Forecasting Periodic Trends by Exponential Smoothing

Some commodities are known to have periodic trends, through seasonal variations and other variations that are repetitive. In forecasting these trends it is desirable to use a set of periodic functions. A method is obtained for the computation of the required coefficients in exponential smoothing when the set of fitting functions consists of a finite number of sine and cosine functions, or such functions multiplied by exponential functions. Explicit expressions are derived for some particular cases.