The Study of a New Method for Forecasting Non-stationary Series

A new method for forecasting non stationary series is developed. Its steps are as follows: Step 1. Data delaminating. Non stationary series is delaminated into several multi scale steady data layers and one trend layer. Step 2. Modeling and forecasting each stationary data layer. Step 3. Imitating trend layer using polynomial. Step 4. Combining the forecasting layers and imitating layer into one series. The EMD (Empirical Mode Decomposition) method suitable to process non stationary series is selected to delaminate data, while ARMA (Auto Regressive Moving Average) model is employed to model and forecast stationary data layer and least square error method for trend layer regression. Aiming at forecasting length, forecasting orientation and selective method, experiments are performed for SAR (Synthetic Aperture Radar) images. Finally, an example is provided, in which the whole SAR image is restored via the method proposed by this paper.

Exponential tilted likelihood for stationary time series models

Depending on the asymptotical independence of periodograms,exponential tilted(ET)likelihood,as an effective nonparametric statistical method,is developed to deal with time series in this paper.Similar to empirical likelihood(EL),it still suffers from two drawbacks:the nondefinition problem of the likelihood function and the under-coverage probability of confidence region.To overcome these two problems,we further proposed the adjusted ET(AET)likelihood.With a specific adjustment level,our simulation studies indicate that the AET method achieves a higher-order coverage precision than the unadjusted ET method.In addition,due to the good performance of ET under moment model misspecification[Schennach,S.M.(2007).Point estimation with exponentially tilted empirical likelihood.The Annals of Statistics,35(2),634–672.https://doi.org/10.1214/009053606000001208],we show that the one-order property of point estimate is preserved for the misspecified spectral estimating equations of the autoregressive coefficient of AR(1).The simulation results illustrate that the point estimates of the ET outperform those of the EL and their hybrid in terms of standard deviation.A real data set is analyzed for illustration purpose.

Parameter Estimation of Varying Coefficients Structural EV Model with Time Series

In this paper, the parameters of a p-dimensional linear structural EV(error-in-variable)model are estimated when the coefficients vary with a real variable and the model error is time series.The adjust weighted least squares(AWLS) method is used to estimate the parameters. It is shown that the estimators are weakly consistent and asymptotically normal, and the optimal convergence rate is also obtained. Simulations study are undertaken to illustrate our AWLSEs have good performance.