1 00:00:11,540 --> 00:00:17,030 In this lecture I want to discuss some other ways you might generate multi-step forecasts. 2 00:00:17,030 --> 00:00:22,100 You may have noticed that the two forecasting methods we used in this section demonstrated some pretty 3 00:00:22,100 --> 00:00:23,770 extreme results. 4 00:00:23,810 --> 00:00:29,960 On one hand we saw that once that forecast can seem artificially good especially when all they do is 5 00:00:29,960 --> 00:00:32,680 just predict the last value or close to it. 6 00:00:32,750 --> 00:00:38,120 On the other hand doing a multi-step forecast iteratively using the models own predictions can lead 7 00:00:38,120 --> 00:00:42,050 to poor results even on simple problems like the sine wave. 8 00:00:42,050 --> 00:00:47,840 Even a nearly perfect sine wave model eventually breaks down due to the build up of numerical position 9 00:00:47,840 --> 00:00:48,410 errors 10 00:00:53,510 --> 00:00:54,230 at this point. 11 00:00:54,230 --> 00:00:57,260 One issue we have to think about is practicality. 12 00:00:57,260 --> 00:01:01,310 In fact it's not necessarily wrong to predict only one step ahead. 13 00:01:01,340 --> 00:01:06,740 It's certainly wrong when you want to make a conclusion such as Wow look how good my model is at predicting 14 00:01:06,740 --> 00:01:08,060 future values. 15 00:01:08,090 --> 00:01:13,520 Of course that doesn't make any sense because you used future values to predict the future values. 16 00:01:13,520 --> 00:01:19,220 In some cases it may make sense to only want a prediction for one time step ahead. 17 00:01:19,220 --> 00:01:22,190 In other cases it may not make sense. 18 00:01:22,220 --> 00:01:27,800 For example if you want to forecast weekly or monthly sales for the next year it doesn't make sense 19 00:01:27,800 --> 00:01:30,950 to only do a one step forecast. 20 00:01:30,950 --> 00:01:34,910 On the other hand maybe you just want to predict the load on your website for tomorrow. 21 00:01:35,030 --> 00:01:38,690 So you know how many Amazon machine instances to spin up. 22 00:01:38,810 --> 00:01:44,060 Either way the method you use is highly dependent on context and the real world constraints of your 23 00:01:44,060 --> 00:01:49,750 problem. 24 00:01:49,750 --> 00:01:54,180 It's also important to benchmark your predictions against a baseline model. 25 00:01:54,310 --> 00:01:59,500 The reason you want to do this is well what if your complicated model performs worse than your baseline 26 00:01:59,500 --> 00:02:00,610 model. 27 00:02:00,610 --> 00:02:05,350 If that happens then you should just use your baseline model as you'll see. 28 00:02:05,360 --> 00:02:11,180 Sometimes you can even prove mathematically that your baseline model is better than your complex model. 29 00:02:11,210 --> 00:02:17,270 One way to establish a baseline is to use what is called a naive forecast a naive forecast does the 30 00:02:17,270 --> 00:02:18,660 dumbest thing possible. 31 00:02:18,710 --> 00:02:22,410 You guessed it it just predicts the last value of the time series. 32 00:02:22,460 --> 00:02:25,430 It's a model with zero parameters. 33 00:02:25,580 --> 00:02:30,950 One interesting fact you will learn about if you ever study finance is that stock prices very closely 34 00:02:30,950 --> 00:02:34,360 follow A Random Walk Model in a random walk model. 35 00:02:34,360 --> 00:02:38,000 A naive forecast is in fact the best forecasts you can make. 36 00:02:38,060 --> 00:02:43,550 So by definition if your time series follows a random walk it doesn't matter how complex your model 37 00:02:43,550 --> 00:02:43,970 is. 38 00:02:44,060 --> 00:02:46,010 You cannot beat a naive forecast 39 00:02:51,200 --> 00:02:56,840 in time series literature classic statistical models such as Auriemma use algorithms that predicts only 40 00:02:56,840 --> 00:03:02,660 one step ahead and then use the iterative method we discussed previously in order to do multi-step forecasts 41 00:03:02,690 --> 00:03:04,290 into the future. 42 00:03:04,310 --> 00:03:09,470 One interesting question to ask is Are there any models that naturally predict multiple steps into the 43 00:03:09,470 --> 00:03:10,490 future. 44 00:03:10,490 --> 00:03:13,690 The answer is yes and we can do so quite trivially. 45 00:03:13,850 --> 00:03:18,650 As you know it's very easy to specify the number of outputs in your neural network model. 46 00:03:18,860 --> 00:03:23,590 You're just passing a number into the dense layer for the number of outputs you want. 47 00:03:23,600 --> 00:03:28,100 So what if you want a model that predicts 12 time steps ahead simultaneously. 48 00:03:28,100 --> 00:03:30,140 In fact that's entirely possible. 49 00:03:30,170 --> 00:03:32,930 Just make a neural network with twelve outputs. 50 00:03:32,930 --> 00:03:37,790 Then as the target you'll use the true values for the next twelve timestamps. 51 00:03:37,850 --> 00:03:42,530 So whereas in this course the target just had one value for a multi head model. 52 00:03:42,530 --> 00:03:44,620 You'll have a target with 12 values. 53 00:03:44,840 --> 00:03:49,130 If you're interested in this kind of thing you might want to give this a try as an exercise 54 00:03:54,300 --> 00:03:59,370 to summarize this lecture what we wanted to do was clarify the difference between the different kinds 55 00:03:59,370 --> 00:04:00,710 of forecasts. 56 00:04:00,750 --> 00:04:06,210 The big mistake a lot of people make is they pretend they are predicting the future when in actuality 57 00:04:06,240 --> 00:04:08,610 they are only predicting one step ahead. 58 00:04:08,640 --> 00:04:14,480 It's not wrong to predict only one step ahead but you must be clear about the results you are presenting. 59 00:04:14,520 --> 00:04:19,530 If you really want to forecast multiple steps into the future then you are not allowed to use data from 60 00:04:19,530 --> 00:04:20,800 the future. 61 00:04:20,820 --> 00:04:26,190 Of course there are some cases where you actually want to make one step forecasts only. 62 00:04:26,190 --> 00:04:31,920 This is dependent on the specifics of your company and your data only you know that and you must design 63 00:04:31,920 --> 00:04:34,560 your model accordingly. 64 00:04:34,570 --> 00:04:39,820 We also discussed the importance of establishing a baseline which in time series analysis is often the 65 00:04:39,820 --> 00:04:46,900 naive forecast where all we do is predict the previous value of the series I mentioned that ran a Walk 66 00:04:46,900 --> 00:04:53,380 Model which often very closely models stock prices a naive forecast is in the best forecast. 67 00:04:53,380 --> 00:04:58,690 In addition we saw that aside from building a one step model and then iteratively applying it to predict 68 00:04:58,690 --> 00:05:05,490 multiple steps into the future there is an easy modification we can simply use a neuron that with multiple 69 00:05:05,520 --> 00:05:09,540 output nodes representing the multiple steps in the future that we want to predict.