Adaptive Estimation in Multiple Time Series with Independent Component Errors

13 Pages Posted: 8 Feb 2017

See all articles by Peter M. Robinson

Peter M. Robinson

London School of Economics & Political Science (LSE) - Department of Economics; National Bureau of Economic Research (NBER)

L. Taylor

London School of Economics & Political Science (LSE) - London School of Economics

Date Written: March 2017

Abstract

This article develops statistical methodology for semiparametric models for multiple time series of possibly high dimension N. The objective is to obtain precise estimates of unknown parameters (which characterize autocorrelations and cross‐autocorrelations) without fully parameterizing other distributional features, while imposing a degree of parsimony to mitigate a curse of dimensionality. The innovations vector is modelled as a linear transformation of independent but possibly non‐identically distributed random variables, whose distributions are nonparametric. In such circumstances, Gaussian pseudo‐maximum likelihood estimates of the parameters are typically √n‐consistent, where n denotes series length, but asymptotically inefficient unless the innovations are in fact Gaussian. Our parameter estimates, which we call ‘adaptive,’ are asymptotically as first‐order efficient as maximum likelihood estimates based on correctly specified parametric innovations distributions. The adaptive estimates use nonparametric estimates of score functions (of the elements of the underlying vector of independent random varables) that involve truncated expansions in terms of basis functions; these have advantages over the kernel‐based score function estimates used in most of the adaptive estimation literature. Our parameter estimates are also √n ‐consistent and asymptotically normal. A Monte Carlo study of finite sample performance of the adaptive estimates, employing a variety of parameterizations, distributions and choices of N, is reported.

Keywords: Multiple time series, independent component analysis, efficient semiparametric estimation, adaptive estimation, stationary processes, forecast error

Suggested Citation

Robinson, Peter M. and Taylor, L., Adaptive Estimation in Multiple Time Series with Independent Component Errors (March 2017). Journal of Time Series Analysis, Vol. 38, Issue 2, pp. 191-203, 2017, Available at SSRN: https://ssrn.com/abstract=2913879 or http://dx.doi.org/10.1111/jtsa.12212

Peter M. Robinson (Contact Author)

London School of Economics & Political Science (LSE) - Department of Economics ( email )

Houghton Street
London WC2A 2AE
United Kingdom

National Bureau of Economic Research (NBER)

1050 Massachusetts Avenue
Cambridge, MA 02138
United States

L. Taylor

London School of Economics & Political Science (LSE) - London School of Economics

United Kingdom

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