Frequency Domain Time Series is an advanced course on foundations and applications of time series. Methods involving periodograms and spectral densities are...More >>
Frequency Domain Time Series is an advanced course on foundations and applications of time series. Methods involving periodograms and spectral densities are emphasized. Linear filtering and spectral representations (stochastic integrals)for stationary time series are used as unifying themes. The second half of the course considers GARCH models, fractals, long memory and fractional cointegration. Again, emphasis is on insights gained from the frequency domain viewpoint. The mathematics used in the course is Fourier analysis, a useful tool for all technically-oriented students. All mathematical results are presented in a self-contained manner. The course grades are based on homework assignments (70% of the grade)and an in-class open-book final exam (30% of the grade). Homeworks can be re-submitted for further credit, at any time. There is a clear need for advanced students in statistics, finance and economics to have a deep understanding of time series in the frequency domain. Increasingly, frequency domain methods and models are being used by practitioners.