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Abstract:
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We propose a notion of central mean dimension reduction subspace for time series which does not require specification of a model but seeks to find a lag(p) times dimension(d) matrix, d is less than or equal to p, so that the d linear combinations include all the information about a series that is available from conditional mean of a series given past values. For known p and d, we estimate the mean central subspace through the Nadaraya-Watson kernel smoother and establish the strong consistency of our estimator. In addition, we propose estimation of d and p using a modified Schwarz Bayesian criterion, if either of d and p is unknown. Finally, we examine the performance of all the estimators extensively through a variety of simulations and provide a new analysis of the well-known Canadian lynx data.
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