t-statistic

Abstract: This paper studies the random walk, in a general time series setting that allows for weakly dependent and heterogeneously distributed innovations. It is shown that simple least squares regression consistently estimates a unit root under very general conditions in spite of the presence of autocorrelated errors. The limiting distribution of the standardized estimator and the associated regression t statistic are found using functional central limit theory. New tests of the random walk hypothesis are developed which permit a wide class of dependent and heterogeneous innovation sequences. A new limiting distribution theory is constructed based on the concept of continuous data recording. This theory, together with an asymptotic expansion that is developed in the paper for the unit root case, explain many of the interesting experimental results recently reported in Evans and Savin (1981, 1984).

Abstract: Part I: INTRODUCTION AND DESCRIPTIVE STATISTICS. 1. Introduction to Statistics. 2. Frequency Distributions. 3. Central Tendency. 4. Variability. Part I Review. Part II: FOUNDATIONS OF INFERENTIAL STATISTICS. 5. Z-Scores: Location of Scores and Standard Distributions. 6. Probability. 7. Probability and Samples: The Distribution of Sample Means. 8. Introduction to Hypothesis Testing. Part II Review. Part III: USING t STATISTICS FOR INFERENCES ABOUT POPULATION MEANS AND MEAN DIFFERENCES. 9. Introduction to the t Statistic. 10. The t test for Two Independent Samples. 11. The t test for Two Related Samples. 12. Estimation. Part III Review. Part IV: ANALYSIS OF VARIANCE: TESTS FOR DIFFERENCES AMONG TWO OR MORE POPULATION MEANS. 13. Introduction to Analysis of Variance. 14. Repeated-Measures and Two-Factor Analysis of Variance. Part IV Review. Part V: CORRELATIONS AND NON-PARAMETRIC TESTS. 15. Correlation and Regression. 16. The Chi-Square Statistic: Tests for Goodness of Fit and Independence. Part V Review. Appendix A: Basic Mathematics Review. Appendix B: Statistical Tables. Appendix C: Solutions for Odd-Numbered Problems in the Text. Appendix D: General Instructions for Using SPSS.

Abstract: This study considers testing for a unit root in a time series characterized by a structural change in its mean. The analysis is in the spirit of Perron (1990a), who showed that the existence of such a shift in a stationary time series biases the usual tests for a unit root toward nonrejection. The approach is, however, different given that we suppose the date of the change to be unknown. The statistic of interest is then the minimal t statistic over all possible breakpoints in regressions similar to those proposed by Perron (1990a). Other related statistics are also discussed. We derive and tabulate the asymptotic distributions of interest. Most of the emphasis, however, is given to the tabulation of finite-sample critical values using simulation experiments. Particular attention is given to the effect, on the finite-sample critical values, of various procedures to select the appropriate order of the estimated autoregressions. We apply the tests to analyze the issue of purchasing power parity between the ...

Abstract: Response surface analysis is used to obtain approximate finite-sample critical values for the augmented Dickey–Fuller (ADF) test. Previous studies estimating the critical values for the test have generally ignored their possible dependence on the lag order. This study shows that the lag order, in addition to the sample size, can affect the finite-sample behavior of the test. The result points to the importance of correcting for the effect of lag order in applying the ADF test.