scholarly journals The probabilities of type I and II error of null of cointegration tests: A Monte Carlo comparison

PLoS ONE ◽  
2022 ◽  
Vol 17 (1) ◽  
pp. e0259994
Author(s):  
Ahmet Faruk Aysan ◽  
Ibrahim Guney ◽  
Nicoleta Isac ◽  
Asad ul Islam Khan
Keyword(s):  
Monte Carlo ◽  
Time Trend ◽  
Type I Error ◽  
Linear Time ◽  
Critical Values ◽  
Type I ◽  
Sample Sizes ◽  
Linear Time Trend ◽  
Lm Test ◽  
Cointegration Tests

This paper evaluates the performance of eight tests with null hypothesis of cointegration on basis of probabilities of type I and II errors using Monte Carlo simulations. This study uses a variety of 132 different data generations covering three cases of deterministic part and four sample sizes. The three cases of deterministic part considered are: absence of both intercept and linear time trend, presence of only the intercept and presence of both the intercept and linear time trend. It is found that all of tests have either larger or smaller probabilities of type I error and concluded that tests face either problems of over rejection or under rejection, when asymptotic critical values are used. It is also concluded that use of simulated critical values leads to controlled probability of type I error. So, the use of asymptotic critical values may be avoided, and the use of simulated critical values is highly recommended. It is found and concluded that the simple LM test based on KPSS statistic performs better than rest for all specifications of deterministic part and sample sizes.

Performance of Monte Carlo Permutation and Approximate Tests for Multivariate Means Comparisons With Small Sample Sizes When Parametric Assumptions are Violated

Methodology ◽  
2009 ◽  
Vol 5 (2) ◽  
pp. 60-70 ◽  
Author(s):  
W. Holmes Finch ◽  
Teresa Davenport
Keyword(s):  
Monte Carlo ◽  
Type I Error ◽  
Permutation Tests ◽  
Error Rates ◽  
Covariance Matrices ◽  
Small Sample ◽  
Type I ◽  
Permutation Testing ◽  
Sample Sizes ◽  
Type I Error Rates

Permutation testing has been suggested as an alternative to the standard F approximate tests used in multivariate analysis of variance (MANOVA). These approximate tests, such as Wilks’ Lambda and Pillai’s Trace, have been shown to perform poorly when assumptions of normally distributed dependent variables and homogeneity of group covariance matrices were violated. Because Monte Carlo permutation tests do not rely on distributional assumptions, they may be expected to work better than their approximate cousins when the data do not conform to the assumptions described above. The current simulation study compared the performance of four standard MANOVA test statistics with their Monte Carlo permutation-based counterparts under a variety of conditions with small samples, including conditions when the assumptions were met and when they were not. Results suggest that for sample sizes of 50 subjects, power is very low for all the statistics. In addition, Type I error rates for both the approximate F and Monte Carlo tests were inflated under the condition of nonnormal data and unequal covariance matrices. In general, the performance of the Monte Carlo permutation tests was slightly better in terms of Type I error rates and power when both assumptions of normality and homogeneous covariance matrices were not met. It should be noted that these simulations were based upon the case with three groups only, and as such results presented in this study can only be generalized to similar situations.

Summarizing Monte Carlo Results in Methodological Research: The One- and Two-Factor Fixed Effects ANOVA Cases

1992 ◽  
Vol 17 (4) ◽  
pp. 315-339 ◽  
Author(s):  
Michael R. Harwell ◽  
Elaine N. Rubinstein ◽  
William S. Hayes ◽  
Corley C. Olds
Keyword(s):  
Monte Carlo ◽  
Error Rate ◽  
Fixed Effects ◽  
Type I Error ◽  
Type I ◽  
F Test ◽  
Unequal Variances ◽  
Type I Error Rate ◽  
Monte Carlo Studies ◽  
The One

Meta-analytic methods were used to integrate the findings of a sample of Monte Carlo studies of the robustness of the F test in the one- and two-factor fixed effects ANOVA models. Monte Carlo results for the Welch (1947) and Kruskal-Wallis (Kruskal & Wallis, 1952) tests were also analyzed. The meta-analytic results provided strong support for the robustness of the Type I error rate of the F test when certain assumptions were violated. The F test also showed excellent power properties. However, the Type I error rate of the F test was sensitive to unequal variances, even when sample sizes were equal. The error rate of the Welch test was insensitive to unequal variances when the population distribution was normal, but nonnormal distributions tended to inflate its error rate and to depress its power. Meta-analytic and exact statistical theory results were used to summarize the effects of assumption violations for the tests.

Comparison of methods to account for autocorrelation in correlation analyses of fish data

1998 ◽  
Vol 55 (9) ◽  
pp. 2127-2140 ◽  
Author(s):  
Brian J Pyper ◽  
Randall M Peterman
Keyword(s):  
Monte Carlo ◽  
Hypothesis Testing ◽  
Type I Error ◽  
Low Frequency ◽  
Error Rates ◽  
Type I ◽  
Testing Procedures ◽  
Type I Error Rates ◽  
Fish Recruitment ◽  
Correlation Analyses

Autocorrelation in fish recruitment and environmental data can complicate statistical inference in correlation analyses. To address this problem, researchers often either adjust hypothesis testing procedures (e.g., adjust degrees of freedom) to account for autocorrelation or remove the autocorrelation using prewhitening or first-differencing before analysis. However, the effectiveness of methods that adjust hypothesis testing procedures has not yet been fully explored quantitatively. We therefore compared several adjustment methods via Monte Carlo simulation and found that a modified version of these methods kept Type I error rates near . In contrast, methods that remove autocorrelation control Type I error rates well but may in some circumstances increase Type II error rates (probability of failing to detect some environmental effect) and hence reduce statistical power, in comparison with adjusting the test procedure. Specifically, our Monte Carlo simulations show that prewhitening and especially first-differencing decrease power in the common situations where low-frequency (slowly changing) processes are important sources of covariation in fish recruitment or in environmental variables. Conversely, removing autocorrelation can increase power when low-frequency processes account for only some of the covariation. We therefore recommend that researchers carefully consider the importance of different time scales of variability when analyzing autocorrelated data.

Parametric Alternatives to the Analysis of Variance

1982 ◽  
Vol 7 (3) ◽  
pp. 207-214 ◽  
Author(s):  
Jennifer J. Clinch ◽  
H. J. Keselman
Keyword(s):  
Monte Carlo ◽  
Analysis Of Variance ◽  
Monte Carlo Methods ◽  
Type I Error ◽  
Type I ◽  
Test Statistic ◽  
F Test ◽  
Assumption Violations ◽  
Mean Equality

The ANOVA, Welch, and Brown and Forsyth tests for mean equality were compared using Monte Carlo methods. The tests’ rates of Type I error and power were examined when populations were non-normal, variances were heterogeneous, and group sizes were unequal. The ANOVA F test was most affected by the assumption violations. The test proposed by Brown and Forsyth appeared, on the average, to be the “best” test statistic for testing an omnibus hypothesis of mean equality.

scholarly journals Subsampling Intervals in Autoregressive Models with Linear Time Trend

Econometrica ◽  
2001 ◽  
Vol 69 (5) ◽  
pp. 1283-1314 ◽  
Author(s):  
Joseph P. Romano ◽  
Michael Wolf
Keyword(s):  
Time Trend ◽  
Linear Time ◽  
Autoregressive Models ◽  
Linear Time Trend

Summarizing Monte Carlo Results in Methodological Research

1992 ◽  
Vol 17 (4) ◽  
pp. 297-313 ◽  
Author(s):  
Michael R. Harwell
Keyword(s):  
Monte Carlo ◽  
Type I Error ◽  
Error Rates ◽  
Type I ◽  
Type I Error Rates ◽  
Power Of A Test ◽  
Methodological Research ◽  
Assumption Violations ◽  
Monte Carlo Studies ◽  
Effective Use

Monte Carlo studies provide information that can assist researchers in selecting a statistical test when underlying assumptions of the test are violated. Effective use of this literature is hampered by the lack of an overarching theory to guide the interpretation of Monte Carlo studies. The problem is exacerbated by the impressionistic nature of the studies, which can lead different readers to different conclusions. These shortcomings can be addressed using meta-analytic methods to integrate the results of Monte Carlo studies. Quantitative summaries of the effects of assumption violations on the Type I error rate and power of a test can assist researchers in selecting the best test for their data. Such summaries can also be used to evaluate the validity of previously published statistical results. This article provides a methodological framework for quantitatively integrating Type I error rates and power values for Monte Carlo studies. An example is provided using Monte Carlo studies of Bartlett’s (1937) test of equality of variances. The importance of relating meta-analytic results to exact statistical theory is emphasized.

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