A1177
Title: Matrix decomposition for multivariate harmonic time series regression models
Authors: Rinka Sagawa - Waseda University (Japan) [presenting]
Abstract: The prediction error matrix is considered when a multivariate time series is misspecified as a multivariate harmonic regression model. In multivariate time series, identifying overall periodicity becomes challenging when individual components exhibit different periodic behaviors. Moreover, even in univariate settings, model misspecification can lead to reduced prediction accuracy and increased prediction error variance. It is shown that under such misspecification, the prediction error matrix can be decomposed into two parts: one derived from an autoregressive model based on the true stationary process and the other representing periodic components characterized by the spectral density matrix of the true process. This result is extendable to functional time series, where it is demonstrated via simulation that the periodic structure is preserved even when the type and number of basis functions used to convert the functional data into multivariate form are changed. Finally, the applicability of the proposed method to model selection is explored through data analysis using temperature data.
