Robust estimators of ar-models : a comparison

Many regression-estimation techniques have been extended to cover the case of dependent observations. The majority of such techniques are developed from the classical least squares, M and GM approaches and their properties have been investigated both on theoretical and empirical grounds. However, the behavior of some alternative methods- with satisfactory performance in the regression case- has not received equal attention in the context of time series. A simulation study of four robust estimators for autoregressive models containing innovation or additive outliers is presented. The robustness and efficiency properties of the methods are exhibited, some finite-sample results are discussed in combination with theoretical properties and the relative merits of the estimators are viewed in connection with the outlier-generating scheme.peer-reviewe

Fourier-type monitoring procedures for strict stationarity

We consider model-free monitoring procedures for strict stationarity of a given time series. The new criteria are formulated as L2-type statistics incorporating the empirical characteristic function. Asymptotic as well as Monte Carlo results are presented. The new methods are also employed in order to test for possible stationarity breaks in time-series data from the financial sector

Fourier methods for analysing piecewise constant volatilities

We develop procedures for testing the hypothesis that a parameter of a distribution is constant throughout a sequence of independent random variables. Our proposals are illustrated considering the variance and the kurtosis. Under the null hypothesis of constant variance, the modulus of a Fourier type transformation of the volatility process is identically equal to one. The approach proposed utilizes this property considering a canonical estimator for this modulus under the assumption of indepen- dent and piecewise identically distributed observations with zero mean. Using blockwise estimators we introduce several test statistics resulting from different weight functions which are all given by simple explicit for- mulae. The methods are compared to other tests for constant volatility in extensive Monte Carlo experiments. Our proposals offer comparatively good power particularly in the case of multiple structural breaks and allow adequate estimation of the positions of the structural breaks. An appli- cation to process control data is given, and it is shown how the methods can be adapted to test for constancy of other quantities like the kurtosis

Characterizations of multinormality and corresponding tests of fit, including for Garch models

We provide novel characterizations of multivariate normality that incorporate both the characteristic function and the moment generating function, and we employ these results to construct a class of affine invariant, consistent and easy-to-use goodness-of-fit tests for normality. The test statistics are suitably weighted L2-statistics, and we provide their asymptotic behavior both for i.i.d. observations as well as in the context of testing that the innovation distribution of a multivariate GARCH model is Gaussian. We also study the finite-sample behavior of the new tests and compare the new criteria with alternative existing tests

Tests for circular symmetry of complex-valued random vectors

We propose tests for the null hypothesis that the law of a complex-valued random vector is circularly symmetric. The test criteria are formulated as $L^2$-type criteria based on empirical characteristic functions, and they are convenient from the computational point of view. Asymptotic as well as Monte-Carlo results are presented. Applications on real data are also reported. An R package called CircSymTest is available from the authors

A class of goodness-of-fit tests for circular distributions based on trigonometric moments

We propose a class of goodness–of–fit test procedures for arbitrary parametric families of circular distributions with unknown parameters. The tests make use of the specific form of the characteristic function of the family being tested, and are shown to be consistent. We derive the asymptotic null distribution and suggest that the new method be implemented using a bootstrap resampling technique that approximates this distribution consistently. As an illustration, we then specialize this method to testing whether a given data set is from the von Mises distribution, a model that is commonly used and for which considerable theory has been developed. An extensive Monte Carlo study is carried out to compare the new tests with other existing omnibus tests for this model. An application involving five real data sets is provided in order to illustrate the new procedure.Peer Reviewe

A Powerful Method of Assessing the Fit of the Lognormal Distribution

When faced with the problem of goodness-of-fit to the Lognormal distribution, testing methods typically reduce to comparing the empirical distribution function of the corresponding logarithmic data to that of the normal distribution. In this article, we consider a family of test statistics which make use of the moment structure of the Lognormal law. In particular, a continuum of moment conditions is employed in the construction of a new statistic for this distribution. The proposed test is shown to be consistent against fixed alternatives, and a simulation study shows that it is more powerful than several classical procedures, including those utilizing the empirical distribution function. We conclude by applying the proposed method to some, not so typical, data sets