Test For Serial Independence Research Articles

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.

A Nonparametric Test of Serial Independence Based on the Empirical Distribution Function

A Nonparametric Test of Serial Independence Based on the Empirical Distribution Function

Tests of Independence in Parametric Models With Applications and Illustrations

Tests of independence between variables in a wide variety of discrete and continuous bivariate and multivariate regression equations are derived using results from the theory of series expansions of joint distributions in terms of marginal distributions and their related orthonormal polynomials. The tests are conditional moment tests based on covariances between pairs of orthonormal polynomials. Examples include tests of serial independence against bilinear and/or autoregressive conditional heteroscedasticity alternatives, tests of dependence in multivariate normal regression models, and dependence in count-data models. Monte Carlo simulation based on bivariate count models is used to evaluate the. size and power properties of the proposed tests. A multivariate count-data model for Australian health-care-utilization data is used to empirically illustrate the tests.

Tests of Independence in Parametric Models with Applications and Illustrations

Tests of independence between variables in discrete and continuous bivariate and multivariate regression equations are derived using series expansions of joint distributions in terms of marginal distributions and their related orthonormal polynomials. Th e tests are conditional moment tests based on covariances between pair s of orthonormal polynomials. Examples include tests of serial independence against bilinear and/or autoregressive conditional heteroskedasticity alternatives, dependence in multivariate normal regression models, and dependence in count data models. Monte Carlo simulations based on bivariate counts are used to evaluate the tests. A multivariate count data model for Australian health-care utilization data is used for illustration. (This abstract was borrowed from another version of this item.) (This abstract was borrowed from another version of this item.) (This abstract was borrowed from another version of this item.) (This abstract was borrowed from another version of this item.) (This abstract was borrowed from another version of this item.) (This abstract was borrowed from another version of this item.) (This abstract was borrowed from another version of this item.)

A nonparametric test of serial independence based on the empirical distribution function

The Blum, Kiefer & Rosenblatt (1961) statistic for testing independence is considered in a time series setting. This test is, under mild conditions, shown to be consistent against lag one dependent alternatives. The null distribution of the test statistic is established, both when the marginal distribution is continuous and when it is discrete. Simulation results giving information on the size and the power of the test are provided, and comparisons are made with other tests of serial dependence. An extension of the test is made to detect higher lag dependence, and finally the test is applied to a real data example

Consistent Nonparametric Entropy-Based Testing

form the test statistic. In order to obtain a normal null limiting distribution, a form of weighting is employed. The test is also shown to be consistent against a class of alternatives. The exposition focusses on testing for serial independence in time series, with a small application to testing the random walk hypothesis for exchange rate series, and tests of some other hypotheses of econometric interest are briefly described. This paper proposes a new class of tests for nonparametric hypotheses, with special reference to the problem of testing for independence in time series in the presence of a nonparametric marginal distribution under the null. The critical region of the tests is the upper tail of the distribution of an estimate of the Kullback-Leibler information criterion, whose desirable properties make it convenient to describe in a reasonably comprehensible fashion some of the consistent directions. A test is consistent against one direction of departure from the null hypothesis if the probability of rejection approaches one no matter how small the departure in that direction. For continuous distributions, two random variables Y and Z are independent if and only if their joint probability density f(y, z) equals the product of the marginal densities g(y) and h(z) for all y, z; our test for independence is consistent wherever f(y, z) deviates from g(y)h(z) by even small amounts on a set of arbitrarily small non-zero measure, providing some regularity conditions hold. It will be helpful to briefly introduce the Kullback-Leibler information criterion and describe some of its properties. Following definitions of the entropy of a distribution by Shannon (1948), Wiener (1948), a measure of information for discriminating between two hypotheses was proposed by Kullback and Leibler (1951). Let X be a p-vector-valued random variable with absolutely continuous distribution function. Consider the hypotheses HI: pdf(X) = f(x) H2: pdf(X) = g(x). The mean information for discrimination between HI and H2 per observation from f is

A Nonparametric Distribution-Free Test for Serial Independence in Stock Returns: A Comment

We have confirmed that Corrado and Schatzberg's (1990) criticism of our test for serial independence in stock returns (Ashley and Patterson (1986)) is correct. The corrected results still favor rejection of the null hypothesis that the daily returns for several stocks (notably Holly Sugar (HLY) and E Systems (ESY)) are serially independent, but only at the 12-percent and 14-percent significance levels, respectively. Evidently, this kind of test is long on simplicity and intuitive appeal, but short on power.

A Nonparametric Distribution-Free Test for Serial Independence in Stock Returns: A Correction

A fundamental statistical test of serial independence developed by Ashley and Patterson (1986) to examine a possible form of serial dependence in daily stock returns is shown to be improperly constructed. As a consequence, the significance probabilities that they ob? tain are overstated. This paper presents a corrected version of their test. The test statistic obtained after correction is shown to possess the same limiting distribution as the Kolmogorov-Smirnov test statistic. Applying the corrected test procedure to data identical to that used by Ashley and Patterson, we find that their original null hypothesis can no longer be rejected at conventional significance levels.

A NEW LOOK AT FLOOD RISK DETERMINATION1

ABSTRACT: The probability distributions of annual peak flows used in flood risk analysis quantify the risk that a design flood will be exceeded. But the parameters of these distributions are themselves to a degree uncertain and this uncertainty increases the risk that the flood protection provided will in fact prove to be inadequate. The increase in flood risk due to parameter uncertainty is small when a fairly long record of data is available and the annual flood peaks are serially independent, which is the standard assumption in flood frequency analysis. But standard tests for serial independence are insensitive to the type of grouping of high and low values in a time series, which is measured by the Hurst coefficient. This grouping increases the parameter uncertainty considerably. A study of 49 annual peak flow series for Canadian rivers shows that many have a high Hurst coefficient. The corresponding increase in flood risk due to parameter uncertainty is shown to be substantial even for rivers with a long record, and therefore should not be neglected. The paper presents a method of rationally combining parameter uncertainty due to serial correlation, and the stochastic variability of peak flows in a single risk assessment. In addition, a relatively simple time series model that is capable of reproducing the observed serial correlation of flood peaks is presented.

A Nonparametric, Distribution-Free Test for Serial Independence in Stock Returns

A fundamental statistical test of serial independence is developed and applied to daily stock returns. Let xt be the deviation of the daily return on a stock from its sample mean after any autocorrelation present has been removed. If xt is serially independent, then the cumulative sum of xt over time is the position of a one-dimensional random walk on a line. The empirical distribution of step lengths over a large sample allows the distribution of the largest absolute excursion in a T-step walk to be calculated by repeated simulation. The observed maximal excursions are found to be significantly smaller than one would expect, based on serial independence and the observed distribution of step lengths. It is concluded that these daily stock returns are not serially independent and that the market value of the corporations studied has a tendency to return to an interval around the trend value.

A Note of Correction to Guilkey's Test for Serial Independence in Simultaneous Equations Models

A Note of Correction to Guilkey's Test for Serial Independence in Simultaneous Equations Models

Testing for Serial Correlation in Least-Squares Regression When Some of the Regressors are Lagged Dependent Variables

The construction of tests of model specification is considered from a general point of view. The results are applied to testing the serial independence of the disturbances in a regression model where some of the regressors are lagged dependent variables. It is shown that the asymptotic distribution of the lag-1 serial correlation coefficient calculated from the least-squares residuals differs from that of the coefficient calculated from the true disturbances. A consequence of this is that tests of serial independence based on the residuals from regression on fixed regressors are invalid when applied to models containing lagged dependent variables even when the null hypothesis of serial independence is true. Tests which are asymptotically valid for the large-sample case are suggested.

Exact tests for serial correlation in vector processes

ABSTRACTExact tests for serial independence in vector Markoff processes have been obtained by considering the system of regressions of the vectors observed at time 2t on the vectors observed at times (2t − 1) and (2t + 1). The tests then reduce to those obtained from canonical correlation procedures in multivariate analysis. Two particular cases are(1) The test for serial independence of a vector of residuals from a system of regressions in which the regressors are all independent of the residuals. At the same time a test of the hypothesis that the regressor and regrediend vectors are independent is obtained.(2) The test for serial correlation or partial serial correlation in a multiple Markoff process (autoregressive process).An investigation of the efficiency of the test so obtained, of the hypothesis that a process is a simple Markoff process (against the alternative that the process is a second-order auto-regression) suggests that the efficiency of all of these tests will be low.

The Power of Two Difference-Sign Tests

SITUATIONS arise in which we are unable to make the assumptions necessary for the application of standard theory based on the normal distribution. Most of the distribution-free tests which have been proposed for such situations are based on statistics which are very easy to compute, and this ease of computation goes some way to compensate for any information, available in the sample, which may be ignored. Quite apart from such situations, it is interesting to investigate the performances of distribution-free tests when the standard normal situation in fact holds good, for if a test is consistent (i.e. if the probability of rejecting a false alternative hypothesis tends to unity with increasing sample size) there must come a point, for any set of alternatives, where the loss of power involved in its use is negligible. In this paper two very simple tests are examined in this light. A distribution-free test of serial independence of N (unequal) observations ordered in time, proposed by Moore and Wallis [6], consists in counting the number of positive first differences in the series. On the null hypothesis that the observations came from the same (continuous) population, every ordering of the observations is equally probable, so that the mean value and variance of the statistic are very simply obtained, and its distribution can easily be shown to be asymptotically normal. A lower bound for the power of the test against a general class of alternatives, implying a trend in the observations, was obtained by Mann [5]. This paper considers its power in the particular case where the alternative is a normal regression model with coefficient ( and residual variance 2. The loss of power entailed by the use of this test at the 95% level of significance is unimportant when either N ? 25, P/caN/2 _ .5, or N> 75, P/crV/2 _ .3. The difference-sign test is easily generalized to the bivariate case for use in testing the correlation between two series. The approximate power of this second test is tabulate(d below against the alternative hypothesis that the pairs of observations were drawn from a bivariate normal population with non-zero correlation p. Much larger sample sizes are required for the power of this test to approach that of the test based on Fisher's transformation of the correlation coefficient. For