1 00:00:11,070 --> 00:00:16,680 In this lecture, we are going to discuss a very simple technique and time series analysis called the 2 00:00:16,680 --> 00:00:18,060 simple moving average. 3 00:00:18,540 --> 00:00:19,740 The way it works is this. 4 00:00:20,160 --> 00:00:24,690 We start with a time series, then suppose we have some fixed length window. 5 00:00:25,230 --> 00:00:31,140 Then at each point in the Time series, we drag the window along and we calculate the sample mean of 6 00:00:31,140 --> 00:00:32,550 all the points in that window. 7 00:00:33,030 --> 00:00:34,850 This is the simple moving average. 8 00:00:35,280 --> 00:00:36,270 Let's do an example. 9 00:00:41,100 --> 00:00:47,370 Suppose we have the numbers to zero eight three six one one six five five and let's say a window is 10 00:00:47,370 --> 00:00:48,380 of size three. 11 00:00:48,900 --> 00:00:51,450 So let's try to calculate the simple moving average. 12 00:00:52,020 --> 00:00:57,110 The first value is going to be the average of two zero and eight, which is three point thirty three. 13 00:00:57,810 --> 00:01:03,140 The second value is going to be the average of zero eight and three, which is three point sixty seven. 14 00:01:03,810 --> 00:01:08,980 The third value is going to be the average of eight, three and six, which is five point six seven. 15 00:01:09,600 --> 00:01:14,160 I would encourage you to try and calculate the rest of the values yourself in case you want a better 16 00:01:14,160 --> 00:01:15,900 understanding of how this is done. 17 00:01:16,830 --> 00:01:22,170 Note that we cannot fill in the first two values, since by definition we don't have three values in 18 00:01:22,170 --> 00:01:23,700 which to calculate an average. 19 00:01:24,210 --> 00:01:29,700 Therefore, this works like the financial return where we leave the values we can calculate as an. 20 00:01:34,810 --> 00:01:40,030 So what is the purpose of the simple moving average, although it might seem extremely simple, it can 21 00:01:40,030 --> 00:01:41,290 actually be quite useful. 22 00:01:41,800 --> 00:01:45,730 For example, suppose that we need to calculate the mean and variance of a stock. 23 00:01:46,120 --> 00:01:49,670 We might use these values to characterise that stock's distribution. 24 00:01:50,620 --> 00:01:53,650 Well, we know that stock returns exhibit volatility clustering. 25 00:01:53,800 --> 00:01:55,350 So we have at two options. 26 00:01:55,780 --> 00:02:01,120 One, we can use all the values in our data set to calculate the mean and variance, or we can just 27 00:02:01,120 --> 00:02:04,460 use the most recent values specified by the window size. 28 00:02:04,960 --> 00:02:10,450 This might give us a better estimate, since probably the return at six months ago or six years ago 29 00:02:10,450 --> 00:02:12,540 might not be relevant for the return today. 30 00:02:13,150 --> 00:02:16,940 Therefore, a moving average might be more useful than an overall average. 31 00:02:17,890 --> 00:02:23,710 In addition, learning the basic calculation behind the simple moving average also sets us up to learn 32 00:02:23,710 --> 00:02:28,300 about the exponentially weighted moving average, which then sets us up to learn a more complicated 33 00:02:28,300 --> 00:02:30,110 at times series forecasting methods. 34 00:02:30,520 --> 00:02:34,870 So think of this as a stepping stone to the more advanced methods in the section. 35 00:02:39,550 --> 00:02:44,980 Let's not discuss how the simple moving average will look in code for this, it's convenient to use 36 00:02:44,980 --> 00:02:46,860 pandas in pandas. 37 00:02:46,870 --> 00:02:52,280 We use the rolling function to specify that we want to do some calculation on a rolling window. 38 00:02:52,810 --> 00:02:55,460 The input argument to this is the window size. 39 00:02:56,110 --> 00:03:00,730 Note that this doesn't return the simple moving average right away, since there are actually multiple 40 00:03:00,730 --> 00:03:03,560 things you might want to calculate from the rolling window. 41 00:03:03,970 --> 00:03:07,840 In fact, this just returns that rolling window itself in pandas. 42 00:03:07,850 --> 00:03:11,880 This is a rolling object from the rolling window return value. 43 00:03:12,130 --> 00:03:17,470 We can calculate different kinds of statistics, such as the sum of the mean, the min, the max, the 44 00:03:17,470 --> 00:03:18,840 variance and so forth. 45 00:03:19,780 --> 00:03:25,030 If you have a rolling window of multiple columns, you can also calculate multi-dimensional statistics 46 00:03:25,210 --> 00:03:27,490 such as the covariance and correlation. 47 00:03:28,120 --> 00:03:31,630 In the next lecture, we will apply this code to actual data.