Functional-coefficient models for nonstationary time series data

This paper studies functional coefficient regression models with nonstationary time series data, allowing also for stationary covariates. A local linear fitting scheme is developed to estimate the coefficient functions. The asymptotic distributions of the estimators are obtained, showing different convergence rates for the stationary and nonstationary covariates. A two-stage approach is proposed to achieve estimation optimality in the sense of minimizing the asymptotic mean squared error. When the coefficient function is a function of a nonstationary variable, the new findings are that the asymptotic bias of its nonparametric estimator is the same as the stationary covariate case but convergence rate differs, and further, the asymptotic distribution is a mixed normal, associated with the local time of a standard Brownian motion. The asymptotic behavior at boundaries is also investigated.     

On statistical inference in concentration measurement

Summary The asymptotic distribution for a certain class of functionals of distribution functions is derived. This result is used to give distribution free asymptotic confidence intervals for these functionals; for this purpose, a strongly consistent estimate for the asymptotic variance is constructed. These results are applied to the Lorenz-curve and the Gini-measure as special cases of the abovementioned class of functionals.     

Spatial local M-estimation under association

We investigate the asymptotic behavior of a robust version of local linear regression estimators with variable bandwidth for spatial associated processes. The weak consistency of the proposed estimators is given under appropriate conditions. Furthermore, we establish the asymptotic normality of the estimators, from which expressions for the asymptotic bias and variance can be derived.     

Asymptotics of SIMEX-based variance estimation

In this paper, we study the asymptotic properties of simulation extrapolation (SIMEX) based variance estimation that was proposed by Wang et al. (J R Stat Soc Series B 71:425–445, 2009). We first investigate the asymptotic normality of the parameter estimator in general parametric variance function and the local linear estimator for nonparametric variance function when permutation SIMEX (PSIMEX) is used. The asymptotic optimal bandwidth selection with respect to approximate mean integrated squared error (AMISE) for nonparametric estimator is also studied. We finally discuss constructing confidence intervals/bands of the parameter/function of interest. Other than applying the asymptotic results so that normal approximation can be used, we recommend a nonparametric Monte Carlo algorithm to avoid estimating the asymptotic variance of estimator. Simulation studies are carried out for illustration.     

Econometric analysis of present value models when the discount factor is near one

This paper develops asymptotic econometric theory to help understand data generated by a present value model with a discount factor near one. A leading application is to exchange rate models. A key assumption of the asymptotic theory is that the discount factor approaches one as the sample size grows. The finite sample approximation implied by the asymptotic theory is quantitatively congruent with the modest departures from random walk behavior that are typically found and with imprecise estimation of a well-studied regression relating spot and forward exchange rates.     

Asymptotic expansion of the power function of the two-sample binomial test with and without randomization

The paper deals with the asymptotic expansion of the power function of the two-sample binomial test. This test is a conditional test which is based upon the hypergeometric distribution, and we consider both the version with and without randomization. First, we give the asymptotic expansion of the hypergeometric distribution function and of its quantiles including randomization weights. Then we describe the asymptotic expansions of the power function of the two test versions and discuss the results.     

A note on a specification test of independence

In a recent paper Zheng (1997a) proposed a new specification test of independence between two random vectors by the kernel method. He showed asymptotic normality under the hypothesis and local alternatives. The present work investigates the asymptotic distribution of the corresponding test statistic under fixed alternatives. In this case asymptotic normality of a standardized statistic is still valid but with a different rate of convergence. Received: January 1999     

Efficient rank tests for semiparametric competing risk models

We consider a semiparametric competing risk model given by k independent survival times. The paper offers an asymptotic treatment of tests for the semiparametric null hypothesis of equality of the underlying risks. It turns out that modified rank tests are asymptotically efficient for certain semiparametric submodels, where the baseline hazard is a nuisance parameter. In addition, the asymptotic relative efficiency of the present tests is derived. A comparison of asymptotic power functions can then be used to classify various tests proposed earlier in the literature. For instance a chi-square type test is efficient for proportional hazards. Data driven tests of likelihood ratio type are proposed for cones of alternatives. We will consider certain stochastically increasing alternatives as a special example. The paper shows how the concept of local asymptotic normality of Le Cam works for hazard oriented models.     

Asymptotic distributions of impulse response functions in short panel vector autoregressions

This paper establishes the asymptotic distributions of the impulse response functions in panel vector autoregressions with a fixed time dimension. It also proves the asymptotic validity of a bootstrap approximation to their sampling distributions. The autoregressive parameters are estimated using the GMM estimators based on the first differenced equations and the error variance is estimated using an extended analysis-of-variance type estimator. Contrary to the time series setting, we find that the GMM estimator of the autoregressive coefficients is not asymptotically independent of the error variance estimator. The asymptotic dependence calls for variance correction for the orthogonalized impulse response functions. Simulation results show that the variance correction improves the coverage accuracy of both the asymptotic confidence band and the studentized bootstrap confidence band for the orthogonalized impulse response functions.     

Point optimal tests of the null hypothesis of cointegration

This paper obtains an asymptotic Gaussian power envelope for tests of the null hypothesis of cointegration. In addition, the paper proposes a feasible point optimal cointegration test whose local asymptotic power function is found to be close to the asymptotic Gaussian power envelope.     

Optimal convergence rates,Bahadur representation,and asymptotic normality of partitioning estimators

This paper studies the asymptotic properties of partitioning estimators of the conditional expectation function and its derivatives. Mean-square and uniform convergence rates are established and shown to be optimal under simple and intuitive conditions. The uniform rate explicitly accounts for the effect of moment assumptions, which is useful in semiparametric inference. A general asymptotic integrated mean-square error approximation is obtained and used to derive an optimal plug-in tuning parameter selector. A uniform Bahadur representation is developed for linear functionals of the estimator. Using this representation, asymptotic normality is established, along with consistency of a standard-error estimator. The finite-sample performance of the partitioning estimator is examined and compared to other nonparametric techniques in an extensive simulation study.     

Asymptotic inference from multi-stage samples

I develop a GMM-based framework for asymptotic inference to analyze data from surveys whose designs involve stratification and clustering. I set up the estimation problem, derive the appropriate asymptotic distribution theory as the number of clusters per stratum tends to infinity and compute asymptotic standard errors that are robust to sample-design effects. The analysis is then extended to nonparametric regression and to semiparametric estimation based on U-processes. Empirical illustrations are provided using consumption expenditure data from the complexly designed Indian national household survey.     

Asymptotic behavior of the estimated weights and of the estimated performance measures of the minimum VaR and the minimum CVaR optimal portfolios for dependent data

In this paper we derive the asymptotic distributions of the estimated weights and of estimated performance measures of the minimum value-at-risk portfolio and of the minimum conditional value-at-risk portfolio assuming that the asset returns follow a strictly stationary process. It is proved that the estimated weights as well as the estimated performance measures are asymptotically multivariate normally distributed. We also present an asymptotic test for the weights and a joint test for the characteristics of both portfolios. Moreover, the asymptotic densities of the estimated performance measures are compared with the corresponding exact densities. It is shown that the asymptotic approximation performs well even for the moderate sample size.     

Estimating non-simultaneous changes in the mean of vectors

A sequence of independent vectors with correlated components is considered. It is supposed that there is one change point in the mean of each component and changes need not occur simultaneously. The asymptotic distribution of the change point estimators is studied. If the true change points are well separated, the explicit asymptotic distribution of the change point estimators is presented. In the case the true change points coincide, it is shown that the limit distribution of properly standardized change points estimates exists. It depends not only on the underlying time series dependence structure, but also on the ratio of the sizes of the changes. The asymptotic distribution function is not known, but due to the invariance principle it can be obtained by simulations.     

Asymptotic behavior for S-estimators in random design linear model with long-range-dependent errors

The asymptotic behavior of S-estimators in a random design linear model with long-range-dependent Gaussian errors is considered. It turns out that the S-estimators of regression parameter and error variance are strongly consistent under mild conditions. Furthermore, the asymptotic distribution of the S-estimator of regression parameter is normal if the design vectors are i.i.d. and is non-normal if the design vectors are long-range dependent Gaussian vectors. We also show that the asymptotic distribution of S-estimator of the error variance is non-normal since the errors are long-range dependent. Supported by National Natural Science Foundation of China (Grant No. 10571159) and Specialized Research Fund for the Doctor Program of Higher Education (Grant No. 2002335090).     

M-estimation in the presence of unequal scale

Abstract  The class of weighted M-estimators is defined. The ratio of the asymptotic variance of the weighted estimator to the asymptotic variance of the optimally weighted estimator is defined as the inefficiency. A K antorovich inequality is proved, its implications are investigated for the misweighted mean and misweighted median, and the results are applied to a batch of demographic data.     

Instrumental variable estimation based on grouped data

The paper considers the estimation of the coefficients of a single equation in the presence of dummy intruments. We derive pseudo ML and GMM estimators based on moment restrictions induced either by the structural form or by the reduced form of the model. The performance of the estimators is evaluated for the non-Gaussian case. We allow for heteroscedasticity. The asymptotic distributions are based on parameter sequences where the number of instruments increases at the same rate as the sample size. Relaxing the usual Gaussian assumption is shown to affect the normal asymptotic distributions. As a result also recently suggested new specification tests for the validity of instruments depend on Gaussianity. Monte Carlo simulations confirm the accuracy of the asymptotic approach.     

Asymptotic and bootstrap prediction regions for vector autoregression

Small sample properties of asymptotic and bootstrap prediction regions for VAR models are evaluated and compared. Monte Carlo simulations reveal that the bootstrap prediction region based on the percentile-t method outperforms its asymptotic and other bootstrap alternatives in small samples. It provides the most accurate assessment of future uncertainty under both normal and non-normal innovations. The use of an asymptotic prediction region may result in a serious under-estimation of future uncertainty when the sample size is small. When the model is near non-stationary, the use of the bootstrap region based on the percentile-t method is recommended, although extreme care should be taken when it is used for medium to long-term forecasting.     

Gaussian semiparametric estimation of multivariate fractionally integrated processes

This paper analyzes the semiparametric estimation of multivariate long-range dependent processes. The class of spectral densities considered is motivated by and includes those of multivariate fractionally integrated processes. The paper establishes the consistency of the multivariate Gaussian semiparametric estimator (GSE), which has not been shown in other work, and the asymptotic normality of the GSE estimator. The proposed GSE estimator is shown to have a smaller limiting variance than the two-step GSE estimator studied by Lobato [1999. A semiparametric two-step estimator in a multivariate long memory model. Journal of Econometrics 90, 129–153]. Gaussianity is not assumed in the asymptotic theory. Some simulations confirm the relevance of the asymptotic results in samples of the size used in practical work.     

Estimation and model adequacy checking for multivariate seasonal autoregressive time series models with periodically varying parameters

We introduce a class of multivariate seasonal time series models with periodically varying parameters, abbreviated by the acronym SPVAR. The model is suitable for multivariate data, and combines a periodic autoregressive structure and a multiplicative seasonal time series model. The stationarity conditions (in the periodic sense) and the theoretical autocovariance functions of SPVAR stochastic processes are derived. Estimation and checking stages are considered. The asymptotic normal distribution of the least squares estimators of the model parameters is established, and the asymptotic distributions of the residual autocovariance and autocorrelation matrices in the class of SPVAR time series models are obtained. In order to check model adequacy, portmanteau test statistics are considered and their asymptotic distributions are studied. A simulation study is briefly discussed to investigate the finite-sample properties of the proposed test statistics. The methodology is illustrated with a bivariate quarterly data set on travelers entering in to Canada.