F-test

Abstract: The panel data unit root test suggested by Levin and Lin (LL) has been widely used in several applications, notably in papers on tests of the purchasing power parity hypothesis. This test is based on a very restrictive hypothesis which is rarely ever of interest in practice. The Im–Pesaran–Shin (IPS) test relaxes the restrictive assumption of the LL test. This paper argues that although the IPS test has been offered as a generalization of the LL test, it is best viewed as a test for summarizing the evidence from a number of independent tests of the sample hypothesis. This problem has a long statistical history going back to R. A. Fisher. This paper suggests the Fisher test as a panel data unit root test, compares it with the LL and IPS tests, and the Bonferroni bounds test which is valid for correlated tests. Overall, the evidence points to the Fisher test with bootstrap-based critical values as the preferred choice. We also suggest the use of the Fisher test for testing stationarity as the null and also in testing for cointegration in panel data.

Abstract: This paper presents a test of independence that can be applied to the estimated residuals of any time series model that can be transformed into a model driven by independent and identically distributed errors. The first order asymptotic distribution of the test statistic is independent of estimation error provided that the parameters of the model under test can be estimated -consistently. Because of this, our method can be used as a model selection tool and as a specification test. Widely used software1 written by Dechert and LeBaron can be used to implement the test. Also, this software is fast enough that the null distribution of our test statistic can be estimated with bootstrap methods. Our method can be viewed as a nonlinear analog of the Box-Pierce Q statistic used in ARIMA analysis.

Abstract: 1. Organizing Data and Some Simple Computations. 2. Confidence Intervals. 3. Correlation and Related Topics. 4. Analysis of Variance. 5. Supplemental Computations for Analysis of Variance. 6. Multivariate Analyses. 7. Nonparametric Tests, Miscellaneous Tests of Significance, and Indexes of Relationships. Appendices. Normal-Curve Areas. Critical Values of "Student's" t Statistic. Critical Values for Sandler's A Statistic. Values of the Chi-Square Statistic. Probabilities of the F Distribution. Fisher's z Transformation for Pearson's r Correlation Coefficient. Critical Values of Pearson's r Correlation Coefficient for Five Alpha Significance Levels. Critical Values of the U Statistic of the Mann-Whitney Test. Critical Values for Hartley's Maximum F Ratio Significance Test for Homogeneity of Variances. Significant Studentized Ranges for Duncan's New Multiple-Range Test. Significant Studentized Ranges for the Newman-Keuls' and Tukey Mulitple-Comparison Tests. Dunnett's Test: Comparison of Treatment Means with a Control. Critical Values of Wilcoxon's t Statistic for the Matched- Pairs, Signed-Ranks Test. Coefficients for Orthogonal Polynomials. Cumulative Probability Distribution for r', the Total Number of Runs Up or Down. Sample Size and Power.