Analysis of High-Frequency Seasonal Time Series

Data of high-frequency time series are widely available nowadays. These data often exhibit certain features that are similar to, yet distinct from those of the low-frequency time series. Conventional time series methods thus become inadequate in analyzing such high-frequency data. In this chapter, we propose a structural approach to overcome the difficulties in analyzing high-frequency time series. In particular, a mixture of deterministic and stochastic components is used, in conjunction with conditional heteroscedasticity, to model the seasonality of the high-frequency series. The usefulness and applicability of the proposed approach is demonstrated by modeling hourly measurements of particulate matter with diameters 2.5 micrometers and smaller (PM \({ }_{2.5}\) ) series over a ten year period with sample size 87600. Extensions to modeling high-frequency seasonal spatio-temporal series are discussed.