Quasi-likelihood Ratio Test Research Articles

On an asymmetric functional-coefficient ARCH-M model

This paper proposes an asymmetric functional-coefficient autoregressive conditional heteroscedasticity in mean (ARCH-M) model, which allows for asymmetry in the volatility. The profile likelihood approach is applied to estimate the parametric and nonparametric components. Under some regularity assumptions, we derive asymptotic behavior of the proposed estimator. To avoid model misspecification, the Wald, quasi-likelihood ratio test statistic and generalized likelihood ratio test statistic are put forward to detect ARCH effect, asymmetric effect and goodness-of-fit, respectively. Moreover, their asymptotic distributions are established under both null and alternative hypotheses. Some Monte Carlo simulations are conducted to evaluate the finite sample performance of the proposed estimation methodology and testing procedure. Also, real data sets are analyzed to demonstrate the applications of the proposed model.

Bipartite network influence analysis of a two-mode network

A two-mode network contains two types of nodes, and edges exist only between any two nodes that are associated with different entities. Owing to the network connections (i.e., edges) between the two types of network nodes, nodal responses are unlikely to be independently and identically distributed, resulting in possible nodal heterogeneity across the two types of nodes. This study proposes a novel bipartite network influence model (BNIM) to evaluate nodal heterogeneity from the perspective of nodal influence. To make the model estimable, we parameterize the influence indices with a set of nodal attributes through a prespecified link function, and employ the quasi-maximum likelihood approach to estimate the unknown parameters. Score tests are presented to examine the heterogeneity of nodal influences across the two types of nodes. To assess the adequacy of the link function, we carry out a quasi-likelihood ratio test and establish its asymptotic properties under the appropriate conditions. Simulation studies and the real data analysis of a fund-stock network are studied to assess the finite-sample performance of BNIM.

Estimation of Realized Asymmetric Stochastic Volatility Models Using Kalman Filter

Despite the growing interest in realized stochastic volatility models, their estimation techniques, such as simulated maximum likelihood (SML), are computationally intensive. Based on the realized volatility equation, this study demonstrates that, in a finite sample, the quasi-maximum likelihood estimator based on the Kalman filter is competitive with the two-step SML estimator, which is less efficient than the SML estimator. Regarding empirical results for the S&P 500 index, the quasi-likelihood ratio tests favored the two-factor realized asymmetric stochastic volatility model with the standardized t distribution among alternative specifications, and an analysis on out-of-sample forecasts prefers the realized stochastic volatility models, rejecting the model without the realized volatility measure. Furthermore, the forecasts of alternative RSV models are statistically equivalent for the data covering the global financial crisis.

Covariance Model with General Linear Structure and Divergent Parameters

For estimating the large covariance matrix with a limited sample size, we propose the covariance model with general linear structure (CMGL) by employing the general link function to connect the covariance of the continuous response vector to a linear combination of weight matrices. Without assuming the distribution of responses, and allowing the number of parameters associated with weight matrices to diverge, we obtain the quasi-maximum likelihood estimators (QMLE) of parameters and show their asymptotic properties. In addition, an extended Bayesian information criteria (EBIC) is proposed to select relevant weight matrices, and the consistency of EBIC is demonstrated. Under the identity link function, we introduce the ordinary least squares estimator (OLS) that has the closed form. Hence, its computational burden is reduced compared to QMLE, and the theoretical properties of OLS are also investigated. To assess the adequacy of the link function, we further propose the quasi-likelihood ratio test and obtain its limiting distribution. Simulation studies are presented to assess the performance of the proposed methods, and the usefulness of generalized covariance models is illustrated by an analysis of the U.S. stock market.

Comprehensively testing linearity hypothesis using the smooth transition autoregressive model

This article examines the null limit distribution of the quasi-likelihood ratio (QLR) statistic for testing linearity condition against the smooth transition autoregressive (STAR) model. We explicitly show that the QLR test statistic weakly converges to a functional of a multivariate Gaussian process under the null of linearity, which is done by resolving the issue of identification problem arises in two different ways under the null. In contrast with the Lagrange multiplier test that is widely employed for testing the linearity condition, the proposed QLR statistic has an omnibus power, and thus, it complements the existing testing procedure. We show the empirical relevance of our test by testing the neglected nonlinearity of the US fiscal multipliers and growth rates of US unemployment. These empirical examples demonstrate that the QLR test is useful for detecting the nonlinear structure among economic variables.

An empirical study on the regulated Chinese agricultural commodity futures market based on skew Ornstein-Uhlenbeck model

This paper describes the regulated agricultural commodity futures market of China, focusing on six actively traded futures: corn, strong gluten wheat, No. 1 soybean, soymeal, cotton, and white sugar. A novel skew Ornstein-Uhlenbeck model is employed to characterize price dynamics with government controls. The empirical analysis reveals significant skew phenomena in these six futures and indicates that the price dynamics are influenced by state policy. The observed skew phenomena are most notable in grain futures, with relatively weaker, but statistically significant, evidence of skew phenomena in oilseed and soft futures markets. In addition, generalized quasi-likelihood ratio tests show that the skew Ornstein-Uhlenbeck model is superior to the Ornstein-Uhlenbeck model.

Generic results for establishing the asymptotic size of confidence sets and tests

This paper provides a set of results that can be used to establish the asymptotic size and/or similarity in a uniform sense of confidence sets and tests. The results are generic in that they can be applied to a broad range of problems. They are most useful in scenarios where the pointwise asymptotic distribution of a test statistic is a discontinuous function of a parameter.The results are illustrated in several examples. These are: (i) the conditional likelihood ratio test of Moreira (2003) for linear instrumental variables models with instruments that may be weak, extended to the case of heteroskedastic errors; (ii) the grid bootstrap confidence interval of Hansen (1999) for the sum of the AR coefficients in a kth order autoregressive model with unknown innovation distribution, and (iii) the standard quasi-likelihood ratio test in a nonlinear regression model where identification is lost when the coefficient on the nonlinear regressor is zero. In addition, as a simple running example, we consider a two-sided equal-tailed CI for the AR coefficient in an AR(1) model, which is a simplified version of the CI in Andrews and Guggenberger (2014).

Quasi-Likelihood Ratio Tests for Homoscedasticity in Linear Regression

Two quasi-likelihood ratio tests are proposed for the homoscedasticity assumption in the linear regression models. They require few assumptions than the existing tests. The properties of the tests are investigated through simulation studies. An example is provided to illustrate the usefulness of the new proposed tests.

A Quasi-Likelihood Approach to Assess Model Fit in Quadratic and Interaction SEM

For the assessment of model fit in linear structural equation modeling (SEM), several fit measures have been developed that use an unconstrained mean and covariance structure, but cannot be readily applied to SEM with quadratic and interaction effects. In this article, we propose the novel quasi-likelihood ratio test (Q-LRT) to evaluate global fit of nonlinear SEM models. The Q-LRT is based on a simplification of the quasi-maximum likelihood method for the estimation of model parameters. An empirical application of the Q-LRT is demonstrated for data in a study about aging in men. Results from a Monte Carlo study show that the Q-LRT performs reliably when sample size is sufficiently large. Also, simulations suggest robustness of Q-LRT for moderately skewed latent exogenous variables.

Partial Cointegrated Vector Autoregressive Models with Structural Breaks in Deterministic Terms

This paper proposes a class of partial cointegrated models allowing for structural breaks in the deterministic terms. Moving-average representations of the models are given. It is then shown that, under the assumption of martingale difference innovations, the limit distributions of partial quasi-likelihood ratio tests for cointegrating rank have a close connection to those for standard full models. This connection facilitates a response surface analysis that is required to extract critical information about moments from large-scale simulation studies. An empirical illustration of the proposed methodology is also provided.

Non-standard inference for augmented double autoregressive models with null volatility coefficients

This paper considers an augmented double autoregressive (DAR) model, which allows null volatility coefficients to circumvent the over-parameterization problem in the DAR model. Since the volatility coefficients might be on the boundary, the statistical inference methods based on the Gaussian quasi-maximum likelihood estimation (GQMLE) become non-standard, and their asymptotics require the data to have a finite sixth moment, which narrows the applicable scope in studying heavy-tailed data. To overcome this deficiency, this paper develops a systematic statistical inference procedure based on the self-weighted GQMLE for the augmented DAR model. Except for the Lagrange multiplier test statistic, the Wald, quasi-likelihood ratio and portmanteau test statistics are all shown to have non-standard asymptotics. The entire procedure is valid as long as the data are stationary, and its usefulness is illustrated by simulation studies and one real example.

Automatic Modulation Classification Using Interacting Multiple Model Kalman Filter for Channel Estimation

A rigorous model for automatic modulation classification (AMC) in cognitive radio systems is proposed in this paper. This is achieved by exploiting the Kalman filter (KF) integrated with an adaptive interacting multiple model (IMM) for resilient estimation of the channel state information. A novel approach is proposed, in adding up the square root singular values of the decomposed channel using the singular value decompositions algorithm. This new scheme, termed Frobenius eigenmode transmission, is chiefly intended to maintain the total power of all individual effective eigenmodes, as opposed to keeping only the dominant one. The analysis is applied over multiple-input multiple-output (MIMO) antennas in combination with a Rayleigh fading channel using a quasi-likelihood ratio test algorithm for AMC. The expectation-maximization is employed for recursive computation of the underlying estimation and classification algorithms. Novel simulations demonstrate the advantages of the combined IMM-KF structure when compared to the perfectly known channel and maximum likelihood estimate, in terms of achieving the targeted optimal performance with the desirable benefit of less computational complexity loads.

Quasi-likelihood ratio tests for cointegration, cobreaking, and cotrending

We consider a set of variables with two types of nonstationary features, stochastic trends and broken linear trends. We develop tests that can determine whether there is a linear combination of these variables under which the nonstationary features can be canceled out. The first test can determine whether stochastic trends can be eliminated and thus whether cointegration holds, regardless of whether structural breaks in linear trends are eliminated. The second test can determine whether both stochastic trends and breaks in linear trends are simultaneously removed and thus whether cointegration and cobreaking simultaneously hold. The third test can determine whether not only breaks in linear trends but also linear trends themselves are eliminated along with stochastic trends and thus whether both cointegration and cotrending hold.

Realized stochastic volatility models with generalized Gegenbauer long memory

Fractionally differenced processes have received a great deal of attention due to their flexibility in financial applications with long memory. In this paper, new realized stochastic volatility (RSV) models are developed: one is a RSV model with general Gegenbauer long memory (GGLM), while the other is a RSV model with seasonal long memory (SLM). The RSV model uses the information from returns and realized volatility measures simultaneously. The long memory structure of both models can describe unbounded peaks, apart from the origin in the power spectrum. For estimating the RSV–GGLM model, a two step method is suggested: the location parameters for the peaks of the power spectrum are estimated in the first step, while the remaining parameters are estimated based on the Whittle likelihood in the second step. Monte Carlo experiments give results for investigating the finite sample properties of the estimators, with a quasi-likelihood ratio test of the RSV–SLM model against the RSV–GGLM model. The RSV–GGLM and RSV–SLM models are applied to three stock market indices, for which the estimation and forecasting results indicate the adequacy of considering general long memory.

Efficiency Loss of Asymptotically Efficient Tests in an Instrumental Variables Regression

In a model with endogenous regressors, heteroskedastic and autocorrelated (HAC) errors and weak instruments, tests that depend on the data only through the Anderson-Rubin (AR) and Lagrange Multiplier (LM) statistics ignore important information on the regression coefficients. This is in contrast to the homoskedastic case, where these statistics, together with the rank statistic, are one-to-one with the maximal invariant. The information loss with heteroskedastic and/or autocorrelated errors can be so extreme that the LM and conditional quasi-likelihood ratio (CQLR) tests have power close to size when it is trivial to distinguish the null from the alternative hypothesis. The severe loss of power can occur if the Hermitian part of the reduced-form covariance matrix has eigenvalues of opposite signs. The conditional invariant likelihood (CIL) test proposed by Moreira and Ridder (2018) does not suffer this power loss. On the contrary, when the CQLR and LM tests fail, the CIL test can have power close to 1 under the alternative, even if its size is close to 0. This implies that the total variation distance between the null and subsets of the alternative is large, so that it is actually easy to distinguish between these hypotheses. We also show that in the HAC-IV model, there are invariant statistics beyond the triad of AR, LM and rank statistics, so that the latter are not maximal invariant in the HAC case. We conclude that the popular LM and CQLR tests use data inefficiently if the equation errors are HAC.

Identification- and Singularity-Robust Inference for Moment Condition Models

This paper introduces two new identification- and singularity-robust conditional quasi-likelihood ratio (SR-CQLR) tests and a new identification- and singularity-robust Anderson and Rubin (1949) (SR-AR) test for linear and nonlinear moment condition models. The paper shows that the tests have correct asymptotic size and are asymptotically similar (in a uniform sense) under very weak conditions. For two of the three tests, all that is required is that the moment functions and their derivatives have 2 + y bounded moments for some y > 0 in i.i.d. scenarios. In stationary strong mixing time series cases, the same condition suffices, but the magnitude of y is related to the magnitude of the strong mixing numbers. For the third test, slightly stronger moment conditions and a (standard, though restrictive) multiplicative structure on the moment functions are imposed. For all three tests, no conditions are placed on the expected Jacobian of the moment functions, on the eigenvalues of the variance matrix of the moment functions, or on the eigenvalues of the expected outer product of the (vectorized) orthogonalized sample Jacobian of the moment functions. The two SR-CQLR tests are shown to be asymptotically efficient in a GMM sense under strong and semi-strong identification (for all k /ge p; where k and p are the numbers of moment conditions and parameters, respectively). The two SR-CQLR tests reduce asymptotically to Moreira's CLR test when p = 1 in the homoskedastic linear IV model. The first SR-CQLR test, which relies on the multiplicative structure on the moment functions, also does so for p /ge 2.

A homoscedasticity test for the accelerated failure time model

The semiparametric accelerated failure time (AFT) model is a popular linear model in survival analysis. AFT model and its associated inference methods assume homoscedasticity of the survival data. It is shown that violation of this assumption will lead to inefficient parameter estimation and anti-conservative confidence interval estimation, and thus, misleading conclusions in survival data analysis. However, there is no valid statistical test proposed to test the homoscedasticity assumption. In this paper, we propose the first novel quasi-likelihood ratio test for the homoscedasticity assumption in the AFT model. Simulation studies show the test performs well. A real dataset is used to demonstrate the usefulness of the developed test.

BinQuasi: a peak detection method for ChIP-sequencing data with biological replicates.

ChIP-seq experiments that are aimed at detecting DNA-protein interactions require biological replication to draw inferential conclusions, however there is no current consensus on how to analyze ChIP-seq data with biological replicates. Very few methodologies exist for the joint analysis of replicated ChIP-seq data, with approaches ranging from combining the results of analyzing replicates individually to joint modeling of all replicates. Combining the results of individual replicates analyzed separately can lead to reduced peak classification performance compared to joint modeling. Currently available methods for joint analysis may fail to control the false discovery rate at the nominal level. We propose BinQuasi, a peak caller for replicated ChIP-seq data, that jointly models biological replicates using a generalized linear model framework and employs a one-sided quasi-likelihood ratio test to detect peaks. When applied to simulated data and real datasets, BinQuasi performs favorably compared to existing methods, including better control of false discovery rate than existing joint modeling approaches. BinQuasi offers a flexible approach to joint modeling of replicated ChIP-seq data which is preferable to combining the results of replicates analyzed individually. Source code is freely available for download at https://cran.r-project.org/package=BinQuasi, implemented in R. Supplementary data are available at Bioinformatics online.

Testing for common breaks in a multiple equations system

The issue addressed in this paper is that of testing for common breaks across or within equations of a multivariate system. Our framework is very general and allows integrated regressors and trends as well as stationary regressors. The null hypothesis is that breaks in different parameters occur at common locations and are separated by some positive fraction of the sample size unless they occur across different equations. Under the alternative hypothesis, the break dates across parameters are not the same and also need not be separated by a positive fraction of the sample size whether within or across equations. The test considered is the quasi-likelihood ratio test assuming normal errors, though as usual the limit distribution of the test remains valid with non-normal errors. Of independent interest, we provide results about the rate of convergence of the estimates when searching over all possible partitions subject only to the requirement that each regime contains at least as many observations as some positive fraction of the sample size, allowing break dates not separated by a positive fraction of the sample size across equations. Simulations show that the test has good finite sample properties. We also provide an application to issues related to level shifts and persistence for various measures of inflation to illustrate its usefulness.

Overidentification in Regular Models

In the unconditional moment restriction model of Hansen (), specification tests and more efficient estimators are both available whenever the number of moment restrictions exceeds the number of parameters of interest. We show that a similar relationship between potential refutability of a model and existence of more efficient estimators is present in much broader settings. Specifically, a condition we name local overidentification is shown to be equivalent to both the existence of specification tests with nontrivial local power and the existence of more efficient estimators of some “smooth” parameters in general semi/nonparametric models. Under our notion of local overidentification, various locally nontrivial specification tests such as Hausman tests, incremental Sargan tests (or optimally weighted quasi likelihood ratio tests) naturally extend to general semi/nonparametric settings. We further obtain simple characterizations of local overidentification for general models of nonparametric conditional moment restrictions with possibly different conditioning sets. The results are applied to determining when semi/nonparametric models with endogeneity are locally testable, and when nonparametric plug‐in and semiparametric two‐step GMM estimators are semiparametrically efficient. Examples of empirically relevant semi/nonparametric structural models are presented.