1 00:00:10,510 --> 00:00:17,380 So in this lecture, we are going to start with answering a very basic question What is a Time series? 2 00:00:17,560 --> 00:00:20,920 Now you may have some intuition about what a Time series is. 3 00:00:20,920 --> 00:00:24,250 For example, the price of a stock or readings from an EKG. 4 00:00:24,820 --> 00:00:30,190 The weather is at other simple, everyday example of a time series that everyone can recognize. 5 00:00:30,340 --> 00:00:33,610 So it's clear that time series data is all around us. 6 00:00:33,610 --> 00:00:37,930 You don't need to be a data scientist to understand intuitively what a Time series is. 7 00:00:42,480 --> 00:00:46,140 But for the purpose of this class, we're going to get a bit more specific. 8 00:00:46,320 --> 00:00:49,590 Let's talk about some things we will not discuss in this class. 9 00:00:50,010 --> 00:00:52,170 One thing we won't discuss is sequence data. 10 00:00:52,170 --> 00:00:58,170 In general, time series data is one kind of sequence data, but sequence data encompasses more than 11 00:00:58,170 --> 00:00:59,340 just time series. 12 00:01:00,000 --> 00:01:04,950 For example, the sentences I'm speaking right now are sequences of words. 13 00:01:04,980 --> 00:01:08,670 We have techniques for dealing with sequences of words from the field of NLP. 14 00:01:09,630 --> 00:01:12,440 Another similar example is genomics data. 15 00:01:12,450 --> 00:01:19,560 You and I are made up of sequences the letters C and G, which represent special molecules or sequences 16 00:01:19,560 --> 00:01:22,920 which are kind of like computer programs for living things. 17 00:01:23,160 --> 00:01:29,520 So the difference between this class and these examples is that these examples are categorical words, 18 00:01:29,520 --> 00:01:34,860 and molecules are not numerical objects, although they form sequences just like a time series. 19 00:01:36,020 --> 00:01:39,770 In this class, A Time series consists of real valued observations. 20 00:01:40,190 --> 00:01:45,290 Now, one side note to keep in mind, though, is that many of the techniques in this course can be 21 00:01:45,290 --> 00:01:47,540 applied to categorical sequences as well. 22 00:01:51,960 --> 00:01:55,770 So here's another example of something we will not cover in this class. 23 00:01:55,890 --> 00:02:00,150 So suppose you have an Apple Watch and every now and then you check your heart rate. 24 00:02:00,690 --> 00:02:05,490 Now, let's say you keep these in some kind of Excel spreadsheet, but you're not very consistent. 25 00:02:05,520 --> 00:02:10,290 So you might have three recordings this week, two recordings the previous week and so forth. 26 00:02:10,410 --> 00:02:13,740 Furthermore, these readings are never taken at the same time. 27 00:02:13,950 --> 00:02:18,480 In other words, these recordings take place at irregularly spaced intervals. 28 00:02:19,230 --> 00:02:25,050 So there are a few techniques to handle irregularly spaced time series, but many more that do not. 29 00:02:26,030 --> 00:02:32,240 Thus, in this class, we'll stick to models that handle discrete time time series sampled at regularly 30 00:02:32,240 --> 00:02:33,500 spaced intervals. 31 00:02:34,040 --> 00:02:40,220 Okay, so for the purpose of this class, a Time series is continuous, valued but discrete in time. 32 00:02:44,630 --> 00:02:49,460 So before we end this lecture, there is one more kind of time series we should consider, which is 33 00:02:49,460 --> 00:02:51,000 a vector time series. 34 00:02:51,020 --> 00:02:53,720 In fact, vector time series are quite common. 35 00:02:54,080 --> 00:02:59,060 We mentioned stock prices earlier, but as we all know, there are many stocks to choose from. 36 00:02:59,270 --> 00:03:05,960 So the collection of stock prices of multiple stocks at each point in time would be a vector time series. 37 00:03:06,200 --> 00:03:10,460 Or you can just have one stock with multiple indicators for each point in time. 38 00:03:10,470 --> 00:03:13,310 And that's another example of a vector time series. 39 00:03:17,610 --> 00:03:20,910 So another one of my favorite examples is brain signals. 40 00:03:21,180 --> 00:03:27,480 Brain machine interfaces might sound futuristic, but in fact some rudimentary examples already exist. 41 00:03:27,660 --> 00:03:33,360 Neuralink is one company whose goal is to improve this technology far beyond what we currently have. 42 00:03:33,780 --> 00:03:38,340 So far, they've built this kind of sewing machine that will implant electrodes in your brain while 43 00:03:38,370 --> 00:03:40,050 being minimally invasive. 44 00:03:40,860 --> 00:03:46,200 So the main idea behind this technology is that your brain works by sending electrical signals between 45 00:03:46,200 --> 00:03:47,080 neurons. 46 00:03:47,100 --> 00:03:51,090 In fact, we'll explore this idea further when we study deep neural networks. 47 00:03:51,660 --> 00:03:57,180 Now, these electrodes can read voltages from different parts of your brain which signal what kind of 48 00:03:57,180 --> 00:03:58,650 activity is going on. 49 00:03:59,070 --> 00:04:03,400 Theoretically, these signals can be decoded in order to read your thoughts. 50 00:04:03,420 --> 00:04:09,480 So, for example, using this technology, we're able to train monkeys to control a computer mouse using 51 00:04:09,480 --> 00:04:10,650 only their minds. 52 00:04:11,010 --> 00:04:15,600 It's also possible not just to read from the brain, but to write to the brain. 53 00:04:15,810 --> 00:04:20,680 Once this technology is perfected, we'll be able to send information to the mind. 54 00:04:20,710 --> 00:04:26,230 So you might, for example, read a book or learn guitar without actually having to pick up that book 55 00:04:26,230 --> 00:04:27,040 or guitar. 56 00:04:27,920 --> 00:04:32,810 And of course, this is an example of a vector time series since there are multiple electrodes, all 57 00:04:32,810 --> 00:04:34,640 reading voltages periodically.