Stochastic Processes Subject to Time-Scale Transformations: An Application to High-Frequency FX Data

Abstract

This paper is a general investigation of temporal aggregation in time series analysis. It encompasses traditional research on time aggregation as a particular case and extends the analysis to irregular intervals of aggregation. The Data Generating Process is allowed to evolve at regular, deterministic-irregular or even stochastic intervals of time (operational time). The time scale of this process is then transformed to generate the observational time process. This transformation can be deterministic (such as the familiar aggregation of monthly data into quarters) or more generally, stochastic (such as aggregating stock market quotes by the hour). In general, the observational time model exhibits persistence, time-varying parameters and non-spherical disturbances. Consequently, we review detection, specification, estimation and structural inference in this context, provide new solutions to these issues, and apply our results to high frequency, FX data.