Multivariate Local Polynomial Regression with Application to Shenzhen Component Index

This study attempts to characterize and predict stock index series in Shenzhen stock market using the concepts of multivariate local polynomial regression. Based on nonlinearity and chaos of the stock index time series, multivariate local polynomial prediction methods and univariate local polynomial prediction method, all of which use the concept of phase space reconstruction according to Takens' Theorem, are considered. To fit the stock index series, the single series changes into bivariate series. To evaluate the results, the multivariate predictor for bivariate time series based on multivariate local polynomial model is compared with univariate predictor with the same Shenzhen stock index data. The numerical results obtained by Shenzhen component index show that the prediction mean squared error of the multivariate predictor is much smaller than the univariate one and is much better than the existed three methods. Even if the last half of the training data are used in the multivariate predictor, the prediction mean squared error is smaller than the univariate predictor. Multivariate local polynomial prediction model for nonsingle time series is a useful tool for stock market price prediction.

Deconvolution of Defocused Image with Multivariate Local Polynomial Regression and Iterative Wiener Filtering in DWT Domain

A novel semiblind defocused image deconvolution technique is proposed, which is based on multivariate local polynomial regression (MLPR) and iterative Wiener filtering (IWF). In this technique, firstly a multivariate local polynomial regression model is trained in wavelet domain to estimate defocus parameter. After obtaining the point spread function (PSF) parameter, iterative wiener filter is adopted to complete the restoration. We experimentally illustrate its performance on simulated data and real blurred image. Results show that the proposed PSF parameter estimation technique and the image restoration method are effective.