Improving inference in integration and cointegration tests

In this thesis, I address three di erent problems in unit root and cointegration models and I propose new methods to improve inference in testing procedures for these models. Two of these problems are related to unit root tests. First one is so-called nonstationary volatility issue, which causes severe size distortions in standard unit root tests. I try to resolve this problem with a nonparametric technique introduced rst by Nielsen (2009). Second, I investigate the unit root testing under regulation, which constraints a time series process on a given interval. In this case, standard tests frequently fail to detect the presence of nonstationarity. I employ a similar methodology as in rst part and provide correct inference in unit root testing for regulated series. The nal problem is related to cointegration models. In these models, if innovations of the system are contaminated by MA type negative serial correlation, cointegration tests spuriously rejects the true null hypothesis. Combining wavelet theory and Nielsen's (2010) variance ratio testing procedure, I manage to reduce the impact of the problematic innovations on cointegration test. All three methods share the common feature of being nonparametric in sense that they do not require any regression or kernel type correction to handle serial correlation.