Test For Serial Independence Research Articles

Tests for independence between categorical variables

I prove the numerical equivalence between Pearson’s independence test statistic for categorical variables and the Lagrange Multiplier and overidentifying restrictions test statistics in several popular linear and non-linear regression models. I also show that its asymptotically equivalent Likelihood Ratio test is numerically identical in the non-linear regression models, and that the heteroskedasticity-robust Wald test statistic in the multivariate linear probability model and the moment condition model coincide with the Wald test statistic in the conditional multinomial model. Finally, I show that all these equivalences also apply to serial independence tests in discrete Markov chains. • Pearson’s independence test is numerically equivalent to the LM in regression models. • LR test is numerically identical in the non-linear regression models. • Heteroskedastic Wald test in LPM and GMM coincide with Wald in multinomial model. • All these equivalences apply to serial independence tests in discrete Markov chains.

Tests of serial dependence for multivariate time series with arbitrary distributions

In this paper, one studies tests of serial independence using a fixed number p of consecutive observations from a stationary time series, first in the univariate case, and then in the multivariate case, where even high-dimensional vectors can be used. The common distribution function is not assumed to be continuous, and the test statistics are based on the multilinear copula process. A bootstrap procedure based on multipliers is also proposed and shown to be valid. Tests based on Spearman’s rho and Kendall’s tau statistics are also considered, extending the results known for the case of continuous distributions. Contiguity results are obtained for some specific models and sufficient conditions for consistency of test statistics are stated, as well as a data-driven procedure to select p. Also, numerical experiments are performed to assess the finite sample level and power of the proposed tests. A case study using a time series of Arctic sea ice extent images is used to illustrate the usefulness of the proposed methodologies. The R package MixedIndTests (Nasri et al., 2022) includes all the methodologies proposed in this article.

Testing serial independence with functional data

We consider tests of serial independence for a sequence of functional observations. The new methods are formulated as L2-type criteria based on empirical characteristic functions and are convenient from the computational point of view. We derive asymptotic normality of the proposed test statistics for both discretely and continuously observed functions. In a Monte Carlo study, we show that the new test is sensitive with respect to functional GARCH alternatives, investigate the choice of necessary tuning parameters, and demonstrate that critical values obtained by resampling lead to a test with good performance in any setup, whereas the asymptotic critical values may be recommended only for a sufficiently fine discretization grid. Finite-sample comparison with a distance (auto)covariance test criterion is also included, and the article concludes with application on a real data set.

Testing for serial independence in vector autoregressive models

We consider tests for serial independence of arbitrary finite order for the innovations in vector autoregressive models. The tests are expressed as L2-type criteria involving the difference of the joint empirical characteristic function and the product of corresponding marginals. Asymptotic as well as Monte-Carlo results are presented.

Testing for Serial Independence: Beyond the Portmanteau Approach

ABSTRACTPortmanteau tests are typically used to test serial independence even if, by construction, they are generally powerful only in presence of pairwise dependence between lagged variables. In this article, we present a simple statistic defining a new serial independence test, which is able to detect more general forms of dependence. In particular, differently from the Portmanteau tests, the resulting test is powerful also under a dependent process characterized by pairwise independence. A diagram, based on p-values from the proposed test, is introduced to investigate serial dependence. Finally, the effectiveness of the proposal is evaluated in a simulation study and with an application on financial data. Both show that the new test, used in synergy with the existing ones, helps in the identification of the true data-generating process. Supplementary materials for this article are available online.

A sequential test for the specification of predictive densities

Summary We develop a specification test of predictive densities, based on the fact that the generalized residuals of correctly specified predictive density models are independent and identically distributed uniform. The proposed sequential test examines the hypotheses of serial independence and uniformity in two stages, wherein the first-stage test of serial independence is robust to violation of uniformity. The approach of the data-driven smooth test is employed to construct the test statistics. The asymptotic independence between the two stages facilitates proper control of the overall type I error of the sequential test. We derive the asymptotic null distribution of the test, which is free of nuisance parameters, and we establish its consistency. Monte Carlo simulations demonstrate excellent finite sample performance of the test. We apply this test to evaluate some commonly used models of stock returns.

Nonparametric testing for serial independence using the NRL statistic

ABSTRACTSerial independence is tested using two measures of the effects of noise reduction in chaotic data, proposed by Orzeszko (2005). The extensive Monte Carlo simulations on the size and power of the new permutation-based tests are performed. Four popular nonparametric tests for serial independence are employed as a benchmark. The conducted simulations show that the new tests may be effective tools for detecting different kinds of dependencies. Moreover, they can distinguish between nonlinearity in the mean and nonlinearity in the variance.

Serial independence tests for innovations of conditional mean and variance models

In this paper, one studies the asymptotic behavior of empirical processes based on consecutive residuals of univariate conditional mean and variance models. These processes are then used to develop tests of serial independence of the innovations. Even if the limiting distributions of the empirical processes depend on unknown parameters, it is shown that a Monte Carlo method based on the so-called multipliers can be applied to estimate the P values of the proposed test statistics. A simulation study is carried out to demonstrate the effectiveness of the proposed tests and the behavior of the statistics is also studied under contiguous alternatives.

Local Gaussian Autocorrelation and Tests for Serial Independence

The traditional and most used measure for serial dependence in a time series is the autocorrelation function. This measure gives a complete characterization of dependence for a Gaussian time series, but it often fails for nonlinear time series models as, for instance, the generalized autoregressive conditional heteroskedasticity model (GARCH), where it is zero for all lags. The autocorrelation function is an example of aglobalmeasure of dependence. The purpose of this article is to apply to time series a well‐definedlocalmeasure of serial dependence called the local Gaussian autocorrelation. It generally works well also for nonlinear models, and it can distinguish between positive and negative dependence. We use this measure to construct a test of independence based on the bootstrap technique. This procedure requires the choice of a bandwidth parameter that is calculated using a cross validation algorithm. To ensure the validity of the test, asymptotic properties are derived for the test functional and for the bootstrap procedure, together with a study of its power for different models. We compare the proposed test with one based on the ordinary autocorrelation and with one based on the Brownian distance correlation. The new test performs well. Finally, there are also two empirical examples.

Nonparametric bootstrap tests for independence of generalized errors

In this paper, we develop a general method of testing for independence when unobservable generalized errors are involved. Our method can be applied to testing for serial independence of generalized errors, and testing for independence between the generalized errors and observable covariates. The former can serve as a unified approach to testing the adequacy of time series models, as model adequacy often implies that the generalized errors obtained after a suitable transformation are independent and identically distributed. The latter is a key identification assumption in many nonlinear economic models. Our tests are based on a classical sample dependence measure, the Hoeffding–Blum–Kiefer–Rosenblatt‐type empirical process applied to generalized residuals. We establish a uniform expansion of the process, thereby deriving an explicit expression for the parameter estimation effect, which causes our tests not to be nuisance‐parameter‐free. To circumvent this problem, we propose a multiplier‐type bootstrap to approximate the limit distribution. Our bootstrap procedure is computationally very simple as it does not require a re‐estimation of the parameters in each bootstrap replication. Simulations and empirical applications to daily exchange rate data highlight the merits of our approach.

Herding During the Stock Market Bubble: An Intraday Analysis

This paper tests for the presence of herding on the New York Stock Exchange (NYSE). We measure the degree of herding from 1998-2001, the “bubble” period and its collapse. We estimate the incidence of herding by applying a test of serial independence in the observed interarrival times of trades. Our first and the most important finding is that the NYSE appears to function efficiently for the most part. However, the market does show some evidence of systemic herding. Second, the herding tends to be confined to larger stocks. Third, we find a weak negative relationship between dispersion of opinion among investors and herding measures. A noteworthy aspect of the analysis is that the data is analyzed using two different herding tests, and the results of the tests are compared using the Cochran-Mantel-Haenszel test for repeated tests of independence.

Adaptive permutation tests for serial independence

Permutation tests for serial independence using three different statistics based on empirical distributions are proposed. These tests are shown to be consistent under the alternative of m‐dependence and are all simple to perform in practice. A small simulation study demonstrates that the proposed tests have good power in small samples. The tests are then applied to Canadian gross domestic product (GDP data), corroborating the random‐walk hypothesis of GDP growth.

Tests of Randomness for Time Series

In this paper, one studies the asymptotic behavior of empirical processes based on consecutive residuals of univariate conditional mean and variance models. These processes are then used to develop tests of serial independence of the innovations. Even if the limiting distributions of the empirical processes depend on unknown parameters, it is shown that a Monte Carlo method based on the so-called multipliers can be applied in order to estimate the P-values of the proposed test statistics. A simulation study is carried out to demonstrate the effectiveness of the proposed tests and the behavior of the statistics is also studied under contiguous alternatives.

Testing for serial independence of panel errors

A test for the serial independence of errors in panel data models is proposed. The test is based on the difference between the joint empirical characteristic function of residuals at different lags and the product of their marginal empirical characteristic functions. The test is nuisance-parameter-free and powerful against any type of pairwise dependence at all lags. A simple random permutation procedure is used to approximate the limit distribution of the test. A Monte Carlo experiment illustrates the finite sample performance of the test, and supports that the test statistic based on the estimated residuals has the same asymptotic distribution as the corresponding statistic based on the unobservable true errors.

Testing Serial Independence via Density-Based Measures of Divergence

This article reviews some nonparametric serial independence tests based on measures of divergence between densities. Among others, the well-known Kullback–Leibler, Hellinger, Tsallis, and Rosenblatt divergences are analyzed. Moreover, their copula-based version is taken into account. Via a wide simulation study, the performances of the considered serial independence tests are compared under different settings. Both single-lag and multiple-lag testing procedures are investigated to find out the best “omnibus” solution.

Efficient market hypothesis: is the Croatian stock market as (in)efficient as the U.S. market

Traditional statistical tests of serial independence of stock price changes often show that stock markets are inefficient. Our analysis on daily and monthly data confirms this finding for the Croatian and U.S. markets in the 2002-2010 period. However, this result seems to be mainly due to the impact of the crisis of 2008-2009. The observation of monthly data in the pre-crisis period suggests market efficiency in the U.S. and (rather surprisingly) in Croatia also. Daily data indicate a high degree of efficiency of the US stock market before the crisis, but it is impossible to conclude with a satisfying level of confidence that the Croatian market was inefficient in that period. Furthermore, an elementary moving average crossover trading system beats the CROBEX and S&P 500 indices from 1997 to 2010, indicating market inefficiency. Still, if the same trading rule is applied to the S&P 500 index in an extended time period between 1950 and 2010, the conclusion about market inefficiency becomes less convincing. It seems that (in)efficiency varies both across markets and in the same markets in the long run, but it still remains unknown which processes are the driving factors behind these changes.

Variations on a theme: diversification of cuticular hydrocarbons in a clade of cactophilic Drosophila

BackgroundWe characterized variation and chemical composition of epicuticular hydrocarbons (CHCs) in the seven species of the Drosophila buzzatii cluster with gas chromatography/mass spectrometry. Despite the critical role of CHCs in providing resistance to desiccation and involvement in communication, such as courtship behavior, mating, and aggregation, few studies have investigated how CHC profiles evolve within and between species in a phylogenetic context. We analyzed quantitative differences in CHC profiles in populations of the D. buzzatii species cluster in order to assess the concordance of CHC differentiation with species divergence.ResultsThirty-six CHC components were scored in single fly extracts with carbon chain lengths ranging from C29 to C39, including methyl-branched alkanes, n-alkenes, and alkadienes. Multivariate analysis of variance revealed that CHC amounts were significantly different among all species and canonical discriminant function (CDF) analysis resolved all species into distinct, non-overlapping groups. Significant intraspecific variation was found in different populations of D. serido suggesting that this taxon is comprised of at least two species. We summarized CHC variation using CDF analysis and mapped the first five CHC canonical variates (CVs) onto an independently derived period (per) gene + chromosome inversion + mtDNA COI gene for each sex. We found that the COI sequences were not phylogenetically informative due to introgression between some species, so only per + inversion data were used. Positive phylogenetic signal was observed mainly for CV1 when parsimony methods and the test for serial independence (TFSI) were used. These results changed when no outgroup species were included in the analysis and phylogenetic signal was then observed for female CV3 and/or CV4 and male CV4 and CV5. Finally, removal of divergent populations of D. serido significantly increased the amount of phylogenetic signal as up to four out of five CVs then displayed positive phylogenetic signal.ConclusionsCHCs were conserved among species while quantitative differences in CHC profiles between populations and species were statistically significant. Most CHCs were species-, population-, and sex-specific. Mapping CHCs onto an independently derived phylogeny revealed that a significant portion of CHC variation was explained by species' systematic affinities indicating phylogenetic conservatism in the evolution of these hydrocarbon arrays, presumptive waterproofing compounds and courtship signals as in many other drosophilid species.

The difference-sign runs length distribution in testing for serial independence

We investigate the sequence of difference-sign runs length of a time series in the context of non-parametric tests for serial independence. This sequence is, under suitable conditioning, a stationary sequence and we prove that the normalized correlation of two consecutive runs length is small (≈0.0427). We use this result in a test based on the relative entropy of the empirical distribution of the runs length. We investigate the performance of the test in simulated series and test serial independence of cardiac data series in atrial fibrillation.

Nonparametric Entropy-Based Tests of Independence Between Stochastic Processes

This article develops nonparametric tests of independence between two stochastic processes satisfying β-mixing conditions. The testing strategy boils down to gauging the closeness between the joint and the product of the marginal stationary densities. For that purpose, we take advantage of a generalized entropic measure so as to build a whole family of nonparametric tests of independence. We derive asymptotic normality and local power using the functional delta method for kernels. As a corollary, we also develop a class of entropy-based tests for serial independence. The latter are nuisance parameter free, and hence also qualify for dynamic misspecification analyses. We then investigate the finite-sample properties of our serial independence tests through Monte Carlo simulations. They perform quite well, entailing more power against some nonlinear AR alternatives than two popular nonparametric serial-independence tests.

Tests of serial independence for continuous multivariate time series based on a Möbius decomposition of the independence empirical copula process

Genest and Remillard have recently studied tests of randomness based on a decomposition of the serial independence empirical copula process into a finite number of asymptotically independent sub-processes. A generalization of this decomposition that can be used to test serial independence in the continuous multivariate time series framework is investigated. The weak limits of the Cramer–von Mises statistics derived from the various processes under consideration are determined. As these statistics are not distribution-free, the consistency of the bootstrap methodology is investigated. Extensive simulations are used to study the finite-sample behavior of the tests for continuous time series of dimension one to three, and comparisons with the portmanteau test are provided, as well as, in the one-dimensional case, with the ranked-based version of the Brock, Dechert, and Scheinkman test. Finally, the studied tests are applied to a real trivariate financial time series.