Abstract
This paper demonstrates a theoretical foundation for integration of trend stationarity (TS) and constrained autoregressive (CAR) tests. Analytical examination suggests that the correlation coefficient between the regressors of the CAR and TS tests approaches unity as the aggregation used by the CAR test increases, suggesting that the TS test is a close substitute for long-memory CAR tests. Monte Carlo simulations for the special case of a random walk with a drift process confirm that the correlation between the two regressors approaches unity as aggregation increases. Our results can be used as platform for development of richer and more informative unit root and mean reversion tests.
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