Sample size determination and stationarity testing in the presence of trend breaks

Traditionally it is believed that most macroeconomic time series represent stationary fluctuations around a deterministic trend. However, simple applications of the Dickey-Fuller test have, in many cases, been unable to show that major macroeconomic variables are stationary univariate time series structure. One possible reason for non-rejection of unit roots is that the simple mean or linear trend function used by the tests are not sufficient to describe the deterministic part of the series. To address this possibility, unit root tests in the presence of trend breaks have been studied by several researchers.;In our work, we deal with some issues associated with unit root testing in time series with a trend break.;The performance of various unit root test statistics is compared with respect to the break induced size distortion problem. We examine the effectiveness of tests based on symmetric estimators as compared to those based on the least squares estimator. In particular, we show that tests based on the weighted symmetric estimator not only eliminate the spurious rejection problem but also have reasonably good power properties when modified to allow for a break.;We suggest alternative test statistics for testing the unit root null hypothesis in the presence of a trend break. Our new test procedure, which we call the "bisection" method, is based on the idea of subgrouping. This is simpler than other methods since the necessity of searching for the break is avoided.;Using stream flow data from the US Geological Survey, we perform a temporal analysis of some hydrologic variables. We first show that the time series for the target variables are stationary, then focus on finding the sample size necessary to detect a mean change if one occurs. Three different approaches are used to solve this problem: OLS, GLS and a frequency domain method. A cluster analysis of stations is also performed using these sample sizes as data. We investigate whether available geographic variables can be used to predict cluster membership.