Joint detection for functional polynomial regression with autoregressive errors

In this article, we are concerned with detecting the true structure of a functional polynomial regression with autoregressive (AR) errors. The first issue is to detect which orders of the polynomial are significant in functional polynomial regression. The second issue is to detect which orders of the AR process in the AR errors are significant. We propose a shrinkage method to deal with the two problems: polynomial order selection and autoregressive order selection. Simulation studies demonstrate that the new method can identify the true structure. One empirical example is also presented to illustrate the usefulness of our method.     

Polynomial spline confidence bands for time series trend

The paper considers the construction of a confidence band for the trend function of a stationary time series. An explicit formula is derived based on polynomial splines and Sunklodas (1984). The performance of the confidence band is illustrated by simulation studies. The proposed method is applied to the analysis of the annual yields of wheat in the United States.     

Nonlinear semiparametric AR(1) model with skew-symmetric innovations

In this paper, we expand a first-order nonlinear autoregressive (AR) model with skew normal innovations. A semiparametric method is proposed to estimate a nonlinear part of model by using the conditional least squares method for parametric estimation and the nonparametric kernel approach for the AR adjustment estimation. Then computational techniques for parameter estimation are carried out by the maximum likelihood (ML) approach using Expectation-Maximization (EM) type optimization and the explicit iterative form for the ML estimators are obtained. Furthermore, in a simulation study and a real application, the accuracy of the proposed methods is verified.     

Regularization and variable selection for infinite variance autoregressive models

Autoregressive models with infinite variance are of great importance in modeling heavy-tailed time series and have been well studied. In this paper, we propose a penalized method to conduct model selection for autoregressive models with innovations having Pareto-like distributions with index α∈(0,2)$\alpha \in (\mathrm{0,2})$. By combining the least absolute deviation loss function and the adaptive lasso penalty, the proposed method is able to consistently identify the true model and at the same time produce efficient estimators with a convergence rate of n^−1/α$n^{-1/\alpha }$. In addition, our approach provides a unified way to conduct variable selection for autoregressive models with finite or infinite variance. A simulation study and a real data analysis are conducted to illustrate the effectiveness of our method.     

Likelihood-Based Inference in Autoregressive Models with Scaled t-Distributed Innovations by Means of EM-Based Algorithms

This article applies the EM-based (ECM and ECME) algorithms to find the maximum likelihood estimates of model parameters in general AR models with independent scaled t-distributed innovations whenever the degrees of freedom are unknown. The ECME, sharing advantages with both EM and Newton–Raphson algorithms, is an extension of ECM, which itself is an extension of the EM algorithm. The ECM and ECME algorithms, which are analytically quite simple to use, are then compared based on the computational running time and the accuracy of estimation via a simulation study. The results demonstrate that the ECME is efficient and usable in practice. We also show how our method can be applied to the Wolfer's sunspot data.     

货币和产出缺口能给通货膨胀提供有用的信息吗？

 ]论文目的是确定货币、产出缺口和国际商品价格指数与我国通货膨胀之间是否有长期的关系,能否给我国通货膨胀预测提供除通货膨胀自身所具有的以外的信息。论文的研究方法主要是自回归分布滞后模型(ARDL),基于自回归分布滞后模型进行通货膨胀与相关经济变量的长期关系检验,并进行预报实验,将预测结果与仅包括通货膨胀自身滞后因子的自回归模型的预测结果比较。实证结果显示：货币供给m2、m1、m0都与通货膨胀有显著的长期关系,但是只有m0含有通货膨胀自身没含有的信息,能给通货膨胀提供额外的信息;产出缺口、国际农产品价格指数分别与通货膨胀有长期的关系,含有通货膨胀自身没含有的信息,能给通货膨胀预测提供额外的信息。最后还提出一些相关建议。     

Strong consistency of the regularized least-squares estimates of infinite autoregressive models

Our main interest is on-line parameter estimation of infinite AR models with exponentially decaying coefficients. The practical importance of the problem follows from the fact that the class of such models includes (but not limited to) all causal invertible ARMA(p,q$p,q$) models. On-line parameter estimation means that the length of the observed data sample is not known a priori and may indefinitely increase. Hence, the parameter estimates should be refined upon arrival of every new observation. So use of the maximum likelihood (ML) method is not feasible due to the high computational burden, and recursive estimation procedures are preferable.     

Bootstrap estimates of the sample bivariate autocorrelation and partial autocorrelation distributions

This paper shows how the bootstrap method can be used to estimate the joint distribution of sample autocorrelations and partial autocorrelations. The exact joint distribution of sample autocorrelations is mathematically intractable and attempts at workable approximations are difficult and rely on special assumptions. The bootstrap offers an accurate solution to this problem without requiring special assumptions and in a way that avoids theoretical difficulties. The bootstrap-estimated joint distributions of the autocorrelations and partial autocorrelations of time series are shown to lead to better ARMA model identification. This is demonstrated using simulated series.     

Robust unit root tests with autoregressive errors

ABSTRACT

This article presents a new test for unit roots based on least absolute deviation estimation specially designed to work for time series with autoregressive errors. The methodology used is a bootstrap scheme based on estimating a model and then the innovations. The resampling part is performed under the null hypothesis and, as it is customary in bootstrap procedures, is automatic and does not rely on the calculation of any nuisance parameter. The validity of the procedure is established and the asymptotic distribution of the statistic proposed is proved to converge to the correct distribution. To analyze the performance of the test for finite samples, a Monte Carlo study is conducted showing a very good behavior in many different situations.     

STAR非线性平稳性检验中误设定的伪检验研究

本文通过理论分析和蒙特卡洛仿真模拟,研究平稳性检验中选用的统计量与数据生成过程不一致时,非线性ESTAR、LSTAR与线性DF检验法能否得出正确的结论.研究表明,二阶LSTAR与ESTAR模型可用相同的检验方法,但前者的非线性特征更强.当数据生成过程为线性AR,或非线性ESTAR、二阶LSTAR模型时,使用DF或ESTAR检验法可得出大致正确的结论,但LSTAR检验法完全失败.数据生成过程的非线性特征越强,ESTAR较DF检验方法的功效增益越高;线性特征越强,DF的功效增益越高.当转移函数F(θ,c,zt)中θ较大导致一阶泰勒近似误差较大或c非0时,标准ESTAR与LSTAR非线性检验法失去应用条件.θ较大或c偏离0较远时,数据生成过程中线性成分增强,用线性DF检验可获得更好的检验结果.     

Asymptotic normality of Huber–Dutter estimators in a linear model with AR(1) processes

The paper studies a linear regression model with first order autoregressive (AR(1)) processes. The Huber–Dutter (HD) estimators of unknown parameters are given, and the asymptotic normality of the HD estimators is investigated. An example is presented to illustrate the proposed method.     

Non-nested model selection based on the quantiles and it’s application in time series

We consider the problem of model selection based on quantile analysis and with unknown parameters estimated using quantile leasts squares. We propose a model selection test for the null hypothesis that the competing models are equivalent against the alternative hypothesis that one model is closer to the true model. We follow with two applications of the proposed model selection test. The first application is in model selection for time series with non-normal innovations. The second application is in model selection in the NoVas method, short for normalizing and variance stabilizing transformation, forecast. A set of simulation results also lends strong support to the results presented in the paper.     

Oracle model selection for correlated data via residuals

This paper concerns model selection for autoregressive time series when the observations are contaminated with trend. We propose an adaptive least absolute shrinkage and selection operator (LASSO) type model selection method, in which the trend is estimated by B-splines, the detrended residuals are calculated, and then the residuals are used as if they were observations to optimize an adaptive LASSO type objective function. The oracle properties of such an adaptive LASSO model selection procedure are established; that is, the proposed method can identify the true model with probability approaching one as the sample size increases, and the asymptotic properties of estimators are not affected by the replacement of observations with detrended residuals. The intensive simulation studies of several constrained and unconstrained autoregressive models also confirm the theoretical results. The method is illustrated by two time series data sets, the annual U.S. tobacco production and annual tree ring width measurements.     

A Multivariate Unit Root Test Based on the Modified Weighted Symmetric Estimator for VAR(p)

Multivariate unit root tests for the VAR model have been commonly used in time series analysis. Several unit root tests were developed. Most of the estimators of coefficient matrices developed in the VAR model are obtained using ordinary least squares estimators. In this paper, we suggest a multivariate unit root test based on a modified weighted symmetric estimator. Using a limited Monte Carlo simulation, we compare the powers of the new test statistic and the test statistic suggested in Fuller (1996).     

Applying multivariate techniques to high-dimensional temporally correlated fMRI data

In first-level analyses of functional magnetic resonance imaging data, adjustments for temporal correlation as a Satterthwaite approximation or a prewhitening method are usually implemented in the univariate model to keep the nominal test level. In doing so, the temporal correlation structure of the data is estimated, assuming an autoregressive process of order one.We show that this is applicable in multivariate approaches too - more precisely in the so-called stabilized multivariate test statistics. Furthermore, we propose a block-wise permutation method including a random shift that renders an approximation of the temporal correlation structure unnecessary but also approximately keeps the nominal test level in spite of the dependence of sample elements.Although the intentions are different, a comparison of the multivariate methods with the multiple ones shows that the global approach may achieve advantages if applied to suitable regions of interest. This is illustrated using an example from fMRI studies.     

Inference on the asymptotic behavior of covariance operator of first-order periodically correlated autoregressive Hilbertian processes

This paper is devoted to a study on the structure of tensorial products of periodically correlated autoregressive (PCAR) processes with values in separable Hilbert spaces. It will be demonstrated that the resulting processes are PCAR with values in the space of Hilbert–Schmidt operators. These processes are applied while studying the convergence rate, limiting behavior and asymptotic distribution of the empirical estimators of the covariance operators of PCAR processes.     

Semiparametric Sieve-Type Generalized Least Squares Inference

This article considers the problem of statistical inference in linear regression models with dependent errors. A sieve-type generalized least squares (GLS) procedure is proposed based on an autoregressive approximation to the generating mechanism of the errors. The asymptotic properties of the sieve-type GLS estimator are established under general conditions, including mixingale-type conditions as well as conditions which allow for long-range dependence in the stochastic regressors and/or the errors. A Monte Carlo study examines the finite-sample properties of the method for testing regression hypotheses.     

A Note on a Partition of the Likelihood Ratio Test for Autoregressive Covariance Structure

A sequence of nested hypotheses is presented for the examination of the assumption of autoregressive covariance structure in, for example, a repeated measures experiment. These hypotheses arise naturally by specifying the joint density of the underlying vector random variable as a product of conditional densities and the density of a subset of the vector random variable. The tests for all but one of the nested hypotheses are well known procedures, namely analysis of variance F-tests and Bartlett's test of equality of variances. While the procedure is based on tests of hypotheses, it may be viewed as an exploratory tool which can lead to model identification. An example is presented to illustrate the method.     

Measurement of Abnormal Returns From Small Firms

Correction for heteroscedasticity in returns from portfolios long in small firms and short in large firms listed on the New York Stock Exchange reduces the estimate of market risk and increases the estimated abnormal return. Greatly improved diagnostic test statistics are obtained, strengthening the evidence for the existence of positive average abnormal returns from small firms. Periodicity of order 6 and 12 months is identified. The estimation procedure operates by exploiting the autoregressive pattern of heteroscedasticity in the return data.     

Bias Reduction through First-order Mean Correction, Bootstrapping and Recursive Mean Adjustment

Standard methods of estimation for autoregressive models are known to be biased in finite samples, which has implications for estimation, hypothesis testing, confidence interval construction and forecasting. Three methods of bias reduction are considered here: first-order bias correction, FOBC, where the total bias is approximated by the O(T^-1) bias; bootstrapping; and recursive mean adjustment, RMA. In addition, we show how first-order bias correction is related to linear bias correction. The practically important case where the AR model includes an unknown linear trend is considered in detail. The fidelity of nominal to actual coverage of confidence intervals is also assessed. A simulation study covers the AR(1) model and a number of extensions based on the empirical AR(p) models fitted by Nelson & Plosser (1982). Overall, which method dominates depends on the criterion adopted: bootstrapping tends to be the best at reducing bias, recursive mean adjustment is best at reducing mean squared error, whilst FOBC does particularly well in maintaining the fidelity of confidence intervals.