|
Abstract:
|
Dimensionality reduction has always been one of the most important and challenging problems in high-dimensional data analysis. In the context of time series analysis, we are interested in estimating and making inferences about the conditional mean and variance functions. Using the central mean and variance dimension reduction subspace, that preserves sufficient information about the response, one can estimate the unknown mean and variance functions of the time series. There are a few approaches in the literature to estimate the time series central mean subspace (TS-CMS). However, those methods are computationally intensive and not feasible in practice. Using the Fourier transform, an explicit estimate of the time series central mean subspace is obtained. The proposed estimators are shown to be consistent, asymptotically normal, and efficient. Simulation studies are conducted to evaluate the performance of the proposed method. The results show that our method is significantly more accurate, and computationally approximately 100 times faster than the existing method. The method is applied to the Canadian Lynx dataset.
|
