Topics on time series resampling and subsampling

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The statistical analysis of time series is of central importance in econometrics. Existing methods for inference in time series analysis, however, often rely on unrealistic and sometimes unverifiable assumptions. This research continues the principal investigator's on-going research in the development of methods of inference for time series analysis that do not rely on unrealistic or unverifiable model assumptions. Resampling and subsampling methods offer viable approaches to obtaining valid distributional approximations while assuming very little about the stochastic mechanism generating time series data, in contrast to existing methods that make unrealistic distributional assumptions about the data. Many important questions still need to be addressed in order for these modern approaches to be applied safely and accurately. This research investigates four main issues: (a) kernel design in accurate residual bootstrap and local block bootstrap schemes as well as the problem of optimal bandwidth/block size choice; (b) resampling schemes for nonstandard/nonstationary situations; (c) methods for conducting powerful bootstrap hypothesis testing as well as accurate resampling inference-such as confidence intervals-under the set-up of a possibly integrated univariate time series; and (d) appropriate resampling mechanisms for multivariate time series with applications to cointegration testing and spurious regressions.The research results will contribute to several areas of time series analysis, including the use of fat-top kernels both in the context of residual bootstrap and in pilot estimators for most accurate bandwidth/block size choice and the development of two different bootstrap schemes, one based on a local blocking technique and the other on residuals, to address data from locally (but not globally) stationary series. (The research will also identify a way to conduct most powerful bootstrap hypothesis tests in linear regressions and consistent/ powerful bootstrap unit root tests are devised in addition to a subsampling procedure that works regardless of the presence of a unit root. Finally, the research also defines a Continuous-Path Block Bootstrap for multivariate data, and its validity in approximating the distribution of several statistics of interest is shown. This research will provide important results for effectively analyzing time series data with minimal assumptions about the data generating process. The results of this research will have practical applications in several areas, such as the analysis of exchange rates, stock market returns, and interest rates variability.