We want to estimate the correlation between LSAT and GPA scores. We have 15 paired observations of student LSAT scores and GPAs. The data used in this tutorial are from Efron and Tibshirani’s (1993) text on bootstrapping (page 19). See our blog post on bootstrapping for more specifics on the formulas used for the different types of bootstrap confidence intervals.
This tutorial demonstrates how to use bootstrapping to calculate confidence intervals in Stata. The bootstrap is most commonly used to estimate confidence intervals. You can calculate a statistic of interest on each of the bootstrap samples and use these estimates to approximate the distribution of the statistic. Min MAIC = 3.295598 at lag 1 with RMSE 5.The bootstrap is a statistical procedure that resamples a dataset (with replacement) to create many simulated samples.
To test whether the yrwd2 series is a random walk with drift, I use dfgls with a maximum of 4 lags for the regression specification in (4).ĭF-GLS tau 1% Critical 5% Critical 10% Critical
The null hypothesis is a random walk with a possible drift with two specific alternative hypotheses: the series is stationary around a linear time trend, or the series is stationary around a possible nonzero mean with no time trend. (1996) show that this test has better power than the ADF test. However, prior to fitting the model in (4), one first transforms the actual series via a generalized least-squares (GLS) regression. The GLS–ADF test proposed by Elliott et al. GLS detrended augmented Dickey–Fuller test Using pperron to test for a unit root in yrwd2 and yt yields a similar conclusion as the ADF test (output not shown here). Pperron performs a PP test in Stata and has a similar syntax as dfuller. The asymptotic distribution of the test statistics and critical values is the same as in the ADF test. As in the Dickey–Fuller test, a regression model as in (3) is fit with OLS.
The tests developed in Phillips (1987) and Phillips and Perron (1988) modify the test statistics to account for the potential serial correlation and heteroskedasticity in the residuals. In this case, we reject the null hypothesis of a random walk with drift. MacKinnon approximate p-value for Z(t) = 0.0000
Similarly, I test the presence of a unit root in the yt series. MacKinnon approximate p-value for Z(t) = 0.2511Īs expected, we fail to reject the null hypothesis of a random walk with a possible drift in yrwd2. Test 1% Critical 5% Critical 10% Critical Hence, I use the option trend to control for a linear time trend in (4).ĭickey-Fuller test for unit root Number of obs = 149 The null hypothesis I am interested in is that yrwd2 is a random walk process with a possible drift, while the alternative hypothesis posits that yrwd2 is stationary around a linear time trend. I begin by testing for a unit root in the series yrwd2 and yt, which correspond to data from a random walk with a drift term of 1 and a linear deterministic time trend model, respectively. 17) lists the distribution of the test statistic for four possible cases. Note that (4) is in a general form and we can restrict \(\alpha\) or \(\delta\) or both to zero for regression specifications that lead to different distributions of the test statistic. \newcommandĪnd tests whether \(\beta=0\).