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In this paper, we apply the wavelet methods in the popular Augmented Dickey-Fuller and M types of unit root tests. Moreover, we provide an extensive comparison of the wavelet based unit root tests which also includes the recent contributions in the literature. Moreover, we derive the asymptotic properties of the wavelet based unit root tests under generalized least squares detrending mechanism. We demonstrate that the wavelet based M tests exhibit better size performance even in problematic cases such as the presence of negative moving average innovations. However, the power performances of the wavelet based unit root tests are quite similar to each other.

In this study, we estimate a time-varying Taylor rule for evaluating the policy reaction function of the Central Bank of the Republic of Turkey (CBRT). Even though the Turkish economy has been continuously evolving in the last 15 years, previous studies that analyze the monetary policy rule of the CBRT mainly use time-invariant monetary policy functions. We propose a flexible two-stage least square regression to deal with both instability and endogeneity problems in the monetary policy functions. By analyzing the period between 2006 and 2019, we clearly show that the monetary policy function of the CBRT changes over time, and using a time-invariant monetary policy rule model would yield misleading results.

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