Frequency Domain

Abstract

Time series analysis in frequency domain has always been an active area of research. Theorists often employ techniques in frequency domain to advance current understanding on complex time series properties and develop useful toolboxes for practical time series analysis. This chapter reviews several concepts from frequency domain that are helpful for forecasting. The main focus is on the intuition behind these techniques rather than a rigorous mathematical introduction. In addition to the traditional frequency domain techniques, this chapter also discusses a time-frequency domain technique called wavelets, which has recently become an active area of research in financial econometrics due to the availability of tall and huge financial data. A novel application of the ZVAR model based on the generalised shift operator will also be introduced. ZVAR has the ability to produce forecasts at a sampling frequency that is different from the sampling frequency of the data. Monte Carlo experiments show that this approach performs relatively well when compared with the forecast performance of the true data generating process. Given the availabilities of big data, one may expect data with different sampling frequencies would become more common. ZVAR would seem to be a complementary method to other mixed frequency approaches such as Mixed Data Sampling (MIDAS).