Finite Sample Performance of Likelihood Ratio Tests for Cointegrating Ranks in Vector Autoregressions

1995 ◽  
Vol 11 (5) ◽  
pp. 1015-1032 ◽  
Author(s):  
Hiro Y. Toda
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Likelihood Ratio ◽  
Test Performance ◽  
Likelihood Ratio Tests ◽  
Nuisance Parameters ◽  
Test Statistics ◽  
Finite Sample ◽  
Vector Autoregressions ◽  
Finite Sample Properties

This paper investigates through Monte Carlo simulation the finite sample properties of likelihood ratio tests for cointegrating ranks that were proposed by Johansen (1991, Econometrica 59, 1551–1580). We transform the model into a canonical form so that the experiment is well controlled without loss of generality and then conduct a comprehensive simulation study. As expected, the test performance is very sensitive to the value of the stationary root(s) of the process. We also find that the test performance depends crucially on the correlation between the innovations that drive the stationary and the nonstationary components of the process. We conclude that 100 observations are not sufficient to ensure reasonably good performance uniformly over the values of the nuisance parameters that affect the distributions of the test statistics.

Multiway Contingency Tables: Monte Carlo Resampling Probability Values for the Chi-Squared and Likelihood-Ratio Tests

2010 ◽  
Vol 107 (2) ◽  
pp. 501-510 ◽  
Author(s):  
Michael A. Long ◽  
Kenneth J. Berry ◽  
Paul W. Mielke
Keyword(s):  
Monte Carlo ◽  
Likelihood Ratio ◽  
Contingency Table ◽  
Contingency Tables ◽  
Likelihood Ratio Tests ◽  
Ratio Test ◽  
Test Statistics ◽  
Test Statistic ◽  
Resampling Methods ◽  
Chi Squared

Monte Carlo resampling methods to obtain probability values for chi-squared and likelihood-ratio test statistics for multiway contingency tables are presented. A resampling algorithm provides random arrangements of cell frequencies in a multiway contingency table, given fixed marginal frequency totals. Probability values are obtained from the proportion of resampled test statistic values equal to or greater than the observed test statistic value.

scholarly journals Monte Carlo Simulation Of The Portfolio-Balance Model Of Exchange Rates: Finite Sample Properties Of The GMM Estimator

2011 ◽  
Vol 6 (1) ◽  
Author(s):  
Hong-Ghi Min
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Exchange Rates ◽  
Balance Model ◽  
Finite Sample ◽  
Gmm Estimator ◽  
Portfolio Balance ◽  
Finite Sample Properties ◽  
Chi Squared ◽  
Better Than

Using Monte Carlo simulation of the Portfolio-balance model of the exchange rates, we report finite sample properties of the GMM estimator for testing over-identifying restrictions in the simultaneous equations model. F-form of Sargans statistic performs better than its chi-squared form while Hansens GMM statistic has the smallest bias.

scholarly journals Testing for Multiple Structural Changes with Non-Homogeneous Regressors

2015 ◽  
Vol 7 (1) ◽  
pp. 1-35 ◽  
Author(s):  
Eiji Kurozumi
Keyword(s):  
Monte Carlo ◽  
Structural Changes ◽  
Linear Trend ◽  
Critical Values ◽  
Test Statistics ◽  
Finite Sample ◽  
Multiple Structural Changes ◽  
Finite Sample Properties ◽  
Polynomial Trends ◽  
Weighted Type

AbstractThis paper investigates tests for multiple structural changes with non-homogeneous regressors, such as polynomial trends. We consider exponential-type, supremum-type and average-type tests as well as the corresponding weighted-type tests suggested in the literature. We show that the limiting distributions depend on regressors in general, and we need to tabulate critical values depending on them. Then, we focus on the linear trend case and obtain the critical values of the test statistics. The Monte Carlo simulations are conducted to investigate the finite sample properties of the tests proposed in the paper, and it is found that the specification of the number of breaks is an important factor for the finite sample performance of the tests. Since it is often the case that we cannot prespecify the number of breaks under the alternative but can suppose only the maximum number of breaks, the weighted-type tests are useful in practice.

Finite Sample Distributions of t and F Statistics in an AR(1) Model with Anexogenous Variable

1987 ◽  
Vol 3 (3) ◽  
pp. 387-408 ◽  
Author(s):  
J.C. Nankervis ◽  
N.E. Savin
Keyword(s):  
Monte Carlo ◽  
Time Trend ◽  
Stable Process ◽  
Asymptotic Approximations ◽  
Test Statistics ◽  
Finite Sample ◽  
Sampling Behavior ◽  
Exogenous Process ◽  
Exogenous Time Series ◽  
F Statistics

The distributions of the test statistics are investigated in the context of an AR(1) model where the root is unity or near unity and where the exogenous process is a stable process, a random walk or a time trend. The finite sample distributions are estimated by Monte Carlo methods assuming normal disturbances. The sensitivity of the distributions to both the values of the parameters of the AR(1) model and the process generating the exogenous time series is examined. The Monte Carlo results motivate several theorems which describe the exact sampling behavior of the test statistics. The analytical and empirical results present a mixed picture with respect to the accuracy of the relevant asymptotic approximations.

scholarly journals Recursive Adjustment for General Deterministic Components and Improved Cointegration Rank Tests

2015 ◽  
Vol 7 (2) ◽  
Author(s):  
Benjamin Born ◽  
Matei Demetrescu
Keyword(s):  
Likelihood Ratio ◽  
Linear Trend ◽  
Generalized Least Squares ◽  
Ratio Test ◽  
Finite Sample ◽  
Vector Autoregressions ◽  
Rank Tests ◽  
Testing Procedures ◽  
Stochastic Component ◽  
Deterministic Components

AbstractThis paper discusses tests for the cointegration rank of integrated vector autoregressions when the series are recursively adjusted for deterministic components. To this end, the asymptotic properties of recursive, or adaptive, procedures for the removal of general additive deterministic components are analyzed in two different, complementary, situations. When the stochastic component of the examined time series is weakly stationary (as would be the equilibrium errors), the effect of recursive adjustment vanishes with increasing sample size. When the suitably normalized stochastic component converges weakly to some limiting continuous-time process with integrable paths (as would be the case with the common stochastic trends), recursive adjustment has a permanent effect even asymptotically: the normalized recursively adjusted process converges weakly to a recursively adjusted version of the limiting process. The null limiting distributions of the cointegration rank tests can be expressed in terms of recursively adjusted Brownian motions. Moreover, the finite-sample properties of the cointegration rank tests with recursive adjustment are examined in cases of empirical relevance: the considered deterministic components are a constant, and a constant and a linear trend, respectively. Compared to the likelihood ratio tests or the tests with generalized least squares adjustment, improvements in terms of empirical rejection frequencies under the null are found in finite samples; improvements are found under the alternative as well, with the likelihood ratio test performing increasingly better as the magnitude of the initial condition increases. Regarding rank selection, a very simple combination of the three testing procedures with different adjustments performs best.

Canonical Cointegrating Regression and Testing for Cointegration in the Presence of I(1) and I(2) Variables

1997 ◽  
Vol 13 (6) ◽  
pp. 850-876 ◽  
Author(s):  
In Choi ◽  
Joon Y. Park ◽  
Byungchul Yu
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Asymptotic Theory ◽  
Finite Sample ◽  
Cointegration Tests ◽  
Simulation Monte Carlo ◽  
Simulation Results ◽  
Canonical Cointegrating Regression

This paper introduces tests for the null of cointegration in the presence of I(1) and I(2) variables. These tests use residuals from Park's (1992, Econometrica 60,119–143) canonical cointegrating regression (CCR) and the leads-and-lags regression of Saikkonen (1991, Econometric Theory 9,1–21) and Stock and Watson (1993, Econometrica 61, 783–820). Asymptotic theory for CCR in the presence of I(1) and I(2) variables is also introduced. The distributions of the cointegration tests are nonstandard, and hence their percentiles are tabulated by using simulation. Monte Carlo simulation results to study the finite sample performance of the CCR estimates and the cointegration tests are also reported.

scholarly journals Local Projections and VARs Estimate the Same Impulse Responses

Econometrica ◽  
2021 ◽  
Vol 89 (2) ◽  
pp. 955-980
Author(s):  
Mikkel Plagborg-Møller ◽  
Christian K. Wolf
Keyword(s):  
Structural Identification ◽  
Finite Sample ◽  
Impulse Responses ◽  
Vector Autoregressions ◽  
Reduction Techniques ◽  
Long Run ◽  
Finite Sample Properties ◽  
Short Run ◽  
Local Projections ◽  
Dimension Reduction Techniques

We prove that local projections (LPs) and Vector Autoregressions (VARs) estimate the same impulse responses. This nonparametric result only requires unrestricted lag structures. We discuss several implications: (i) LP and VAR estimators are not conceptually separate procedures; instead, they are simply two dimension reduction techniques with common estimand but different finite‐sample properties. (ii) VAR‐based structural identification—including short‐run, long‐run, or sign restrictions—can equivalently be performed using LPs, and vice versa. (iii) Structural estimation with an instrument (proxy) can be carried out by ordering the instrument first in a recursive VAR, even under noninvertibility. (iv) Linear VARs are as robust to nonlinearities as linear LPs.

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