Abstract
It is of great practical significance to fit and predict actual time series. Based on the theories of time series analysis and unconstrained optimization, a new spectral conjugate gradient method–autoregressive integrated moving average combined model (FHS spectral CG–ARIMA combined model) is proposed to fit and predict the actual time series. First, combining the characteristics and advantages of different CG methods, we propose Fang–Hestenes–Stiefel algorithm (FHS). FHS satisfies the automatic descent property and has global convergence under the reasonable assumptions and Wolfe search. Second, many numerical results have been given there: compared with other related algorithms, FHS algorithm has obvious advantages. Third, FHS spectral CG–ARIMA combined model is given in detail. Fourth, the combined model is applied to fit the actual time series and the fitting effect is found to be remarkable.
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