460 If there's anything in this lecture you didn't understand or you think I missed a step or didn't explain 9 00:00:48,460 --> 00:00:51,690 why we were doing something, please use the Q&A to inquire. 10 00:00:52,300 --> 00:00:57,310 As usual, you can look at the title of the notebook to determine what notebook we are currently looking 11 00:00:57,310 --> 00:00:57,640 at. 12 00:00:58,990 --> 00:01:01,930 Let's start by importing the exponential smoothing class. 13 00:01:05,460 --> 00:01:07,960 Next, we're going to create an instance of our model. 14 00:01:08,610 --> 00:01:13,290 This time we're not going to bother fitting a model to the entire data set, but rather we're going 15 00:01:13,290 --> 00:01:15,330 to skip right away to the train to split. 16 00:01:16,910 --> 00:01:22,880 So the first variation we're going to try is the additive trend and additive seasonality, we set the 17 00:01:22,880 --> 00:01:28,580 seasonal periods, the 12, since we know that the data cycles yearly and the frequency of the data 18 00:01:28,580 --> 00:01:29,390 is monthly. 19 00:01:30,290 --> 00:01:32,030 Next, we call the fit function. 20 00:01:33,530 --> 00:01:34,550 So let's run this. 21 00:01:38,570 --> 00:01:43,940 Next, we assign the fitted values to the whole Winters' column of our original data frame for the train 22 00:01:43,940 --> 00:01:44,540 rose. 23 00:01:47,790 --> 00:01:53,250 Next, we call the forecast function for and test the steps in a sign the results to our original data 24 00:01:53,250 --> 00:01:55,080 frame for the test rose. 25 00:01:58,800 --> 00:02:02,550 Next, we plot the whole winter's column along with the original data set. 26 00:02:08,660 --> 00:02:14,840 So this is very encouraging, unlike the simple exponential smoothing model and the whole linear trend 27 00:02:14,840 --> 00:02:15,240 model. 28 00:02:15,560 --> 00:02:22,100 This model fits very well for both a train and test notice, importantly, that the predictions are 29 00:02:22,100 --> 00:02:24,320 not lagging behind the Time series. 30 00:02:24,710 --> 00:02:29,810 So hopefully now you are convinced that it is not correct to shift it backwards by one step. 31 00:02:30,020 --> 00:02:34,750 And in fact, the lagging is only due to model mis specification. 32 00:02:35,300 --> 00:02:37,100 Remember that you have to be consistent. 33 00:02:37,400 --> 00:02:40,850 If you shift back for one model, you have to shift back for all of them. 34 00:02:41,330 --> 00:02:46,220 And for this model, that would be very silly because then the predictions would be ahead of the data, 35 00:02:46,340 --> 00:02:47,750 which doesn't make any sense. 36 00:02:52,150 --> 00:02:57,760 Now that we know our model fits decently well, it would be a good idea to calculate some metrics. 37 00:02:58,270 --> 00:03:03,450 Although there are many metrics which are used in time series analysis, the root mean squared error, 38 00:03:03,490 --> 00:03:04,870 we'll be just fine for us. 39 00:03:05,440 --> 00:03:10,570 This metric makes more sense, in my opinion, than something like the absolute error, because these 40 00:03:10,570 --> 00:03:13,370 models actually minimize the squared error directly. 41 00:03:13,900 --> 00:03:18,700 Therefore, it would make less sense to check the absolute error because we didn't optimize for that 42 00:03:18,700 --> 00:03:19,820 in the first place. 43 00:03:20,500 --> 00:03:24,340 If you're going to check the absolute error, then you may as well make the absolute error. 44 00:03:24,340 --> 00:03:26,890 Your lost function in the root mean square. 45 00:03:26,890 --> 00:03:32,230 There is just the square root of the square there, which puts it on the same scale as the original 46 00:03:32,230 --> 00:03:32,690 data. 47 00:03:33,130 --> 00:03:38,690 So minimizing the mean squared error is equivalent to minimizing the root mean squared error. 48 00:03:39,370 --> 00:03:40,710 So here's how we calculate it. 49 00:03:41,230 --> 00:03:46,930 We take why the predictions and t the targets, although it doesn't really matter which is which and 50 00:03:46,930 --> 00:03:48,120 then we subtract them. 51 00:03:48,730 --> 00:03:50,790 This does an element y subtraction. 52 00:03:51,490 --> 00:03:53,050 Next we square the result. 53 00:03:53,530 --> 00:03:55,850 This is also an element y's operation. 54 00:03:57,310 --> 00:03:58,580 Next we call the mean. 55 00:03:58,600 --> 00:04:00,760 So now we have the mean squared error. 56 00:04:01,510 --> 00:04:05,530 Finally we take the square root so we get the root mean squared error or. 57 00:04:08,050 --> 00:04:12,540 Now, just out of curiosity, I would also like to calculate the mean absolute error. 58 00:04:12,970 --> 00:04:14,730 This calculation is a little simpler. 59 00:04:15,220 --> 00:04:20,880 We just take the difference between why and t take the absolute value and then take the mean, hence 60 00:04:20,890 --> 00:04:22,480 mean absolute error. 61 00:04:27,850 --> 00:04:34,060 Next, we check the RNC on both the train and test set, as you recall, the train predictions are stored 62 00:04:34,060 --> 00:04:39,010 in the fitted values attribute and the test predictions are made using the forecast function. 63 00:04:40,060 --> 00:04:44,740 As you can see, I've already switched around, which is the prediction and which is the target, since 64 00:04:44,740 --> 00:04:49,120 it doesn't really matter, which is why and which is t you will get the same answer either way. 65 00:04:53,790 --> 00:04:59,070 All right, so the train pharmacy is about 11 something and the test pharmacy is about 17. 66 00:05:04,430 --> 00:05:10,010 When we checked the mean absolute air, we get about nine something for train and 13 something for test. 67 00:05:13,580 --> 00:05:17,960 Next, we're going to try the whole Winters' model again, but with different parameters. 68 00:05:18,590 --> 00:05:24,220 Recall that it seems that the amplitude of the cycle increases with the level of the Time series. 69 00:05:24,770 --> 00:05:28,310 This suggests that a multiplicative model may fit better. 70 00:05:28,910 --> 00:05:34,140 So for this model, we're going to have an additive trend and a multiplicative seasonality. 71 00:05:34,730 --> 00:05:40,040 Again, we call it a sign the trend predictions and the test predictions to the data frame and then 72 00:05:40,040 --> 00:05:40,870 plot the result. 73 00:05:42,390 --> 00:05:47,540 So we're just doing it all in one step, since you already know how each of these steps works. 74 00:05:53,370 --> 00:05:59,200 So from my perspective, at least, this model appears to fit better than the purely additive model. 75 00:05:59,670 --> 00:06:01,740 But let's check our accuracy metrics. 76 00:06:08,750 --> 00:06:13,850 So when we check the pharmacy, we get about nine something for the train set and about 15 something 77 00:06:13,850 --> 00:06:14,420 for the tests. 78 00:06:15,230 --> 00:06:20,290 This gives us a better trainer and a better test there compared to the purely additive model. 79 00:06:20,960 --> 00:06:22,940 Therefore, we would prefer this model. 80 00:06:27,720 --> 00:06:33,780 If we check the mean absolute air, we see the same thing, both the trainer and the tester have improved. 81 00:06:37,880 --> 00:06:43,910 Next, let's try Hault Winters again, but with the multiplicative trend and the multiplicative seasonality, 82 00:06:44,480 --> 00:06:49,080 this kind of makes sense because the trend in the Time series is not exactly a straight line. 83 00:06:49,640 --> 00:06:52,560 The growth actually seems to be accelerating over time. 84 00:06:53,180 --> 00:06:57,550 Again, we call it a sign the predictions to our data frame and plot the result. 85 00:07:03,620 --> 00:07:09,080 It's difficult to tell whether this is a better or worse fate, so let's check our accuracy metrics. 86 00:07:14,010 --> 00:07:19,770 All right, so here we see an interesting pattern, the train arm is about nine something and the test 87 00:07:19,770 --> 00:07:22,300 arm AC is about twenty five something. 88 00:07:22,770 --> 00:07:26,510 So the trainer is better, but the test error is much worse. 89 00:07:30,590 --> 00:07:35,930 We see the same thing for the mean absolute error, the train error has gone down, but the test there 90 00:07:35,930 --> 00:07:38,150 has gone up to about 20 something. 91 00:07:38,750 --> 00:07:44,540 Therefore, while this Time series may look like a multiplicative model is a better fit, it actually 92 00:07:44,540 --> 00:07:47,810 overfit to the training data and we get a worse result.