Overcoming Spurious Regression Using time-Varying Fourier Amplitude Approach
Non-stationary time series data have been traditionally analyzed in the frequency domain by assuming constant amplitudes regardless of the timelag. A new approach called time-varying amplitude method (TVAM) is presented here. Oscillations are analyzed for changes in the magnitude of Fourier Coefficients which are analyzed for predictive and diagnostic purposes. To obtain an estimate for the time varying changes in the Fourier Coefficients of non-stationary data, a weighted least square approachproduced results from an empirical data that are now presented. Time-varying Fourier Transform are presented in the new Adaptive Scheme. Results from the Adaptive Amplitude model showed a decrease of over 40% in the fitted error sum of squares compared with result from the traditional or classical method with constant amplitude. More importantly, time-varying amplitude model has eliminated the spurious regression syndrome that has plagued non-stationary signals when modelled by Fourier analysis Method.
Keywords: Classical Fourier Coefficients. Cosine and Sine Transforms, Spurious regression, Time-Varying Amplitude Model