AN INFORMATIC APPROACH TO A LONG MEMORY STATIONARY PROCESS

Long memory is an important phenomenon that arises sometimes in the analysis of time series or spatial data.Most of the definitions concerning the long memory of a stationary process are based on the second-order properties of the process.The mutual information between the past and future I_(p−f) of a stationary process represents the information stored in the history of the process which can be used to predict the future.We suggest that a stationary process can be referred to as long memory if its I_(p−f) is infinite.For a stationary process with finite block entropy,I_(p−f) is equal to the excess entropy,which is the summation of redundancies that relate the convergence rate of the conditional(differential)entropy to the entropy rate.Since the definitions of the I_(p−f) and the excess entropy of a stationary process require a very weak moment condition on the distribution of the process,it can be applied to processes whose distributions are without a bounded second moment.A significant property of I_(p−f) is that it is invariant under one-to-one transformation;this enables us to know the I_(p−f) of a stationary process from other processes.For a stationary Gaussian process,the long memory in the sense of mutual information is more strict than that in the sense of covariance.We demonstrate that the I_(p−f) of fractional Gaussian noise is infinite if and only if the Hurst parameter is H∈(1/2,1).

A case study on the shareholder network effect of stock market data:An SARMA approach

One of the key research problems in financial markets is the investigation of inter-stock dependence.A good understanding in this regard is crucial for portfolio optimization.To this end,various econometric models have been proposed.Most of them assume that the random noise associated with each subject is independent.However,dependence might still exist within this random noise.Ignoring this valuable information might lead to biased estimations and inaccurate predictions.In this article,we study a spatial autoregressive moving average model with exogenous covariates.Spatial dependence from both response and random noise is considered simultaneously.A quasi-maximum likelihood estimator is developed,and the estimated parameters are shown to be consistent and asymptotically normal.We then conduct an extensive analysis of the proposed method by applying it to the Chinese stock market data.

Polynomial network autoregressive models with divergent orders

We propose a novel polynomial network autoregressive model by incorporating higher-order connected relationships to simultaneously model the effects of both direct and indirect connections. A quasimaximum likelihood estimation method is proposed to estimate the unknown influence parameters, and we demonstrate its consistency and asymptotic normality without imposing any distribution assumption. Moreover,an extended Bayesian information criterion is set for order selection with a divergent upper order. The application of the proposed polynomial network autoregressive model is demonstrated through both the simulation and the real data analysis.

High dimensional cross-sectional dependence test under arbitrary serial correlation

In panel data analysis,the cross-sectional dependence(CD)test has been extensively used to test the cross-sectional dependence.However,this traditional CD test does not take serial correlation into consideration,which commonly occurs in many fields.To solve this problem,we propose an adjusted CD test which is able to effectively handle serial correlation.More specifically,the serial correlation can be of arbitrary form in our work.Furthermore,we establish the theoretical properties of the proposed adjusted CD test.Our extensive Monte Carlo experiments show that the traditional CD test cannot work well under serial correlation,while the proposed adjusted CD test does provide rather satisfactory performance.

Dynamically integrated regression model for online auction data

We propose a dynamically integrated regression model to predict the price of online auctions,including the final price.Different from existing models,the proposed method uses not only the historical price but also the information from bidding time.Consequently,the prediction accuracy is improved compared with the existing methods.An estimation method based on B-spline approximation is proposed for the estimation and the inference of parameters and nonparametric functions in this model.The minimax rate of convergence for the prediction risk and large-sample results including the consistency and the asymptotic normality are established.Simulation studies verify the finite sample performance and the appealing prediction accuracy and robustness.Finally,when we apply our method to a 7-day auction of iPhone 6s during December 2015 and March 2016,the proposed method predicts the ending price with a much smaller error than the existing models.

Truncated L1 Regularized Linear Regression:Theory and Algorithm

Truncated L1 regularization proposed by Fan in[5],is an approximation to the L0 regularization in high-dimensional sparse models.In this work,we prove the non-asymptotic error bound for the global optimal solution to the truncated L1 regularized linear regression problem and study the support recovery property.Moreover,a primal dual active set algorithm(PDAS)for variable estimation and selection is proposed.Coupled with continuation by a warm-start strategy leads to a primal dual active set with continuation algorithm(PDASC).Data-driven parameter selection rules such as cross validation,BIC or voting method can be applied to select a proper regularization parameter.The application of the proposed method is demonstrated by applying it to simulation data and a breast cancer gene expression data set(bcTCGA).