What can we forecast?

Before we move ahead, there is another aspect of time series forecasting that we have to understand—the predictability of a time series. The most basic assumption when we forecast a time series is that the future depends on the past. But not all time series are equally predictable.

Let's take a look at a few examples and try to rank these in order of predictability (from easiest to hardest), as follows:

• High tide next Monday
• Lottery numbers next Sunday
• The stock price of Tesla next Friday

Intuitively, it is very easy for us to rank them. High tide next Monday is going to be the easiest to predict because it is so predictable, the lottery numbers are going to be very hard to predict because these are pretty much random, and the stock price of Tesla next Friday is going to be difficult to predict, but not impossible.

Note

However, for people thinking that they can forecast stock prices with the awesome techniques covered in the book and get rich, that won't happen. Although it is worthy of a lengthy discussion, we can summarize the key points in a short paragraph.

Share prices are not a function of their past values but an anticipation of their future values, and this thereby violates our first assumption while forecasting. And if that is not bad enough, financial stock prices typically have a very low signal-to-noise ratio. The final wrench in the process is the efficient-market hypothesis (EMH). This seemingly innocent hypothesis proclaims that all known information about a stock price is already factored into the price of the stock. The implication of the hypothesis is that if you can forecast accurately, many others will also be able to do that, and thereby the market price of the stock already reflects the change in price that this forecast brought about.

Coming back to the topic at hand—predictability—three main factors form a mental model for this, as follows:

• Understanding the DGP: The better you understand the DGP, the higher the predictability of a time series.
• Amount of data: The more data you have, the better your predictability is.
• Adequately repeating pattern: For any mathematical model to work well, there should be an adequately repeating pattern in your time series. The more repeatable the pattern is, the better your predictability is.

Even though you have a mental model of how to think about predictability, we will look at more concrete ways of assessing the predictability of time series in Chapter 3, Analyzing and Visualizing Time Series Data, but the key takeaway is that not all time series are equally predictable.

In order to fully follow the discussion in the coming chapters, we need to establish a standard notation and get updated on terminology that is specific to time series analysis.