1 00:00:11,050 --> 00:00:17,280 In this lecture, we are going to come back to the Akef in the pickoff and apply them to stock returns. 2 00:00:17,830 --> 00:00:20,750 So why are we doing this now in this kind of weird order? 3 00:00:21,220 --> 00:00:24,520 Now, you might at first think these lectures are totally disorganised. 4 00:00:24,970 --> 00:00:27,320 Why are the Arima coding lectures all split up? 5 00:00:28,000 --> 00:00:34,300 Why do we look at the HCF in the pickoff so many lectures ago only to return to them now for stock returns? 6 00:00:34,840 --> 00:00:36,720 Well, there is a method to the madness. 7 00:00:37,180 --> 00:00:40,150 I think it's important to start with the most obvious approach. 8 00:00:40,150 --> 00:00:46,630 First, in the case of a Arima, the most obvious approach, if you have the choice between Otto Arima 9 00:00:46,630 --> 00:00:50,280 and the old school methods, I think most of you would choose Otto Auriemma. 10 00:00:50,770 --> 00:00:56,790 And yet we've seen that Otto Arima does not always give us what we might consider to be the best model. 11 00:00:57,340 --> 00:01:01,120 That is when we disagree with the AKG information criteria. 12 00:01:01,840 --> 00:01:07,720 So the goal of this lecture is to take a step back and consider what would we do if Otto Arima didn't 13 00:01:07,720 --> 00:01:08,440 exist? 14 00:01:10,650 --> 00:01:14,640 OK, so let's start by downloading our S&P 500 at CSFI. 15 00:01:17,330 --> 00:01:23,180 Next, let's import our usual library's pandas dumping matplotlib plot AKF and apply. 16 00:01:27,460 --> 00:01:31,540 Next, let's bring in our Naqvi using a read CSFI. 17 00:01:34,580 --> 00:01:37,430 Next, let's filter out all of Google's clothes prices. 18 00:01:40,610 --> 00:01:46,640 Next, let's write a helper function to calculate the log return of a series, so as input, we're going 19 00:01:46,640 --> 00:01:48,440 to take in a series called Price. 20 00:01:49,220 --> 00:01:53,000 Next, we'll calculate the log price by taking the log of the price. 21 00:01:53,750 --> 00:01:59,210 Next, we call the function to take the first difference over the log price, which is the log return. 22 00:02:01,930 --> 00:02:07,420 OK, so you might be wondering why are we taking the log return, why is this what we care about? 23 00:02:08,260 --> 00:02:13,510 Well, you may have forgotten by this point, but remember that when we apply the AMA model of a Arima, 24 00:02:13,660 --> 00:02:17,860 we want that signal to be stationary and our stationary lectures. 25 00:02:17,860 --> 00:02:23,380 We already established that taking the first difference over the log prices, i.e. the log returns, 26 00:02:23,680 --> 00:02:25,220 yields a stationary signal. 27 00:02:25,960 --> 00:02:30,700 Of course, you could do the test again in this script, but I'll leave that to you as an exercise. 28 00:02:33,020 --> 00:02:37,790 Next will apply a function to calculate the log return on Google stock prices. 29 00:02:40,700 --> 00:02:45,320 Max, let's do a deep dive head to make sure our data frame contains the right thing. 30 00:02:47,330 --> 00:02:48,590 Hey, and it does. 31 00:02:51,740 --> 00:02:55,250 Next, let's plot the chief of Google's log returns. 32 00:02:55,850 --> 00:02:59,660 Remember, this is for choosing the order of the auto regressive model. 33 00:03:06,140 --> 00:03:07,490 OK, so what do we see? 34 00:03:08,120 --> 00:03:12,990 Well, pretty much that there is no autocorrelation for any order greater than zero. 35 00:03:13,580 --> 00:03:18,820 We see a couple values just slightly outside the confidence bounds, but these are likely due to chance, 36 00:03:19,400 --> 00:03:23,330 as you recall, even idee noise can lead to the same plot. 37 00:03:24,260 --> 00:03:28,520 OK, so according to the pickoff, we would choose P equals zero. 38 00:03:33,040 --> 00:03:36,340 Next, let's check out the auto correlation or the Assif. 39 00:03:41,370 --> 00:03:47,470 So this looks pretty much the same as the scarf, in other words, we would choose Q equals zero also. 40 00:03:48,090 --> 00:03:55,560 So what can we conclude if we use the offensive method to choose our Arima orders, we would choose 41 00:03:55,560 --> 00:03:57,260 Arima zero one zero. 42 00:03:57,870 --> 00:03:59,610 What is Arima zero one zero? 43 00:04:00,060 --> 00:04:01,650 Well, that is a random walk. 44 00:04:04,860 --> 00:04:06,940 OK, so maybe that was just a fluke. 45 00:04:07,230 --> 00:04:09,450 Let's now try Apple's stock price instead. 46 00:04:10,230 --> 00:04:10,590 All right. 47 00:04:10,590 --> 00:04:12,450 So this is all the same code as before. 48 00:04:12,600 --> 00:04:14,880 Let's filter out Apple's close price. 49 00:04:18,180 --> 00:04:20,540 Next, let's calculate Apple's log returns. 50 00:04:24,100 --> 00:04:26,530 Next, let's look at the picks for Apple. 51 00:04:30,780 --> 00:04:34,960 OK, so what do we see again, pretty much the same picture. 52 00:04:35,430 --> 00:04:41,010 There are really no significant values and therefore we would choose P equals zero. 53 00:04:45,900 --> 00:04:47,940 OK, so what about the akef? 54 00:04:52,220 --> 00:04:59,510 Again, this looks pretty much exactly like the Earth, so we choose Q equals zero, so what do we conclude? 55 00:05:00,080 --> 00:05:06,210 If we go by the Akef method, we would conclude that Apple's stock price follows a random walk. 56 00:05:11,150 --> 00:05:14,210 OK, let's try again, this time with the IBM. 57 00:05:17,030 --> 00:05:18,940 All right, so here's the akef. 58 00:05:20,820 --> 00:05:24,660 And again, we see the same pattern we choose P equals zero. 59 00:05:27,160 --> 00:05:28,420 How about the Assif? 60 00:05:32,090 --> 00:05:35,160 Again, the same pattern we choose Q equals zero. 61 00:05:36,290 --> 00:05:42,680 Notice how closely the ATF and the ATF tracked each other for all the plots we've looked at, consider 62 00:05:42,680 --> 00:05:44,050 why this might be the case. 63 00:05:44,570 --> 00:05:48,700 It should make sense when you think about the formula for calculating the ATF. 64 00:05:49,580 --> 00:05:53,010 In any case, for IBM is pretty much the same situation. 65 00:05:53,030 --> 00:05:57,320 We choose a zero one zero or in other words, we choose random walk. 66 00:06:01,280 --> 00:06:05,030 OK, so let's try this one more time, this time for Starbucks. 67 00:06:07,920 --> 00:06:09,740 All right, so here's the pickoff. 68 00:06:13,680 --> 00:06:18,750 Now, notice for Starbucks, there's kind of a non-zero value at like three, but I would consider this 69 00:06:18,750 --> 00:06:21,340 pretty unlikely to be actually significant. 70 00:06:22,350 --> 00:06:25,020 I would be comfortable saying that P is equal to zero. 71 00:06:28,120 --> 00:06:29,590 How about for the Akef? 72 00:06:32,370 --> 00:06:34,340 Again, it looks just like the picture. 73 00:06:34,500 --> 00:06:36,630 So let's say Q is equal to zero. 74 00:06:38,360 --> 00:06:45,020 All right, so for every stock we looked at in this lecture, if we use the AKF PKF method of choosing 75 00:06:45,020 --> 00:06:49,170 Arima orders, we would choose a rhema zero one zero every time. 76 00:06:49,760 --> 00:06:55,940 In other words, the Randhawa is actually a pretty nice fitting parsimonious model for stock prices.