The univariate moving window spectral method

A major difficulty encountered in time series analysis is the bias in model parameter estimates, resulting in multiple-period lead time forecast error divergence. An approach, which mitigates the effect of this bias, is described. The spectral approach offers the potential for better estimation of cyclical components in time series. When recombined by the moving window spectral (MWS) paradigm, better long range forecasts are possible. Illustration is by comparisons to 24 other models, applied to complex non-linear multiple component time series, and 111 empirical time series. The MWS method requires the least user expertise, it explains, and it forecasts the time series the best. It is applicable to a broad range of time series associated with the physical, economic, and social sciences.