Unit root tests applied to data with strong seasonality

[alvarezcc]

Hi, I applied both Dickey-Fuller and Phillips-Perron unit root tests to a variable with a strong seasonal pattern. But I would like to know if not accounting for such seasonality when performing these tests (or unit root tests in general) can provide biased results then leading me to wrong conclusions about the presence or not of a unit root. For the original series both tests don´t reject the null of a unit root. But when applying these tests to the filtered series (to remove seasonality) that null is rejected. I would really appreciate if someone can help me about these issue.

Thanks in advance

[TomDoan]

Hi, I applied both Dickey-Fuller and Phillips-Perron unit root tests to a variable with a strong seasonal pattern. But I would like to know if not accounting for such seasonality when performing these tests (or unit root tests in general) can provide biased results then leading me to wrong conclusions about the presence or not of a unit root. For the original series both tests don´t reject the null of a unit root. But when applying these tests to the filtered series (to remove seasonality) that null is rejected. I would really appreciate if someone can help me about these issue.

Thanks in advance

A series with a strong seasonal will generally have a seasonal unit root. A seasonal unit root includes a simple unit root plus other harmonics. (For quarterly data, (1-L^4)=(1-L)(1+L+L^2+L^3)). As a result, if you do a DF regression, you'll probably see something close to a zero coefficient on the lagged dependent variable. However, the null in the DF regression is that dy is a stationary process which won't be true if seasonal differencing is appropriate. While the lagged y has a zero coefficient under the null, the asymptotics are wrong since the assumptions are violated. There's a separate test for seasonal unit roots, known as the HEGY test (S. Hylleberg, R. Engle, W. Granger, and B. Yoo(1990), "Seasonal Integration and Cointegration", Journal of Econometrics, vol 44, pp. 215-238). There's a HEGY procedure for quarterly data and MHEGY for monthly.

[alvarezcc]

Thank you very much Tom for your prompt response.