On consistent testing for serial correlation in seasonal time series models

The author considers serial correlation testing in seasonal time series models. He proposes a test statistic based on a spectral approach. Many tests of this type rely on kernel-based spectral density estimators that assign larger weights to low order lags than to high ones. Under seasonality, however, large autocorrelations may occur at seasonal lags that classical kernel estimators cannot take into account. The author thus proposes a test statistic that relies on the spectral density estimator of Shin (2004), whose weighting scheme is more adapted to this context. The distribution of his test statistic is derived under the null hypothesis and he studies its behaviour under fixed and local alternatives. He establishes the consistency of the test under a general fixed alternative. He also makes recommendations for the choice of the smoothing parameters. His simulation results suggest that his test is more powerful against seasonality than alternative procedures based on classical weighting schemes. He illustrates his procedure with monthly statistics on employment among young Americans.     

Dimension reduction for the conditional mean and variance functions in time series

This paper deals with the nonparametric estimation of the mean and variance functions of univariate time series data. We propose a nonparametric dimension reduction technique for both mean and variance functions of time series. This method does not require any model specification and instead we seek directions in both the mean and variance functions such that the conditional distribution of the current observation given the vector of past observations is the same as that of the current observation given a few linear combinations of the past observations without loss of inferential information. The directions of the mean and variance functions are estimated by maximizing the Kullback–Leibler distance function. The consistency of the proposed estimators is established. A computational procedure is introduced to detect lags of the conditional mean and variance functions in practice. Numerical examples and simulation studies are performed to illustrate and evaluate the performance of the proposed estimators.     

Adaptive test for mean vectors of high-dimensional time series data with factor structure

Statistical inference of high-dimensional time series data is of increasing interest in various fields such as social sciences and biology. In this article, we consider the problem of testing the equality of high-dimensional mean vectors in the approximate factor model, which allows for time series dependence among distinct observations and more flexible dependence within observations. We propose a data-adaptive test based on the factor-adjusted data rather than on the directly observed data. By combining the tests with different norms, the proposed test adapts to various alternative scenarios and thus overcomes the shortcomings of the tests based either on $L_2$-norm or $L_{\infty }$-norm. Multiplier bootstrap method is utilized to approximate the true underlying distribution of the proposed test statistics. Theoretical analysis shows that the proposed test enjoys desirable properties. Besides, we conduct thorough numerical study to compare the empirical performance of the proposed test with some state-of-the-art tests. A real stock market data set is analyzed to show the empirical usefulness of the proposed test.     

Tests of serial independence based on Kendall's process

The authors propose new rank statistics for testing the white noise hypothesis in a time series. These statistics are Cramér‐von Mises and Kolmogorov‐Smirnov functionals of an empirical distribution function whose mean is related to a serial version of Kendall's tau through a linear transform. The authors determine the asymptotic behaviour of the underlying serial process and the large‐sample distribution of the proposed statistics under the null hypothesis of white noise. They also present simulation results showing the power of their tests.     

On testing for causality in variance between two multivariate time series

Verifying the existence of a relationship between two multivariate time series represents an important consideration. In this article, the procedure developed by Cheung and Ng [A causality-in-variance test and its application to financial market prices, J. Econom. 72 (1996), pp. 33–48] designed to test causality in variance for univariate time series is generalized in several directions. A first approach proposes test statistics based on residual cross-covariance matrices of squared (standardized) residuals and cross products of (standardized) residuals. In a second approach, transformed residuals are defined for each residual vector time series, and test statistics are constructed based on the cross-correlations of these transformed residuals. Test statistics at individual lags and portmanteau-type test statistics are developed. Conditions are given under which the new test statistics converge in distribution towards chi-square distributions. The proposed methodology can be used to determine the directions of causality in variance, and appropriate test statistics are presented. Monte Carlo simulation results show that the new test statistics offer satisfactory empirical properties. An application with two bivariate financial time series illustrates the methods.     

Testing for a unit root in a nonlinear quantile autoregression framework

The nonlinear unit root test of Kapetanios, Shin, and Snell (2003 Kapetanios, G., Shin, Y., Snell, A. (2003). Testing for a unit root in the nonlinear STAR framework. Journal of Econometrics 112:359–379.[Crossref], [Web of Science ®] , [Google Scholar]) (KSS) has attracted much recent attention. However, the KSS test relies on the ordinary least squares (OLS) estimator, which is not robust to a heavy-tailed distribution and, in practice, the test suffers from a large power loss. This study develops three kinds of quantile nonlinear unit root tests: the quantile t-ratio test; the quantile Kolmogorov–Smirnov test; and the quantile Cramer–von Mises test. A Monte Carlo simulation shows that these tests have significantly better power when an innovation follows a non-normal distribution. In addition, the quantile t-ratio test can reveal the heterogeneity of the asymmetric dynamics in a time series. In our empirical studies, we investigate the unit root properties of U.S. macroeconomic time series and the real effective exchange rates for 61 countries. The results show that our proposed tests reject the unit roots more often, indicating that the series are likely to be asymmetric nonlinear reverting processes.     

An Empirical Analysis of Some Nonparametric Goodness-of-Fit Tests for Censored Data

In this article, we consider some nonparametric goodness-of-fit tests for right censored samples, viz., the modified Kolmogorov, Cramer–von Mises–Smirnov, Anderson–Darling, and Nikulin–Rao–Robson χ² tests. We also consider an approach based on a transformation of the original censored sample to a complete one and the subsequent application of classical goodness-of-fit tests to the pseudo-complete sample. We then compare these tests in terms of power in the case of Type II censored data along with the power of the Neyman–Pearson test, and draw some conclusions. Finally, we present an illustrative example.     

Test for the existence of finite moments via bootstrap

This paper develops a bootstrap hypothesis test for the existence of finite moments of a random variable, which is nonparametric and applicable to both independent and dependent data. The test is based on a property in bootstrap asymptotic theory, in which the m out of n bootstrap sample mean is asymptotically normal when the variance of the observations is finite. Consistency of the test is established. Monte Carlo simulations are conducted to illustrate the finite sample performance and compare it with alternative methods available in the literature. Applications to financial data are performed for illustration.     

New Goodness of Fit Tests Based on Stochastic EDF

A new approach of randomization is proposed to construct goodness of fit tests generally. Some new test statistics are derived, which are based on the stochastic empirical distribution function (EDF). Note that the stochastic EDF for a set of given sample observations is a randomized distribution function. By substituting the stochastic EDF for the classical EDF in the Kolmogorov–Smirnov, Cramér–von Mises, Anderson–Darling, Berk–Jones, and Einmahl–Mckeague statistics, randomized statistics are derived, of which the qth quantile and the expectation are chosen as test statistics. In comparison to existing tests, it is shown, by a simulation study, that the new test statistics are generally more powerful than the corresponding ones based on the classical EDF or modified EDF in most cases.     

Hybrid regions for post-change mean in a sequence of normal variables

The hybrid bootstrap uses resampling ideas to extend the duality approach to the interval estimation for a parameter of interest when there are nuisance parameters. The confidence region constructed by the hybrid bootstrap may perform much better than the ordinary bootstrap region in a situation where the data provide substantial information about the nuisance parameter, but limited information about the parameter of interest. We apply this method to estimate the post-change mean after a change is detected by a stopping procedure in a sequence of independent normal variables. Since distribution theory in change point problems is generally a challenge, we use bootstrap simulation to find empirical distributions of test statistics and calculate critical thresholds. Both likelihood ratio and Bayesian test statistics are considered to set confidence regions for post-change means in the normal model. In the simulation studies, the performance of hybrid regions are compared with that of ordinary bootstrap regions in terms of the widths and coverage probabilities of confidence intervals.     

Comparison of pivotals for confidence bounds and intervals for the mean of a stationary time series

We construct new pivotals to obtain confidence bounds and confidence intervals for the mean of a stationary process. These follow the approach based on estimating functions. The new pivotals are compared with the standard pivotal based on studentization. We study the first four cumulants of each of these pivotals and explain why the pivotals based on the estimating function approach result in better coverage probabilities. Some simulation results comparing these pivotals have been reported.     

Model selection criteria for reduced rank multivariate time series: a simulation study

The main focus of our paper is to compare the performance of different model selection criteria used for multivariate reduced rank time series. We consider one of the most commonly used reduced rank model, that is, the reduced rank vector autoregression (RRVAR (p, r)) introduced by Velu et al. [Reduced rank models for multiple time series. Biometrika. 1986;7(31):105–118]. In our study, the most popular model selection criteria are included. The criteria are divided into two groups, that is, simultaneous selection and two-step selection criteria, accordingly. Methods from the former group select both an autoregressive order p and a rank r simultaneously, while in the case of two-step criteria, first an optimal order p is chosen (using model selection criteria intended for the unrestricted VAR model) and then an optimal rank r of coefficient matrices is selected (e.g. by means of sequential testing). Considered model selection criteria include well-known information criteria (such as Akaike information criterion, Schwarz criterion, Hannan–Quinn criterion, etc.) as well as widely used sequential tests (e.g. the Bartlett test) and the bootstrap method. An extensive simulation study is carried out in order to investigate the efficiency of all model selection criteria included in our study. The analysis takes into account 34 methods, including 6 simultaneous methods and 28 two-step approaches, accordingly. In order to carefully analyse how different factors affect performance of model selection criteria, we consider over 150 simulation settings. In particular, we investigate the influence of the following factors: time series dimension, different covariance structure, different level of correlation among components and different level of noise (variance). Moreover, we analyse the prediction accuracy concerned with the application of the RRVAR model and compare it with results obtained for the unrestricted vector autoregression. In this paper, we also present a real data application of model selection criteria for the RRVAR model using the Polish macroeconomic time series data observed in the period 1997–2007.     

Detection of patterns in noisy time series

In the context of a research project in ergonomy, myoelectric signals monitored over two to three hour periods gave rise to long noisy time series, which were smoothed using running medians. Tests developed by the authors show that the patterns displayed by the smoothed time series are not artifacts of smoothed white noise. Indeed, the smoothed series show amplitude fluctuations and short‐term correlations which are larger than those obtained by applying running medians to independent, identically distributed data. The key idea is that of reduction of data to binary signals.     

Polynomial trends in time series

The J^* test which was previously proposed by the present author for the detection of a trend in a time series does not depend on any quantitative assumptions, but in the case of a polynomial trend it depends on its degree; if this degree is too high, the test cannot be applied. The author finds a bound of the significance level at which the test can be applied when the sample size, as well as a bound of the degree of the trend, are given. Asymptotic results are used only when we trust the asymptotic distribution of J^* under the null hypothesis.     

Portmanteau tests for linearity of stationary time series

This article considers the problem of testing for linearity of stationary time series. Portmanteau tests are discussed which are based on generalized correlations of residuals from a linear model (that is, autocorrelations and cross-correlations of different powers of the residuals). The finite-sample properties of the tests are assessed by means of Monte Carlo experiments. The tests are applied to 100 time series of stock returns.     

Intervention time series analysis of voluntary,counselling and testing on HIV infections in West African sub-region: the case of Ghana

In this paper, intervention time series models were developed to examine the effectiveness of the voluntary counselling and testing (VCT) programme in the northern and southern sectors of Ghana. Pre-intervention data of HIV reported cases in the northern and southern sectors were first modelled as Box–Jenkins univariate time series. Second, the adopted models from the pre-intervention data were extended to include the intervention variable. The intervention variable was coded as zero for the pre-intervention period (1 January 1996–31 December 2002) and one for the post-intervention period (1 January 2003–31 December 2007). The models developed were applied to the entire data for the two sectors to estimate the effect of the VCT programme. Our findings indicate that the VCT programme was found to be associated with detection of 20 and 40 new HIV infections per 100,000 persons per month in the northern and southern sectors (p?相似文献   

A Goodness-of-Fit Test for a Class of Autoregressive Conditional Duration Models

This article develops a method for testing the goodness-of-fit of a given parametric autoregressive conditional duration model against unspecified nonparametric alternatives. The test statistics are functions of the residuals corresponding to the quasi maximum likelihood estimate of the given parametric model, and are easy to compute. The limiting distributions of the test statistics are not free from nuisance parameters. Hence, critical values cannot be tabulated for general use. A bootstrap procedure is proposed to implement the tests, and its asymptotic validity is established. The finite sample performances of the proposed tests and several other competing ones in the literature, were compared using a simulation study. The tests proposed in this article performed well consistently throughout, and they were either the best or close to the best. None of the tests performed uniformly the best. The tests are illustrated using an empirical example.     

Priors and component structures in autoregressive time series models

New approaches to prior specification and structuring in autoregressive time series models are introduced and developed. We focus on defining classes of prior distributions for parameters and latent variables related to latent components of an autoregressive model for an observed time series. These new priors naturally permit the incorporation of both qualitative and quantitative prior information about the number and relative importance of physically meaningful components that represent low frequency trends, quasi-periodic subprocesses and high frequency residual noise components of observed series. The class of priors also naturally incorporates uncertainty about model order and hence leads in posterior analysis to model order assessment and resulting posterior and predictive inferences that incorporate full uncertainties about model order as well as model parameters. Analysis also formally incorporates uncertainty and leads to inferences about unknown initial values of the time series, as it does for predictions of future values. Posterior analysis involves easily implemented iterative simulation methods, developed and described here. One motivating field of application is climatology, where the evaluation of latent structure, especially quasi-periodic structure, is of critical importance in connection with issues of global climatic variability. We explore the analysis of data from the southern oscillation index, one of several series that has been central in recent high profile debates in the atmospheric sciences about recent apparent trends in climatic indicators.     

Testing time series for interpolability and whiteness

We propose a test to decide if a time series is represented by its linear interpolator better than by its mean value. The same test can be employed to decide if a time series has to be considered white noise. The test is based on a new estimate of the index of linear determinism (Battaglia, 1983, Inverse autocovariances and a measure of linear determinism for a stationary process, J. Time Series Anal. 4, 79-87) and its asymptotic distribution is derived. Comparison with the popular Ljung-Box portmanteau test has been performed based on both asymptotic power and a simulation experiment. The new test