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One of the most popular applications of Time series analysis isn't finance, although this is not the

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only application of Time series, it's one that I know a lot of you are thinking about now.

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Unfortunately, a lot, of course, is out there.

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Simply take the price of a stock and treat that like any other time series seems completely reasonable.

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What's the difference between a one time series and another?

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Well, in this course you're going to learn that there's actually a huge difference.

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None of this is obvious at first, but I hope that throughout this course you will build your skill

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to a level necessary to understand what I'm saying.

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You might start this course with a naive perspective, but by the end of this course, this perspective

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will mature.

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If your logic right now is Lithium's plus stock price prediction equals profit, then I would consider

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you as someone who falls into this naive category.

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Now, don't consider this to be a bad thing, but a good thing.

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You are going to get the most out of this course.

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So this lecture is a Financial Times series primer.

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There are certain operations and definitions you simply have to know about when you're dealing with

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stock price data.

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Now, although I've taught financial engineering elsewhere very in depth, you can think of this lecture

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as like a summary of those concepts.

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OK, so clearly the stock price over time is an example of a time series, it's continuous, valued,

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and it can be thought of as discrete time.

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For example, when you download stock price data from Yahoo!

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Finance, you might get daily data or hourly data in regularly spaced intervals.

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In more advanced courses.

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You can think of stock prices as continuous time, although, as mentioned, that would be a separate

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course.

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Now, in practice, what we are interested in is not the stock price, but rather the stock return.

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Let's think about the intuition behind this.

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We learned earlier that when we talk about forecasting metrics, it's nice when they are a scale invariant.

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If your guess for the price of a one million dollar house is off by one thousand.

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That's not so bad.

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But if your guess for the price of a five dollar coffee is off by five dollars, that's a pretty bad

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yes.

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So it's more natural to think in terms of percentages.

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The percent change tells us how much money we've made or lost on a stock that we own.

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We call this the stock return.

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The equation is very simple.

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And of course, you've seen this before.

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It's the final price minus the initial price divided by the initial price.

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Now, in practice, because we index our prices by time measured in periodic intervals, it's common

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to consider the return for each of those periods also index by time.

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So we say our privacy is equal to T minus T minus one, divided by T minus one.

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Note that this is also equal to T, divided by T minus one, minus one.

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And also note that we sometimes call this the net return, although I usually won't make this distinction.

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So here's one modern reason why understanding returns is important, you see very often people considering

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investment into crypto currencies, they think Bitcoin is expensive because one Bitcoin costs fifty

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thousand dollars.

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On the other hand, some random cryptocurrency only cost a few cents.

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So they think that this random cryptocurrency is a good investment because it's quote unquote cheap.

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Of course, this fact is irrelevant.

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If you have one thousand dollars to spend, then you'll buy one fiftieth of a Bitcoin.

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Or if you buy random coin, then you'll buy 10000 random coins, assuming each one costs 10 cents.

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But owning ten thousand random coins doesn't give you more value than owning one fiftieth of a Bitcoin.

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If random coin goes down to five cents, you've lost 50 percent of your wealth and the value of your

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investment is now just five hundred dollars.

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If Bitcoin goes up to one hundred thousand, then you double your wealth and the value of your investment

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is now two thousand dollars.

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So, as Albert Einstein said, everything is relative.

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Now, you recall that a common time series transformation is to take the log of the data.

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In fact, this is central to financial analysis.

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The log of the price is simply called the log price.

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Note that we typically use lowercase letters for the log variable in uppercase letters for the original.

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Now, before we get to log returns, we're going to define another kind of return called the gross return.

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The gross return is simply one plus the return from before.

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So why is this useful?

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Well, it's a convenient way to see how much our wealth has multiplied.

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So, for example, if I invested one hundred dollars and I got back one hundred twenty dollars, then

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my gross return is one point two.

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In other words, my wealth was multiplied by one point two.

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If I invested one hundred dollars and I lost twenty dollars, then I now have eighty dollars in my gross

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return is zero point eight.

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In other words, my wealth was multiplied by zero point eight.

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So a gross return, less than one is a loss and a gross return.

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Greater than one is a gain.

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The log return is simply the log of the gross return.

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So why do we take the log of the gross return and not the log of the net return?

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Well, let's see why this is the most natural thing to do.

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We can start by noticing that the net return can be negative.

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If you lose twenty dollars on a one hundred dollar investment, then your net return is minus 20 percent.

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And of course, you can't take the log of minus 20 percent.

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Furthermore, you'll recognize that the log return corresponds to the log transformation where we had

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one before taking the log.

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So this provides some intuition behind why we had one and not some other random number.

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Finally, notice how the log return is simply the difference in log prices.

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This is very convenient, since in computers, adding and subtracting is much more efficient and numerically

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stable than multiplying and dividing.

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In fact, the first difference is a very important operation in Time series analysis.

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We'll see it applied again and again in this course.

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So it's kind of a happy coincidence that these financial concepts, such as taking the log and taking

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differences, happened to also be critical operations in TIME series analysis.

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OK, so in the next part of this lecture, we are going to take a quick look at what financial data

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actually looks like.

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The most common format for stock price data is open, high, low, close adjusted, close in volume.

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Note again, how time goes along.

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The rows and different attributes go along the columns.

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So what are these attributes?

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Well, recall that each row of data corresponds to a period in time.

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For example, one day or one hour, the open price is the price.

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At the beginning of the period, the closed price is the price.

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At the end of the period, the high price is the maximum price for the period and the low price is the

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minimum price for the period.

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Volume is the number of trades that occurred during the period.

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So if you've ever looked at a candlestick chart, you'll recognize these quantities.

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These charts basically give you a picture of what happened in the market for that period.

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We use the color red when the closed price is less than the open price and green when the closed price

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is greater than the open price.

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So what is adjusted, close adjusted closes a special column that accounts for stock splits and dividends

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in the close price.

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Note that the closed price is typically what is used for analysis, which is why there's no adjusted

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open or adjusted low.

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So basically, dividends are amounts that are paid in cash into your cash account.

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This is money you earn, but it effectively makes the stock price less.

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So the return you compute from the closed price is less if you do not account for the dividend payment.

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The net return, which takes into account dividend payments, is shown here.

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But note that we will not use this in the course since it just adds coding work without any benefit,

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we would have to spend extra effort in finding the dividend payments, which typically do not come with

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these data sets.

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You could potentially compute them on your own, but again, that takes work.

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Note that this equation makes sense because again, DFT, the dividend is money that you actually earn.

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Now, some resources out there suggest using the adjusted clothes when computing the return, which

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gives you an approximation to the true return.

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I'll leave it for you as an exercise to check whether or not they are equal in practice.

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If you're building a trading bot, it would be my preference to use the true values and actually accumulate

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the dividends instead of using the adjusted clothes.

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So the final component of the just the close is the stock split.

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Now, I mentioned this for informational purposes, but note that it's not actually needed in our analysis

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because all stock prices in our API will already be adjusted for stock splits.

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Basically, the reason for stock splits is this.

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Imagine that a share of a stock is one hundred thousand dollars.

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This is too large for many people to afford and it's not possible to buy fractional shares.

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So to ameliorate this problem, the stock will be split, for example, two for one split or a three

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for one split.

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This will result in the stock price going down by a factor of two for a two for one split or three for

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a three for one split.

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If you already own shares of the stock, you'll now own two or three times more so that the value of

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what you own is the same.

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So, as mentioned in this course, we will focus on the non adjusted close price, if you want to do

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an exact analysis, you're always welcome to download dividend data separately using whatever API you

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normally use.

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The reason we want to use the noninterest to close prices, as you recall, the other columns are not

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adjusted.

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So if you want to do a multi-dimensional analysis, this is not possible using the adjusted close since

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it's not on the same scale as the open, high and low values.