Nestacionarumo tikrinimas su artimomis alternatyvomis AR(1) modelyje

This master thesis examines unit root testing with the sequence of local alternatives. We analyse first order autoregressive process AR(1) and as test statistics we use $n(\hat{\phi}_n - 1)$, where $\hat{\phi}_n$ is a least squares estimator of an autoregressive parameter $\phi$. As an alternative we use the definition and various parameterizations of nearly nonstationary AR(1) process. The empirical cumulative distribution functions and size-adjusted test power curves are analysed in the paper using the most famous parameterizations of coefficient of nearly nonstationary process. We prove limiting distribution of test statistics under alternative with root near unity, confirm the results graphically, with test power analysis we check the probability of making type II error. According to size-adjusted test power curves there is a big possibility to reject a null hypothesis that first order autoregressive model is nonstationary process when it is false