WEBVTT 00:01.020 --> 00:06.360 In the last video she worked with rolling such as Six and all of our calculations were based on fixed 00:06.360 --> 00:08.350 size rolling windows. 00:08.400 --> 00:16.200 So for instance when we calculated the simple moving average 50 for the S&P 500 at each point in time 00:16.230 --> 00:21.140 we included the last 50 observations and to our mean calculations. 00:21.150 --> 00:26.760 So the last 50 observations does not necessarily mean the last 50 calendar days. 00:26.880 --> 00:32.910 And as you might know in finance we typically have no trading prices on bank holidays and weekends and 00:32.910 --> 00:39.120 therefore having a fixed size window of 50 means that we are probably looking back more than 50 calendar 00:39.120 --> 00:44.790 days to get the last 50 observations and the last the 50 year trading prices. 00:44.850 --> 00:51.870 So let's have a look in an example and we are still imported the Apple Boeing data frame and let's have 00:51.870 --> 01:01.010 a look at the first seven rows so you may have to stock prices for Apple and Boeing starting with the 01:01.040 --> 01:07.970 thirty first of December 2009 and already here we can see that we have not on each and every calendar 01:07.970 --> 01:10.100 day a trading price. 01:10.100 --> 01:16.400 We have no trading price on the first of January because this is a bank holiday and we also have no 01:16.400 --> 01:24.530 trading prices on the 2nd and 3rd of January because these this Saturday and Sunday and the next trading 01:24.530 --> 01:32.560 price we can observe on the 4th of January and then also here the 9th and the 10th of January. 01:32.700 --> 01:35.990 Also again Saturday and Sunday. 01:35.990 --> 01:41.300 And let's assume that you want to calculate the simple moving average with a window of 3. 01:41.390 --> 01:47.320 Then we can pass uh the integer 3 to the window parameter and we change the mean method. 01:47.330 --> 01:48.260 So let's have a look here. 01:50.550 --> 01:55.410 So it's no surprise that on the first two timestamps we have any invalid use. 01:55.410 --> 02:01.860 And then starting with the third timestamp we actually F on each timestamp the mean stock price for 02:01.860 --> 02:05.780 these three immediately preceding observations. 02:05.850 --> 02:13.520 So he on the 5th of January we have the stock prices on the thirty first the 4th and the 5th and if 02:13.530 --> 02:13.740 year. 02:13.740 --> 02:16.850 The average actually saw pennies simply takes a year. 02:16.860 --> 02:23.220 The last the three observations and obviously this does not mean that these are the last three calendar 02:23.220 --> 02:29.160 days and actually penned US ignores at the time increments between those observations. 02:29.160 --> 02:30.550 So here we are four days. 02:30.570 --> 02:32.210 And here we have only one day. 02:32.250 --> 02:39.030 However we can change this behavior by passing a fixed size time offset rather than a fixed number of 02:39.030 --> 02:41.520 observations through the window parameter. 02:41.880 --> 02:49.340 So let's again have a look at the first seven observations and let's assume that you want to calculate 02:49.370 --> 02:56.560 the simple moving average of the last three calendar days and instead of passing near the end that uh 02:56.630 --> 03:04.840 three to the windows per meter is simply passing a fixed time offset and we can do this as a string. 03:04.840 --> 03:06.980 So here we have uh three days. 03:06.980 --> 03:08.710 So this is actually nothing new 03:14.270 --> 03:20.450 and that our very first glance we can see here that uh we do not get any any end values at the beginning 03:20.750 --> 03:24.490 and therefore it might be a good idea to have a look at the documentation. 03:24.500 --> 03:25.660 So let's have a look here. 03:29.160 --> 03:31.640 So here we have the window perimeter. 03:32.030 --> 03:34.740 And here we can define the size of the moving window. 03:34.740 --> 03:39.930 And this is the number of observations used for calculating these statistics. 03:39.930 --> 03:42.890 And each window will be a fixed size. 03:42.900 --> 03:51.080 So this is here the above example we FCA a fixed sized window of three and now comes our new example. 03:51.350 --> 03:57.890 If it's an offset so here three days then this will be the time period of each window and each window 03:57.890 --> 04:03.140 will be a variable size based on the observations included in the time period. 04:03.230 --> 04:06.590 And that's also if I look at the parameter Min periods. 04:06.740 --> 04:11.780 So this is the minimum number of observations and window required to have a value. 04:12.140 --> 04:17.840 And otherwise the result is an A and for a window that is specified by an offset. 04:17.840 --> 04:22.980 So this is our new example here than men periods will default to 1. 04:23.210 --> 04:27.920 Otherwise that means we have a sick fixed sized window of three. 04:28.220 --> 04:33.110 So otherwise men period will default to the size of the window. 04:33.110 --> 04:38.290 So if you pass the fixed size then the main period is by default. 04:38.390 --> 04:44.760 The same as our window here three and therefore we get here at the very first two time stamps and they 04:44.770 --> 04:51.900 end values and by passing a time offset the mean periods parameter the default value is 1. 04:52.010 --> 04:58.570 So on each of the timestamps here we have at least the one value and the last the three calendar days 04:58.580 --> 05:01.790 and therefore we do not have you any missing values. 05:01.940 --> 05:09.090 And of course we could also change this and pass uh also here maybe a three to the min periods per metre 05:09.110 --> 05:09.920 so let's say this 05:15.310 --> 05:23.750 and let's have a look and if we can see that we have a lot of any end values and intuitively we actually 05:23.750 --> 05:29.150 only get on the weekdays uh Wednesday Thursday and Friday. 05:29.170 --> 05:36.350 Well use here because only on these days are the days themselves and the immediately two preceding days 05:36.400 --> 05:44.650 uh weekdays and this is actually quite uncomfortable because we have fear many missing values and uh 05:44.690 --> 05:50.190 therefore pen associate quite clever by changing the default parameter to a one period. 05:50.190 --> 05:58.830 If we are working here with time offsets so working with a fixed size time offset is an additional alternative 05:59.130 --> 06:05.220 how to work with uh rolling statistics and in particular this makes a lot of sense when we are working 06:05.220 --> 06:08.100 with irregular times series. 06:08.370 --> 06:12.900 So we are finishing with this video and I hope to see you also in the next one by.