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Abstract:
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Time series which have more than one time dependent variable require building an appropriate model in which the variables not only have relationships with each other, but also depend on previous values in time. Based on developments for a univariate dimension reduction technique, we investigate a new class of multiple time series models without parametric assumptions. First, for the dependent and independent time series, we simply use a univariate time series central subspace to estimate the autoregressive lags of the series. Secondly, we extract the successive direction to estimate the time series central subspace for regressors which include past lags of dependent and independent series in a mutual information multiple-index time series. Lastly, we estimate a multiple time series model for the reduced directions which include linear combination of dependent and independent series. We propose a data dependent approach of minimal dimension for situations in which the dimension for multiple regressors is unknown. We check the accuracy for the multiple time series central subspace method using the simulated data sets. Furthermore, we present an analysis using real data.
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