Frequency domain estimation of cointegrating vectors with mixed frequency and mixed sample data

Marcus J Chambers

doi:10.1016/j.jeconom.2019.10.010

Abstract

This paper proposes a simple method for exploiting the information contained in mixed frequency and mixed sample data in the estimation of cointegrating vectors. The asymptotic properties of easy-to-compute spectral regression estimators of the cointegrating vectors are derived and these estimators are shown to belong to the class of optimal cointegration estimators. Furthermore, Wald statistics based on these estimators have asymptotic chi-square distributions which enable inferences to be made straightforwardly. Simulation experiments suggest that the spectral regression estimators considered perform well in finite samples and are at least as good as time domain fully modified estimators. The finite sample size and power properties of the spectral regression-based Wald statistic are also found to be good.

Highlights

The concept of cointegration plays a prominent role in the analysis of multivariate time series with unit roots, and a large variety of methods is available to the applied researcher for handling such data
Prominent among these methods is the vector error correction model (VECM) which is a convenient reparameterisation of a vector autoregressive (VAR) system that accounts for the cointegration between the variables
In addition to the ordinary least squares (OLS)-based test we report results for the spectral regression estimators using the largest number of periodogram ordinates (FD3, FDA3 and ASD3) as well as the fully modified (FM) estimator based on the smallest number of autocovariances (FM1) — these correspond to the estimators that typically have the lowest RMSE

Summary

Introduction

The concept of cointegration plays a prominent role in the analysis of multivariate time series with unit roots, and a large variety of methods is available to the applied researcher for handling such data. In this paper we adapt the spectral regression approach of Phillips (1991a) to the estimation of cointegrating vectors using mixed frequency data. The first, indicated above, is the derivation of a model that can be used with mixed frequency and mixed sample data for the estimation of cointegrating vectors In this sense its motivation is very similar to that of Miller (2016), some of whose results are used in the proofs. Phillips (1991a) proposed a class of spectral regression estimators for a single cointegrating vector and for time series sampled at a common frequency.

The model and a mixed frequency representation

Estimation in the frequency domain

Simulation results

Concluding comments