Practical Time Series Analysis

Seasonal differencing

When a time series exhibits seasonality of a known time period of m time indices, it can be stationarized by taking seasonal differences between x_t and x_t-m. These differences taken at lags of length m are indicative of the seasons or quarters in a year. In this case m = 12 and the differences are taken between original observations that are a year apart from each other. The seasonal differences can be expressed as follows:

x^'_t = x_t - x_t-m = Є_t

To demonstrate the effect of seasonal differencing we would revisit the time series on daily mean temperatures of Fisher River. We have already seen the original time series and the monthly mean, both of which apparently exhibit strong seasonal behavior. The monthly mean can be ...