Tests for Equality of Survival Distributions Against Non-Location Alternatives

We propose new two andk-sample tests for evaluating the equality of survival distributions against alternatives that include crossing of survival functions, and proportional and monotone hazard ratios. The tests allow for right censored data. The asymptotic power against local alternatives is investigated. Simulation results demonstrate that the new tests are more powerful than known tests when survival functions cross. We apply the tests to a well known study of chemo- and radio-therapy conducted by the Gastrointestinal Tumor Study Group. TheP-values for both proposed tests are much smaller than for other known tests.     

On testing for multivariate ARCH effects in vector time series models

Using a spectral approach, the authors propose tests to detect multivariate ARCH effects in the residuals from a multivariate regression model. The tests are based on a comparison, via a quadratic norm, between the uniform density and a kernel‐based spectral density estimator of the squared residuals and cross products of residuals. The proposed tests are consistent under an arbitrary fixed alternative. The authors present a new application of the test due to Hosking (1980) which is seen to be a special case of their approach involving the truncated uniform kernel. However, they typically obtain more powerful procedures when using a different weighting. The authors consider especially the procedure of Robinson (1991) for choosing the smoothing parameter of the spectral density estimator. They also introduce a generalized version of the test for ARCH effects due to Ling & Li (1997). They investigate the finite‐sample performance of their tests and compare them to existing tests including those of Ling & Li (1997) and the residual‐based diagnostics of Tse (2002).Finally, they present a financial application.     

Double threshold autoregressive conditionally heteroscedastic model building by genetic algorithms

Asymmetric behaviour in both mean and variance is often observed in real time series. The approach we adopt is based on double threshold autoregressive conditionally heteroscedastic (DTARCH) model with normal innovations. This model allows threshold nonlinearity in mean and volatility to be modelled as a result of the impact of lagged changes in assets and squared shocks, respectively. A methodology for building DTARCH models is proposed based on genetic algorithms (GAs). The most important structural parameters, that is regimes and thresholds, are searched for by GAs, while the remaining structural parameters, that is the delay parameters and models orders, vary in some pre-specified intervals and are determined using exhaustive search and an Asymptotic Information Criterion (AIC) like criterion. For each structural parameters trial set, a DTARCH model is fitted that maximizes the (penalized) likelihood (AIC criterion). For this purpose the iteratively weighted least squares algorithm is used. Then the best model according to the AIC criterion is chosen. Extension to the double threshold generalized ARCH (DTGARCH) model is also considered. The proposed methodology is checked using both simulated and market index data. Our findings show that our GAs-based procedure yields results that comparable to that reported in the literature and concerned with real time series. As far as artificial time series are considered, the proposed procedure seems to be able to fit the data quite well. In particular, a comparison is performed between the present procedure and the method proposed by Tsay [Tsay, R.S., 1989, Testing and modeling threshold autoregressive processes. Journal of the American Statistical Association, Theory and Methods, 84, 231–240.] for estimating the delay parameter. The former almost always yields better results than the latter. However, adopting Tsay's procedure as a preliminary stage for finding the appropriate delay parameter may save computational time specially if the delay parameter may vary in a large interval.     

Test of Normality Against Generalized Exponential Power Alternatives

The family of symmetric generalized exponential power (GEP) densities offers a wide range of tail behaviors, which may be exponential, polynomial, and/or logarithmic. In this article, a test of normality based on Rao's score statistic and this family of GEP alternatives is proposed. This test is tailored to detect departures from normality in the tails of the distribution. The main interest of this approach is that it provides a test with a large family of symmetric alternatives having non-normal tails. In addition, the test's statistic consists of a combination of three quantities that can be interpreted as new measures of tail thickness. In a Monte-Carlo simulation study, the proposed test is shown to perform well in terms of power when compared to its competitors.     

Splines for financial volatility

Summary.  We propose a flexible generalized auto-regressive conditional heteroscedasticity type of model for the prediction of volatility in financial time series. The approach relies on the idea of using multivariate B -splines of lagged observations and volatilities. Estimation of such a B -spline basis expansion is constructed within the likelihood framework for non-Gaussian observations. As the dimension of the B -spline basis is large, i.e. many parameters, we use regularized and sparse model fitting with a boosting algorithm. Our method is computationally attractive and feasible for large dimensions. We demonstrate its strong predictive potential for financial volatility on simulated and real data, and also in comparison with other approaches, and we present some supporting asymptotic arguments.     

A Locally Most Mean Powerful Based Score Test for ARCH and GARCH Regression Disturbances

This article considers the twin problems of testing for autoregressive conditional heteroscedasticity (ARCH) and generalized ARCH disturbances in the linear regression model. A feature of these testing problems, ignored by the standard Lagrange multiplier test, is that they are onesided in nature. A test that exploits this one-sided aspect is constructed based on the sum of the scores. The small-sample-size and power properties of two versions of this test under both normal and leptokurtic disturbances are investigated via a Monte Carlo experiment. The results indicate that both versions of the new test typically have superior power to two versions of the Lagrange multiplier test and possibly also more accurate asymptotic critical values.     

A Critical Review and a Comparative Study on Conditional Permutation Tests for Two-Way ANOVA

Two-way ANOVA methodology is surely one of the most important models in the framework of the experimental design theory, as suggested by the great number of proposed solutions given in literature. Among these, some solutions are nonparametric and particularly, thanks to the availability of modern powerful computing equipments, those based on conditional on observations permutation test have gained great interest. The aim of this work is to present and compare such proposals and to illustrate their possible advantages and disadvantages when applied to some real data-sets.     

Robust parametric tests of constant conditional correlation in a MGARCH model

This article provides a rigorous asymptotic treatment of new and existing asymptotically valid conditional moment (CM) testing procedures of the constant conditional correlation (CCC) assumption in a multivariate GARCH model. Full and partial quasi maximum likelihood estimation (QMLE) frameworks are considered, as is the robustness of these tests to non-normality. In particular, the asymptotic validity of the LM procedure proposed by Tse (2000 Tse, Y. K. (2000). A test for constant correlations in a multivariate GARCH model. Journal of Econometrics 98 (1):107–127.[Crossref], [Web of Science ®] , [Google Scholar]) is analyzed, and new asymptotically robust versions of this test are proposed for both estimation frameworks. A Monte Carlo study suggests that a robust Tse test procedure exhibits good size and power properties, unlike the original variant which exhibits size distortion under non-normality.     

A Conditional Variance Model for Daily Deviations of an Exchange Rate

A model for the distribution of daily deviations of an exchange rate is suggested. The distribution is Gaussian with a variance that depends on previous deviations. The model is applied to the exchange rate of the U.S. dollar to special drawing rights.     

The Asymptotic Power Of Jonckheere-Type Tests For Ordered Alternatives

For the c -sample location problem with ordered alternatives, the test proposed by Barlow et al . (1972 p. 184) is an appropriate one under the model of normality. For non-normal data, however, there are rank tests which have higher power than the test of Barlow et al ., e.g. the Jonckheere test or so-called Jonckheere-type tests recently introduced and studied by Büning & Kössler (1996). In this paper the asymptotic power of the Jonckheere-type tests is computed by using results of Hájek (1968) which may be considered as extensions of the theorem of Chernoff & Savage (1958). Power studies via Monte Carlo simulation show that the asymptotic power values provide a good approximation to the finite ones even for moderate sample sizes.     

Evaluation of Linear Trend Tests Using Resampling Techniques

A number of parametric and non-parametric linear trend tests for time series are evaluated in terms of test size and power, using also resampling techniques to form the empirical distribution of the test statistics under the null hypothesis of no linear trend. For resampling, both bootstrap and surrogate data are considered. Monte Carlo simulations were done for several types of residuals (uncorrelated and correlated with normal and nonnormal distributions) and a range of small magnitudes of the trend coefficient. In particular for AR(1) and ARMA(1, 1) residual processes, we investigate the discrimination of strong autocorrelation from linear trend with respect to the sample size. The correct test size is obtained for larger data sizes as autocorrelation increases and only when a randomization test that accounts for autocorrelation is used. The overall results show that the type I and II errors of the trend tests are reduced with the use of resampled data. Following the guidelines suggested by the simulation results, we could find significant linear trend in the data of land air temperature and sea surface temperature.     

Tests for Bivariate Symmetry Against Ordered Alternatives in Square Contingency Tables

Let X and Y denote two ordinal response variables, each having I levels. When subjects are classified on both variables, there are I 2 possible combinations of classifications. Let pij = Pr (X = i, Y = j) . This paper introduces a family of tests based on φ –divergence measures for testing H₀: pij = pji against H1: pij ≥ pji (I≥ j) ; and for testing H1 against H2: pij unrestricted. A simulation study assesses some of the family of tests introduced in this paper in comparison to the likelihood ratio test.     

Lag Length Selection in DF-GLS Unit Root Tests

We reinvestigate the empirical problem of lag length selection in unit root tests when using the augmented Dickey–Fuller test based on GLS-detrending. We extend the Ng and Perron (1995 Ng , S. , Perron , P. ( 1995 ). Unit root tests in ARMA models with data-dependent methods for the selection of the truncation lag . Journal of American Statistical Association 90 : 268 – 281 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) work on this issue by applying the finite sample critical values calculated using the formulae proposed by Cheung and Lai (1995 Cheung , Y. W. , Lai , K. S. ( 1995 ). Lag order and critical values of a modified Dickey–Fuller test . Oxford Bulletin of Business and Economics 57 : 411 – 418 .[Crossref] , [Google Scholar]). Unlike Ng and Perron (2001 Ng , S. , Perron , P. (2001). Lag length selection and the construction of unit root tests with good size and power. Econometrica 69:1519–1554.[Crossref], [Web of Science ®] , [Google Scholar]) we find through simulation studies that the method of selecting lag length using the sequential t-test in the ADF regression of GLS-detrended series performs the best in most cases.     

A Joint Test for Conditional Heteroscedasticity in Dynamic Panel Data Models

This article proposes a joint test for conditional heteroscedasticity in dynamic panel data models. The test is constructed by checking the joint significance of estimates of second to pth-order serial correlation in the squares sequence of the first differenced errors. To avoid any distribution assumptions of the errors and the effects, we adopt the GMM estimation for the parameter coefficient and higher order moment estimation for the errors. Based on the estimations, a joint test is constructed for conditional heteroscedasticity in the error. The resulted test is asymptotically chi-squared under the null hypothesis and easy to implement. The small sample properties of the test are investigated by means of Monte Carlo experiments. The evidence shows that the test performs well in dynamic panel data with large number n of individuals and short periods T of time. A real data is analyzed for illustration.     

Detecting Randomness: A Review of Existing Tests with New Comparisons

In this article we review and compare a number of existing tests for detecting randomness in time series data, with emphasis on stock market index data. By comparing variance ratio tests with traditional statistical tests, we have the most extensive simulation comparison of such procedures. The investigated tests are compared over a diverse group of distributions, models, and stock market applications. In our stock market data analysis, the choice of data transformation can have a noticeable effect on test results. This study provides the reader with a guide as to which test and transformation is most appropriate for their use.     

Conditional Studentized Survival Tests for Randomly Censored Models

It is shown that in the case of heterogenous censoring distributions Studentized survival tests can be carried out as conditional permutation tests given the order statistics and their censoring status. The result is based on a conditional central limit theorem for permutation statistics. It holds for linear test statistics as well as for sup-statistics. The procedure works under one of the following general circumstances for the two-sample problem: the unbalanced sample size case, highly censored data, certain non-convergent weight functions or under alternatives. For instance, the two-sample log rank test can be carried out asymptotically as a conditional test if the relative amount of uncensored observations vanishes asymptotically as long as the number of uncensored observations becomes infinite. Similar results hold whenever the sample sizes and are unbalanced in the sense that and hold.     

Modelling asymmetric volatility dynamics by multivariate BL-GARCH models

The class of Multivariate BiLinear GARCH (MBL-GARCH) models is proposed and its statistical properties are investigated. The model can be regarded as a generalization to a multivariate setting of the univariate BL-GARCH model proposed by Storti and Vitale (Stat Methods Appl 12:19–40, 2003a; Comput Stat 18:387–400, 2003b). It is shown how MBL-GARCH models allow to account for asymmetric effects in both conditional variances and correlations. An EM algorithm for the maximum likelihood estimation of the model parameters is derived. Furthermore, in order to test for the appropriateness of the conditional variance and covariance specifications, a set of robust conditional moments test statistics are defined. Finally, the effectiveness of MBL-GARCH models in a risk management setting is assessed by means of an application to the estimation of the optimal hedge ratio in futures hedging.     

Conditional heteroscedasticity test for Poisson autoregressive model

In this article, the problem of interest is testing the conditional heteroscedasticity of Poisson autoregressive model. We construct a non parametric test statistic based on empirical likelihood method. The asymptotic distribution of the proposed statistic is derived and its finite-sample property is examined through Monte Carlo simulations. The simulation results show that the proposed method is good for practical use.     

Weighted Logrank Permutation Tests for Randomly Right Censored Life Science Data

In biomedical research, weighted logrank tests are frequently applied to compare two samples of randomly right censored survival times. We address the question how to combine a number of weighted logrank statistics to achieve good power of the corresponding survival test for a whole linear space or cone of alternatives, which are given by hazard rates. This leads to a new class of semiparametric projection tests that are motivated by likelihood ratio tests for an asymptotic model. We show that these tests can be carried out as permutation tests and discuss their asymptotic properties. A simulation study together with the analysis of a classical data set illustrates the advantages.