04. Advanced Time Series Models

Seasonal Adjustments using ARIMA (SARIMA)

Time series data tends to have seasonal patterns. For instance, natural gas prices may increase during winter months, when it’s used for heating homes. Similarly, it may also increase during peak summer months, when natural gas generators are used to produce the extra electricity that is used for air conditioning. Retail sales also has expected increases during the holiday shopping season, such as Black Friday in the US (November), and Singles’ Day in China (also in November).

Stocks may potentially have seasonal patterns as well. One has to do with writing off losses in order to minimize taxes. Funds and individual investors have unrealized capital gains or losses when the stock price increases or decreases from the price at which they bought the stock. Those capital gains or losses become “realized capital gains” or “realized capital losses” when they sell the stock. At the end of the tax year (which may be December, but not necessarily), an investor may decide to sell their underperforming stocks in order to realize capital losses, which may potentially reduce their taxes. Then, at the start of the next tax year, they may buy back the same stocks in order to maintain their original portfolio. This is sometimes referred to as the “January effect.”

Removing seasonal effects can help to make the resulting time series stationary, and therefore more useful when feeding into an autoregressive moving average model.

To remove seasonality, we can take the difference between each data point and another data point one year prior. We’ll refer to this as the “seasonal difference”. For instance, if you have monthly data, take the difference between August 2018 and August 2017, and do the same for the rest of your data. It’s common to take the “first difference” either before or after taking the seasonal difference. If we took the “first difference” from the original time series, this would be taking August 2018 and subtracting July 2018. Next, to take the seasonal difference of the first difference, this would mean taking the difference between (August 2018 - July 2018) and (August 2017 - July 2017).

You can check if the resulting time series is stationary, and if so, run this stationary series through an autoregressive moving average model.

Side Note

Kendall Lo, one of the subject matter experts of our course, recommends this book: “Way of the Turtle: The Secret Methods that Turned Ordinary People into Legendary Traders”. The book is about how a successful investor trained his students (his “turtles”) to follow his trend-following trading strategy. The book illustrates the concepts of using trading signals, back-testing, position sizing, and risk management.
The story is also summarized in this article Turtle Trading: A Market Legend