Determination of multiple and seasonal unit roots with bridge estimator

Economic series may have unit roots. There are different methods to test unit roots in the literature. Recent studies show the importance of using Bridge estimator for choosing the lag length of single unit root tests and parameter estimation. This method penalizes the parameters of the model with a positive shrinkage parameter. For a suitable choice of the shrinkage parameter, Bridge estimator finds parameter estimates as zero asymptotically when the true value of the parameter is zero for stationary series. This feature is called the oracle property and in this way the Bridge estimator provides a method that can be used for the model selection and estimation simultaneously. It is known in the literature that Bridge estimator does the model selection while simultaneously distinguishing between stationary and unit root models for series with a unit root as well. However, it is known that time series can sometimes contain more than one unit root. Based on this, in the study firstly, Bridge estimator is proposed to determine the integration order of series with more than one unit root. In order to do this, Bridge estimator is applied to Dickey-Pantula model. With a simulation study Bridge estimator is compared with the existent Dickey-Pantula test in terms of determining the order of integration. The results are also supported with an econometric application. The second part of the thesis, using of the Bridge estimator is proposed for the seasonal unit root. Seasonality is very substantial factor for numerous economic time series and there are so many methods to test seasonal unit roots in the literature. In addition to these methods, in this study, Bridge estimator is also defined to test seasonal unit root in a HEGY model. A Monte-Carlo experiment is applied to test the efficiency of this technique and compare size and power of this approach with HEGY test. Furthermore, the method is applied on real data set and the results are compared. The analyses and comparisons has shown that Bridge estimator is a good alternative to determine both multiple unit root and seasonal unit root. Keywords: Bridge estimator, model selection, oracle property, unit root test, multiple unit root, seasonal unit root.