Testing the random walk hypothesis with variance ratio statistics

Mestrado em Finanças

Likelihood ratio tests for variance components in linear mixed models

Although the asymptotic distributions of the likelihood ratio for testing hypotheses of null variance components in linear mixed models derived by Stram and Lee [1994. Variance components testing in longitudinal mixed effects model. Biometrics 50, 1171-1177] are valid, their proof is based on the work of Self and Liang [1987. Asymptotic properties of maximum likelihood estimators and likelihood tests under nonstandard conditions. J. Amer. Statist. Assoc. 82, 605-610] which requires identically distributed random variables, an assumption not always valid in longitudinal data problems. We use the less restrictive results of Vu and Zhou [1997. Generalization of likelihood ratio tests under nonstandard conditions. Ann. Statist. 25, 897-916] to prove that the proposed mixture of chi-squared distributions is the actual asymptotic distribution of such likelihood ratios used as test statistics for null variance components in models with one or two random effects. We also consider a limited simulation study to evaluate the appropriateness of the asymptotic distribution of such likelihood ratios in moderately sized samples. (C) 2008 Elsevier B.V. All rights reserved.

Testing Mean-Variance Efficiency in CAPM with Possibly Non-Gaussian Errors : An Exact Simulation-Based Approach

In this paper we propose exact likelihood-based mean-variance efficiency tests of the market portfolio in the context of Capital Asset Pricing Model (CAPM), allowing for a wide class of error distributions which include normality as a special case. These tests are developed in the frame-work of multivariate linear regressions (MLR). It is well known however that despite their simple statistical structure, standard asymptotically justified MLR-based tests are unreliable. In financial econometrics, exact tests have been proposed for a few specific hypotheses [Jobson and Korkie (Journal of Financial Economics, 1982), MacKinlay (Journal of Financial Economics, 1987), Gib-bons, Ross and Shanken (Econometrica, 1989), Zhou (Journal of Finance 1993)], most of which depend on normality. For the gaussian model, our tests correspond to Gibbons, Ross and Shanken’s mean-variance efficiency tests. In non-gaussian contexts, we reconsider mean-variance efficiency tests allowing for multivariate Student-t and gaussian mixture errors. Our framework allows to cast more evidence on whether the normality assumption is too restrictive when testing the CAPM. We also propose exact multivariate diagnostic checks (including tests for multivariate GARCH and mul-tivariate generalization of the well known variance ratio tests) and goodness of fit tests as well as a set estimate for the intervening nuisance parameters. Our results [over five-year subperiods] show the following: (i) multivariate normality is rejected in most subperiods, (ii) residual checks reveal no significant departures from the multivariate i.i.d. assumption, and (iii) mean-variance efficiency tests of the market portfolio is not rejected as frequently once it is allowed for the possibility of non-normal errors.

A comparison of discriminant logistic regression and Item Response Theory Likelihood-Ratio Tests for Differential Item Functioning (IRTLRDIF) in polytomous short tests

Resumen tomado de la publicaci??n

Signed likelihood ratio tests in the Birnbaum-Saunders regression model

The Birnbaum-Saunders regression model is becoming increasingly popular in lifetime analyses and reliability studies. In this model, the signed likelihood ratio statistic provides the basis for testing inference and construction of confidence limits for a single parameter of interest. We focus on the small sample case, where the standard normal distribution gives a poor approximation to the true distribution of the statistic. We derive three adjusted signed likelihood ratio statistics that lead to very accurate inference even for very small samples. Two empirical applications are presented. (C) 2010 Elsevier B.V. All rights reserved.

Skovgaard`s adjustment to likelihood ratio tests in exponential family nonlinear models

Likelihood ratio tests can be substantially size distorted in small- and moderate-sized samples. In this paper, we apply Skovgaard`s [Skovgaard, I.M., 2001. Likelihood asymptotics. Scandinavian journal of Statistics 28, 3-321] adjusted likelihood ratio statistic to exponential family nonlinear models. We show that the adjustment term has a simple compact form that can be easily implemented from standard statistical software. The adjusted statistic is approximately distributed as X(2) with high degree of accuracy. It is applicable in wide generality since it allows both the parameter of interest and the nuisance parameter to be vector-valued. Unlike the modified profile likelihood ratio statistic obtained from Cox and Reid [Cox, D.R., Reid, N., 1987. Parameter orthogonality and approximate conditional inference. journal of the Royal Statistical Society B49, 1-39], the adjusted statistic proposed here does not require an orthogonal parameterization. Numerical comparison of likelihood-based tests of varying dispersion favors the test we propose and a Bartlett-corrected version of the modified profile likelihood ratio test recently obtained by Cysneiros and Ferrari [Cysneiros, A.H.M.A., Ferrari, S.L.P., 2006. An improved likelihood ratio test for varying dispersion in exponential family nonlinear models. Statistics and Probability Letters 76 (3), 255-265]. (C) 2008 Elsevier B.V. All rights reserved.

8p23 beta-defensin copy number determination by single-locus pseudogene-based paralog ratio tests risk bias due to low-frequency sequence variations.

BACKGROUND The copy number variation (CNV) in beta-defensin genes (DEFB) on human chromosome 8p23 has been proposed to contribute to the phenotypic differences in inflammatory diseases. However, determination of exact DEFB CN is a major challenge in association studies. Quantitative real-time PCR (qPCR), paralog ratio tests (PRT) and multiplex ligation-dependent probe amplification (MLPA) have been extensively used to determine DEFB CN in different laboratories, but inter-method inconsistencies were observed frequently. In this study we asked which one is superior among the three methods for DEFB CN determination. RESULTS We developed a clustering approach for MLPA and PRT to statistically correlate data from a single experiment. Then we compared qPCR, a newly designed PRT and MLPA for DEFB CN determination in 285 DNA samples. We found MLPA had the best convergence and clustering results of the raw data and the highest call rate. In addition, the concordance rates between MLPA or PRT and qPCR (32.12% and 37.99%, respectively) were unacceptably low with underestimated CN by qPCR. Concordance rate between MLPA and PRT (90.52%) was high but PRT systematically underestimated CN by one in a subset of samples. In these samples a sequence variant which caused complete PCR dropout of the respective DEFB cluster copies was found in one primer binding site of one of the targeted paralogous pseudogenes. CONCLUSION MLPA is superior to PRT and even more to qPCR for DEFB CN determination. Although the applied PRT provides in most cases reliable results, such a test is particularly sensitive to low-frequency sequence variations preferably accumulating in loci like pseudogenes which are most likely not under selective pressure. In the light of the superior performance of multiplex assays, the drawbacks of such single PRTs could be overcome by combining more test markers.

A comparison of read-around-ratio tests in Williams IV and Williams II /

"October 3, 1951"

External shocks and tourist arrivals to Cambodia

This article investigates how external shocks affect tourist arrivals to Cambodia. The study relies on the random walk approach to test whether the shocks to tourist arrivals are temporary or persistent in nature. To facilitate the empirical investigation, the study applies and compares the results from different unit root tests and variance-ratio tests to the monthly tourists' arrival data from 1994 to December 2012. Both tests provide evidence of random walk hypothesis, implying that shocks to tourists' arrival to Cambodia have a persistent effect requiring short- to medium-term policies to combat the vulnerability due to those shocks. Public-private coordinated policies could reduce the impact, as we found that once the crisis (external shocks) is minimized, the magnitude of the shocks decays slowly.

Interday and intraday volatility: additional evidence from the Shanghai Stock Exchange

After examining both the interday and intraday return volatility of the Shanghai Composite Stock Index, it was found that the open-to-open return variance is consistently greater than the close-to-close variance. Examining the volatility of interday returns and variance ratio tests with five-minute intervals reveals an L-shaped pattern, or more precisely, two L-shaped patterns, starting with a small hump during both the morning and the afternoon sessions, with the morning session having a much higher interday volatility than the afternoon session. This L -shaped interday volatility is supported by the similarly shaped intraday volatility pattern. This result suggests that the high volatility of intraday returns for the market open is not entirely due to the trading mechanisms (call auction in the market opening) but also due to both the accumulated overnight information and the trading halt effect. The five-minute breaks after the auction and blind auction procedures are the two major driving forces which exaggerate the high intraday volatility observed at the market open.

An empirical analysis on the efficiency of the microfinance investment market

This paper empirically analyzes the market efficiency of microfinance investment funds. For the empirical analysis, we use an index of the microfinance investment funds and apply two kinds of variance ratio tests to examine whether or not this index follows a random walk. We use the entire sample period from December 2003 to June 2010 as well as two sub-samples which divide the entire period before and after January 2007. The empirical evidence demonstrates that the index does not follow a random walk, suggesting that the market of the microfinance investment funds is not efficient. This result is not affected by changes in either empirical techniques or sample periods.

Assessment of variance components in nonlinear mixed-effects elliptical models

The issue of assessing variance components is essential in deciding on the inclusion of random effects in the context of mixed models. In this work we discuss this problem by supposing nonlinear elliptical models for correlated data by using the score-type test proposed in Silvapulle and Silvapulle (1995). Being asymptotically equivalent to the likelihood ratio test and only requiring the estimation under the null hypothesis, this test provides a fairly easy computable alternative for assessing one-sided hypotheses in the context of the marginal model. Taking into account the possible non-normal distribution, we assume that the joint distribution of the response variable and the random effects lies in the elliptical class, which includes light-tailed and heavy-tailed distributions such as Student-t, power exponential, logistic, generalized Student-t, generalized logistic, contaminated normal, and the normal itself, among others. We compare the sensitivity of the score-type test under normal, Student-t and power exponential models for the kinetics data set discussed in Vonesh and Carter (1992) and fitted using the model presented in Russo et al. (2009). Also, a simulation study is performed to analyze the consequences of the kurtosis misspecification.

A method to quantify a descriptor's illumination variance

This paper presents a new metric, which we call the lighting variance ratio, for quantifying descriptors in terms of their variance to illumination changes. In many applications it is desirable to have descriptors that are robust to changes in illumination, especially in outdoor environments. The lighting variance ratio is useful for comparing descriptors and determining if a descriptor is lighting invariant enough for a given environment. The metric is analysed across a number of datasets, cameras and descriptors. The results show that the upright SIFT descriptor is typically the most lighting invariant descriptor.

The Power of Bootstrap Tests of Cointegration Rank with Financial Time Series

Bootstrap likelihood ratio tests of cointegration rank are commonly used because they tend to have rejection probabilities that are closer to the nominal level than the rejection probabilities of the correspond- ing asymptotic tests. The e¤ect of bootstrapping the test on its power is largely unknown. We show that a new computationally inexpensive procedure can be applied to the estimation of the power function of the bootstrap test of cointegration rank. The bootstrap test is found to have a power function close to that of the level-adjusted asymp- totic test. The bootstrap test estimates the level-adjusted power of the asymptotic test highly accurately. The bootstrap test may have low power to reject the null hypothesis of cointegration rank zero, or underestimate the cointegration rank. An empirical application to Euribor interest rates is provided as an illustration of the findings.