Standard Lagrange Multiplier Test Research Articles

Robust LM tests for spatial dynamic panel data models

In this study, we introduce adjusted Rao's score test statistics (Lagrange multiplier (LM) tests) for a spatial dynamic panel data (SDPD) model that includes a contemporaneous spatial lag, a time lag and a spatial-time lag. The maximum likelihood estimator for the estimation of SDPD models can have asymptotic bias because of individual and time fixed effects. Bias arises since the limiting distributions of the score functions derived from the corresponding concentrated log-likelihood functions are not centered on zero. First, we show how the score functions should be adjusted to avoid the effect of asymptotic bias on the standard LM test statistics. Second, we further adjust score functions such that the resulting LM test statistics are valid when there is local parametric misspecification in the alternative model. Our adjusted LM test statistics can be used to test the presence of the contemporaneous spatial lag, time lag and spatial-time lag in an SDPD model. In a Monte Carlo study, we demonstrate that our suggested test statistics have good finite sample size and power properties. Finally, we illustrate implementation of these tests in an application on public capital productivity in 48 contiguous US states.

Testing for misspecification in the short-run component of GARCH-type models

Abstract In this article, a misspecification test in conditional volatility and GARCH-type models is presented. We propose a Lagrange Multiplier type test based on a Taylor expansion to distinguish between (G)ARCH models and unknown GARCH-type models. This new test can be seen as a general misspecification test of a large set of GARCH-type univariate models. It focuses on the short-term component of the volatility. We investigate the size and the power of this test through Monte Carlo experiments and we compare it to two other standard Lagrange Multiplier tests, which are more restrictive. We show the usefulness of our test with an illustrative empirical example based on daily exchange rate returns.

Robust LM Tests for Spatial Dynamic Panel Data Models

In this study, we introduce adjusted Rao's score test statistics (Lagrange multiplier (LM) tests) for a spatial dynamic panel data (SDPD) model that includes a contemporaneous spatial lag, a time lag and a spatial-time lag. The maximum likelihood estimator for the estimation of SDPD models can have asymptotic bias because of individual and time fixed effects. Bias arises since the limiting distribution of the score functions derived from the corresponding concentrated log-likelihood functions are not centered on zero. First, we show how the score functions should be adjusted to avoid the effect of asymptotic bias on the standard LM test statistics. Second, we further adjust score functions such that the resulting LM test statistics are valid when there is local parametric misspecification in the alternative model. Our adjusted LM test statistics can be used to test the presence of the contemporaneous spatial lag, time lag and spatial-time lag in an SDPD model. In a Monte Carlo study, we demonstrate that our suggested test statistics have good finite sample size and power properties. Finally, we illustrate implementation of these tests in an application on public capital productivity in contiguous 48 US states.

TESTING STATIONARITY WITH UNOBSERVED-COMPONENTS MODELS

In the aftermath of the global financial crisis, competing measures of the trend in macroeconomic variables such as U.S. real GDP have featured prominently in policy debates. A key question is whether large shocks to macroeconomic variables will have permanent effects—i.e., in econometric terms, do the data contain stochastic trends? Unobserved-components models provide a convenient way to estimate stochastic trends for time series data, with their existence typically motivated by stationarity tests that allow at most a deterministic trend under the null hypothesis. However, given the small sample sizes available for most macroeconomic variables, standard Lagrange multiplier tests of stationarity will perform poorly when the data are highly persistent. To address this problem, we propose the use of a likelihood ratio test of stationarity based directly on the unobserved-components models used in estimation of stochastic trends. We demonstrate that a bootstrap version of this test has far better small-sample properties for empirically relevant data-generating processes than bootstrap versions of the standard Lagrange multiplier tests. An application to U.S. real GDP produces stronger support for the presence of large permanent shocks using the likelihood ratio test than using the standard tests.

Testing Stationarity for Unobserved Components Models

In the aftermath of the global financial crisis, competing measures of the trend in macroeconomic variables such as US real GDP have featured prominently in policy debates. A key question is whether the large shocks to macroeconomic variables will have permanent effects — i.e., in econometric terms, do the data contain stochastic trends? Unobserved components models provide a convenient way to estimate stochastic trends for time series data, with their existence typically motivated by stationarity tests that allow for at most a deterministic trend under the null hypothesis. However, given the small sample sizes available for most macroeconomic variables, standard Lagrange multiplier tests of stationarity will perform poorly when the data are highly persistent. To address this problem, we propose the use of a likelihood ratio test of stationarity based directly on the unobserved components models used in estimation of stochastic trends. We demonstrate that a bootstrap version of this test has far better small-sample properties for empirically-relevant data generating processes than bootstrap versions of the standard Lagrange multiplier tests. An application to US real GDP produces stronger support for the presence of large permanent shocks when using the likelihood ratio test as compared to the standard tests.

On detecting the optimal structure of a neural network under strong statistical features in errors

The purpose of this article is to investigate the empirical performance of various statistical techniques for detecting the optimal structure of a neural network (NN) regression model. We are particularly concerned with the specification of the NN architecture when the error component is characterized by special statistical properties, such as heteroskedasticity and non-normality. We consider the sequential testing procedure based on standard Lagrange multiplier (LM) tests for neglected nonlinearity and also examine three modifications of this test that are robust to heteroskedasticity. By means of Monte Carlo simulations, we investigate the ability of these procedures to detect the right structure of the NN under different types of heteroskedasticity and noise distributions. Simulation results show that robustified LM tests allow the researcher to control the complexity of the NN without having to explicitly model all statistical aspects of the data-generating process, something which is not generally feasible with the standard LM test. The combination of robust regression-based testing with bootstrapping and generalized autoregressive conditional heteroskedasticity modelling techniques increases the efficiency of the statistical sequential procedure in eliciting the optimal NN architecture.

A Lagrange multiplier stationarity test using covariates

A stationarity test based on the Lagrange multiplier using covariates is proposed. The tests are shown to have more power than standard Lagrange multiplier tests if the covariates are highly correlated with the stationary part of the data.

Detecting Autoregressive Conditional Heteroskedasticity in Non-Gaussian Time Series

In economic time series conditional heteroskedasticity and conditional non-normality may occur simultaneously. Well known examples include time series of financial returns. The present paper examines a new test for (generalized) autoregressive conditional heteroskedasticity in Monte Carlo experiments with normal, fat-tailed and/or skewed conditional distributions. In the experiments the size of the new test is accurate and the test has good power against the considered ARCH and GARCH alternatives. Under conditional normality the test is as powerful as the standard Lagrange multiplier test for ARCH effects and a robust ARCH test. Under conditional non-normality the new test has often substantially more power then the other two tests.

The wild bootstrap and heteroskedasticity-robust tests for serial correlation in dynamic regression models

Conditional heteroskedasticity is a common feature of financial and macroeconomic time series data. When such heteroskedasticity is present, standard checks for serial correlation in dynamic regression models are inappropriate. In such circumstances, it is obviously important to have asymptotically valid tests that are reliable in finite samples. Monte Carlo evidence reported in this paper indicates that asymptotic critical values fail to give good control of finite sample significance levels of heteroskedasticity-robust versions of the standard Lagrange multiplier test, a Hausman-type check, and a new procedure. The application of computer-intensive methods to removing size distortion is, therefore, examined. It is found that a particularly simple form of the wild bootstrap leads to well-behaved tests. Some simulation evidence on power is also given.

A Locally Most Mean Powerful Based Score Test for ARCH and GARCH Regression Disturbances

This article considers the twin problems of testing for autoregressive conditional heteroscedasticity (ARCH) and generalized ARCH disturbances in the linear regression model. A feature of these testing problems, ignored by the standard Lagrange multiplier test, is that they are onesided in nature. A test that exploits this one-sided aspect is constructed based on the sum of the scores. The small-sample-size and power properties of two versions of this test under both normal and leptokurtic disturbances are investigated via a Monte Carlo experiment. The results indicate that both versions of the new test typically have superior power to two versions of the Lagrange multiplier test and possibly also more accurate asymptotic critical values.