Trend Estimation of Multivariate Time Series with Controlled Smoothness

• Activity Number: 563
• Type: Contributed
• Date/Time: Wednesday, August 12, 2015 : 11:35 AM to 12:20 PM
• Sponsor: Government Statistics Section
• Author(s): Lilia L. Ramirez Ramirez* and Victor Guerrero and Alejandro Islas-Camargo
• Companies: Instituto Tecnológico Autónomo de México and Instituto Tecnológico Autónomo de México and Instituto Tecnológico Autónomo de México
• Keywords: Signal extraction ; Smoothness index ; Penalized Least Squares ; Generalized Least Squares

Abstract

We present an extension to filtering techniques to estimate trends of multivariate time series. The proposed method is based on a vector signal-plus-noise representation of Penalized Least Squares that requires only the first two sample moments, and introduces an index of smoothness. This index allows setting in advance a desired amount of smoothness to achieve. It is also a function of the correlation between the noises of the series and the sample size. Our proposal arises from a statistical solution to a multivariate GLS problem. Such a solution leads to an index of smoothness that is applicable in the general multivariate case, but we pay special attention to the bivariate situation. Here we show the closed-form expressions for calculating trend estimates with their corresponding variance-covariance matrices, and present the proposed algorithm for smoothing bivariate time series. We discuss the results on simulated data and a real application (Mexican and U.S. GDP data).