Terasvirta test and stationarity

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Terasvirta test and stationarity

Georgii
Good afternoon, everyone I have a question about terasvirta test in "fNonlinear" and "tseries" packages. I have a stationary time-series of stock returns, that I have proved with adf.test, kpss.test and pp.test. All three tests showed that the time-series is stationary, so, it means that the mean of this series is constant and so on. After that, I tried to use a terasvirta test and it has shown the very small p-value (Chi-squared: 0.0002348, F: 0.0002395), so I should reject the the H0 hypothesis of linearity in "mean" but how this can happen? The time-series is stationary, so the mean is constant and that means that there is no nonlinearity in mean at all...Am I right? The White test showed almost the same. The original time-series is a stock market quotes but on the original series (before taking differences) the terasvirta test show the p-value = 0.3447... This is a little bit strange I think

Moreover, I would like to ask you to write some packages that can help me to test the linearity in "mean"... I could not find anything except terasvirta test and white test and I am a bit confused about Keenan and Tsay tests, because I'm not sure-whether they test linearity in "mean" or linearity in "variance".

Thanks a lot!