Transforming Time Series

It is often useful to transform time series for analysis or forecasting. Many time series analysis and forecasting methods are most appropriate for time series with an unrestricted range, a linear trend, and a constant variance. Series that do not conform to these assumptions can often be transformed to series for which the methods are appropriate.

Transformations can be useful for the following:

• range restrictions. Many time series cannot have negative values or can be limited to a maximum possible value. You can often create a transformed series with an unbounded range.

• nonlinear trends. Many economic time series grow exponentially. Exponential growth corresponds to linear growth in the logarithms of the series.

• series variability that changes over time. Various transformations can be used to stabilize the variance.

• nonstationarity. The %DFTEST macro can be used to test a series for nonstationarity which can then be removed by differencing.