A filter bank approach for modeling and forecasting seasonal patterns

Abstract

A novel method for modeling and forecasting seasonal time series is proposed. Unlike the traditional approach that depends solely on dynamic models, the proposed method combines stochastic dynamic modeling with an analysis filter bank designed to reduce dimensionality and to extract persistent components for reliable long-term forecasting. The filter bank decomposes the time series of interest into seasonal components, and only those components that are highly coherent across the periods are selected for subsequent modeling and forecasting. Experiments show that under suitable conditions, the use of highly coherent components not only reduces the modeling complexity and the required amount of training data but also limits the impact of noise and occasional corruption in the training data and thus provides robust forecasts with reduced variability. Fourier and wavelet filter banks are discussed in detail. Simulated and real-data examples are used to illustrate the method.