Amplitude-Modulated Sinusoidal Model for the Sinusoidal Components of SSA Decomposition

SSA-based forecasting model combines all component models of SSA decomposition linearly. Hence, its performance is influenced by each component model, including the sinusoidal with time-varying amplitude model. This work presents the algorithm to obtain the model for sinusoidal series with time-varying amplitude. The three types of amplitude-modulated sinusoidal series commonly found in SSA decomposition are discussed. The algorithm consists of three steps. They are a determination of the best fit function for the standardized envelope series, determination of the stationary sinusoidal function, and determination the amplitude-modulated sinusoidal model. Based on the evaluation error of the estimated parameters of the three type models, it can be seen that the algorithm produces consistent estimators as the sample sizes increase. In the implementation of the sinusoidal components of the monthly electricity production in Australia, the presented algorithm yields the models that fit the oscillations well. The finding of this study supports the advancement of SSA-based hybrid models.