Practical Time Series Analysis

Time series decomposition using moving averages

While analysing the quarterly beer production data we developed a methodology of stationarizing a non-stationary time series using seasonal MA and seasonal differences. We used the seasonal moving average as an estimate of the trend-cycle component and computed periodic differences on the residuals left by the MA.

Another approach could have been deducting both the seasonal MA and seasonal residuals from the original series and checking for randomness of the final residuals. This approach assumes that the beer production series is an additive sum of the trend-cycle and seasonal components and what is left after removing the aforementioned two are random variations. Indeed, moving averages can ...