3 Going on a random walk

In the previous chapter, we compared different naive forecasting methods and learned that they often serve as benchmarks for more sophisticated models. However, there are instances where the simplest methods will yield the best forecasts. This is the case when we face a random walk process.

In this chapter, you will learn what a random walk process is, how to recognize it, and how to make forecasts using random walk models. Along the way, we will look at the concepts of differencing, stationarity, and white noise, which will come back in later chapters as we develop more advanced statistical learning models.

For this chapter’s examples, suppose that you want to buy shares of Alphabet Inc. (GOOGL). Ideally, you would want to buy if the closing price of the stock is expected to go up in the future; otherwise, your investment will not be profitable. Hence, you decide to collect data on the daily closing price of GOOGL over 1 year and use time series forecasting to determine the future closing price of the stock. The closing price of GOOGL from April 27, 2020, to April 27, 2021, is shown in figure 3.1. At the time of writing, data beyond April 27, 2021, was not available yet.

3.1 The random walk process

3.1.1 Simulating a random walk process

3.2 Identifying a random walk

3.2.1 Stationarity

3.2.2 Testing for stationarity

3.2.3 The autocorrelation function

3.2.4 Putting it all together

3.2.5 Is GOOGL a random walk?

3.3 Forecasting a random walk

3.3.1 Forecasting on a long horizon

3.3.2 Forecasting the next timestep

3.4 Next steps