Test For Serial Independence Research Articles

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 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-Rosenblat-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 reestimation of the parameters in each bootstrap replication. In a simulation study, we apply our method to test the adequacy of ARMA-GARCH and Hansen (1994) skewed t models, and document a good finite sample performance of our test. Finally, an empirical application to daily exchange rate data highlights the merits of our approach.

Formula omitted]-dependence statistics for mutual and serial independence of categorical variables

The Möbius transformation of probability cells in a multi-way contingency table is used to partition the Pearson chi-square test of mutual independence into A-dependence statistics. A similar partition is proposed for a universal and consistent test of serial independence in a stationary sequence of a categorical variable. The partition proposed can be adapted whether using estimated or theoretical marginal probabilities. With the aim of detecting a dependence of high order in a long sequence, A-dependence terms of the partition measuring increasing lagged dependences can be combined in a Box–Pierce type test of serial independence. A real data analysis of a nucleotides sequence using the Box–Pierce type test is provided.

Cyclone Tolerance in New World Arecaceae: Biogeographic Variation and Abiotic Natural Selection

Consistent abiotic factors can affect directional selection; cyclones are abiotic phenomena with near-discrete geographic limits. The current study investigates selective pressure of cyclones on plants at the species level, testing for possible natural selection. New World Arecaceae (palms) are used as a model system, as plants with monopodial, unbranched arborescent form are most directly affected by the selective pressure of wind load. Living specimens of known provenance grown at a common site were affected by the same cyclone. Data on percentage mortality were compiled and analysed in biogeographic and phylogenetic contexts. Palms of cyclone-prone provenance exhibited a much lower (one order of magnitude) range in cyclone tolerance, and significantly lower (P < 0.001) mean percentage mortality than collections from cyclone-free areas. Palms of cyclone-free provenance had much greater variation in tolerance, and significantly greater mean percentage mortality. A test for serial independence recovered no significant phylogenetic autocorrelation of percentage mortality. Variation in cyclone tolerance in New World Arecaceae correlates with biogeography, and is not confounded with phylogeny. These results suggest natural selection of cyclone tolerance in cyclone-prone areas.

Testing spatial randomness based on empirical distribution function: A study on lattice data

In this article, we extended the empirical distribution function based test statistic I k of Skaug and Tjostheim [1993. Nonparametric test of serial independence based on the empirical distribution function. Biometrika 80, 591–602] in the time series setting to D n for spatial lattice data and derived the asymptotic distribution of the proposed test statistic D n under the null hypothesis of spatial independence. The size and power of the proposed test statistic under conditional autoregressive model (CAR) were simulated. We applied D n , Moran's I and Geary's c to the transformed and well-studied sudden infant death syndrome data from North Carolina and found that D n produced a much smaller p -value in testing spatial independence.

Rank-based Entropy Tests for Serial Independence

In nonparametric tests for serial independence the marginal distribution of the data acts as an infinite dimensional nuisance parameter. The decomposition of joint distributions in terms of a copula density and marginal densities shows that in general empirical marginals carry no information on dependence. It follows that the order of ranks is sufficient for inference, which motivates transforming the data to a pre-specified marginal distribution prior to testing. As a test statistic we use an estimator of the marginal redundancy. We numerically study the finite sample properties of the tests obtained when the data are transformed to uniform as well as normal marginals. For comparison purposes we also derive a rank-based test against local ARCH alternatives. The performance of the new tests is compared with a modified version of the BDS test and with the Ljung-Box test.

Testing for phylogenetic signal in phenotypic traits: New matrices of phylogenetic proximities

Abouheif adapted a test for serial independence to detect a phylogenetic signal in phenotypic traits. We provide the exact analytic value of this test, revealing that it uses Moran's I statistic with a new matrix of phylogenetic proximities. We introduce then two new matrices of phylogenetic proximities highlighting their mathematical properties: matrix A which is used in Abouheif test and matrix M which is related to A and biodiversity studies. Matrix A unifies the tests developed by Abouheif, Moran and Geary. We discuss the advantages of matrices A and M over three widely used phylogenetic proximity matrices through simulations evaluating power and type-I error of tests for phylogenetic autocorrelation. We conclude that A enhances the power of Moran's test and is useful for unresolved trees. Data sets and routines are freely available in an online package and explained in an online supplementary file.

A test of serial independence of deviations from cointegrating relations

In this paper, we develop a method of testing whether deviations from a cointegration relationship are serially independent. Because whether deviations are serially independent is an important issue in the study of economics, the test offers benefits to practitioners.

Nonparametric Tests for Serial Independence Based on Quadratic Forms

Tests for serial independence and goodness-of-fit based on divergence notions between probability distributions, such as the Kullback-Leibler divergence or Hellinger distance, have recently received much interest in time series analysis. The aim of this paper is to introduce tests for serial independence using kernel-based quadratic forms. This separates the problem of consistently estimating the divergence measure from that of consistently estimating the underlying joint densities, the existence of which is no longer required. Exact level tests are obtained by implementing a Monte Carlo procedure using permutations of the original observations. The bandwidth selection problem is addressed by introducing a multiple bandwidth procedure based on a range of different bandwidth values. After numerically establishing that the tests perform well compared to existing nonparametric tests, applications to estimated time series residuals are considered. The approach is illustrated with an application to financial returns data.

Detecting serial dependence in tail events: a test dual to the BDS test

A test for serial independence is proposed which is related to the BDS test but focuses on tail event probabilities to obtain a test more suitable for detecting structure in standardized residuals of financial time series. The new test can be implemented easily by slight modification of the standard BDS test, and is also suitable for model identification. For all non-linear stochastic time series models examined the new test has increased power.

Adaptation of metabolism and evaporative water loss along an aridity gradient.

Broad-scale comparisons of birds indicate the possibility of adaptive modification of basal metabolic rate (BMR) and total evaporative water loss (TEWL) in species from desert environments, but these might be confounded by phylogeny or phenotypic plasticity. This study relates variation in avian BMR and TEWL to a continuously varying measure of environment, aridity. We test the hypotheses that BMR and TEWL are reduced along an aridity gradient within the lark family (Alaudidae), and investigate the role of phylogenetic inertia. For 12 species of lark, BMR and TEWL decreased along a gradient of increasing aridity, a finding consistent with our proposals. We constructed a phylogeny for 22 species of lark based on sequences of two mitochondrial genes, and investigated whether phylogenetic affinity played a part in the correlation of phenotype and environment. A test for serial independence of the data for mass-corrected TEWL and aridity showed no influence of phylogeny on our findings. However, we did discover a significant phylogenetic effect in mass-corrected data for BMR, a result attributable to common phylogenetic history or to common ecological factors. A test of the relationship between BMR and aridity using phylogenetic independent constrasts was consistent with our previous analysis: BMR decreased with increasing aridity.

Tests of serial independence based on Kendall's process

AbstractThe 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.

Detecting Serial Dependence in Tail Events: A Test Dual to the BDS Test

A test for serial independence is proposed which is related to the BDS test but focuses on tail event probabilities rather than probabilities near the center of the distribution. The motivation behind this approach is to obtain a test more suitable for detecting structure in the tails, such as remaining ARCH or GARCH type structure in standardized residuals of financial time series. The new test can be implemented easily by slight modification of the standard BDS test, and is also suitable for model identification. The BDS test and the modified version are compared numerically. To enable fair power comparisons, both tests are implemented as exact level Monte Carlo tests, enabling power calculations of the tests at identical actual sizes. The Monte Carlo implementation allows the use of test statistics which are considerably simpler than for the standard BDS test. For all nonlinear stochastic time series models examined the power of the new test is found to be uniformly larger over all practically reasonable values of the bandwidth parameter. The test is illustrated with an empirical application.

Tests for Serial Independence and Linearity Based on Correlation Integrals

We propose information theoretic tests for serial independence and linearity in time series against nonlinear dependence on lagged variables, based on the conditional mutual information. The conditional mutual information, which is a general measure for dependence, is estimated using the correlation integral from chaos theory. The significance of the test statistics is determined by means of bootstrap methods. The size and power properties of the tests are examined by simulation and illustrated with applications to real US GNP data.

A Nonparametric Test of Serial Independence for Time Series and Residuals

This paper presents nonparametric tests of independence that can be used to test the independence of p random variables, serial independence for time series, or residuals data. These tests are shown to generalize the classical portmanteau statistics. Applications to both time series and regression residuals are discussed.

A nonparametric test for serial independence of regression errors

A test for serial independence of regression errors is proposed that is consistent in the direction of serial dependence alternatives of first order. The test statistic is a function of a Hoeffding-Blum-Kiefer-Rosenblatt type of empirical process, based on residuals. The resultant statistic converges, surprisingly, to the same limiting distribution as the corresponding statistic based on true errors.

Nonparametric testing of the high-frequency efficiency of the 1997 Asian foreign exchange markets

Sherry’s nonparametric pattern tests for neural information processing are used to ascertain if the Asian foreign exchange (FX) rates followed random walks [Sherry, C.J., 1992. The Mathematics of Technical Analysis: Applying Statistics to Trading Stocks, Options and Futuresm Probus, Chicago]. The stationarity and serial independence of the price changes are tested on minute-by-minute data for nine Asian currencies from 1 January 1997 to 30 December 1997. The efficiency of these FX markets before and after the Asian currency ‘regime discontinuity’ are compared. The Thai baht (THB), Malaysian ringgit (MYR), Indonesian rupiah (IDR) and Singapore dollar (SGD) exhibited non-stationary behavior during the entire year, and gave evidence of a trading regime break, while the Phillipines’ peso (PHP), Taiwan dollar (TWD), Japanese yen (JYP) and German deutschmark (DEM) remained stationary, with the US dollar (USD) as numeraire. However, each half-year regime showed stationarity, indicating stable and nonchaotic trading regimes for all currencies, despite their high volatilities, except for the MYR, which exhibited non-stationarity in the second half of 1997. The Thai baht traded nonstationarily in the first half of 1997, but stationarily in the second half. while the TWD reversed that trading pattern. Based on Sherry’s four tests for serial independence, none of the currencies exhibited complete independence. Thus no Asian currency market—including the JYP—exhibited complete efficiency in 1997, in particular when compared with the highly efficient DEM. Remarkably, the PHP remained as efficient as the JYP throughout 1997.

Nonparametric Testing of the High-Frequency Efficiency of the 1997 Asian Foreign Exchange Markets

For the first time, non-parametric statistical tests, originally developed by Sherry (1992) to test the efficiency of information processing in nervous systems, are used to ascertain if the Asian FX rates followed random walks. The stationarity and serial independence of the price changes are tested on minute-by-minute data for nine currencies for the period from January 1, 1997 to December 30, 1997. Tested were the Thai baht, Indonesian rupiah, Malaysian ringgit, Philippines' peso, Singapore dollar, Taiwan dollar and the Hong Kong dollar, with the Japanese Yen and German Deutschmark as benchmarks (The U.S. Dollar is the base currency). The efficiency of these FX markets before and after the onset of the Asian currency turmoil (i.e., January 1 - June 30, 1997 and July 1 - December 30, 1997) are compared. The Thai baht, Malaysian ringgit, Indonesian rupiah and Singapore dollar exhibited non-stationary behavior during the entire year, and gave evidence of a trading regime break, while the Phillipines' peso, Taiwan dollar, Yen and Deutschmark remained stationary (The Hong Kong dollar was pegged). However, each half-year regime showed stationarity by itself, indicating stable and nonchaotic trading regimes for all currencies, despite the high volatilities, except the Malaysian ringgit, which exhibited non-stationarity in the second half of 1997. The Thai baht traded nonstationarily in the first half of 1997, but stationarily in the second half, while the Taiwan dollar reversed that trading pattern. Regarding Sherry's four serial independence tests of differential spectrum, relative price changes, temporal trading windows of at least 20 minutes long and price change category transitions: none of the currencies exhibited complete independence. Thus no Asian currency market - including the Yen - exhibited complete efficiency in 1997 regarding both stationarity and independence, in particular when compared with the highly efficient Deutschmark. But, remarkably, the Phillippines' peso remained as efficient as the Japanese Yen throughout 1997.

Testing for Pairwise Serial Independence Via the Empirical Distribution Function

Summary Built on Skaug and Tjøstheim's approach, this paper proposes a new test for serial independence by comparing the pairwise empirical distribution functions of a time series with the products of its marginals for various lags, where the number of lags increases with the sample size and different lags are assigned different weights. Typically, the more recent information receives a larger weight. The test has some appealing attributes. It is consistent against all pairwise dependences and is powerful against alternatives whose dependence decays to zero as the lag increases. Although the test statistic is a weighted sum of degenerate Cramér–von Mises statistics, it has a null asymptotic N(0, 1) distribution. The test statistic and its limit distribution are invariant to any order preserving transformation. The test applies to time series whose distributions can be discrete or continuous, with possibly infinite moments. Finally, the test statistic only involves ranking the observations and is computationally simple. It has the advantage of avoiding smoothed nonparametric estimation. A simulation experiment is conducted to study the finite sample performance of the proposed test in comparison with some related tests.

A consistent nonparametric test for serial independence

We propose a nonparametric test for serial independence against serial dependence of fixed order that is consistent against all such alternatives. The conditions required are weak, the asymptotic distribution under the null is χ 1 2, and the test works regardless of the underlying distribution. Also included are a nuisance parameter result, Monte Carlo simulations, a theoretical efficiency study, an empirical example, and a review of possible extensions. In addition, we derive a similar consistent test for lack of serial dependence of order one against serial dependence of order one.

Nonparametric statistics for testing of linearity and serial independence

For a series of independent identically distributed random variables {X t } the conditional mean and the conditional variance are given by M t (x)=E(X t ) and V k (x) = var(X t ). respectively This is used to construct a test of serial independence for a time series via a functional involving nonparametric estimates of M k (x) and V k (x). The resulting test is compared to a number of existing tests of serial independence, including the so-called BDS test, A linearity test can similarly be obtained by comparing M k (x) and V k, e (x) to ρ k x and . where ρ k = corr (X t X t−k ), and where V k.e (x) and are the conditional variance and the variance for the residual process from a linear fit. Resampling is essential to obtain an approximately correct size of the test, as asymptotic theory performs poorly. The tests are illustrated in a number of simulation experiments and on two real data examples.