Interval Time Series Analysis with an Application to the Sterling-Dollar Exchange Rate

Traditional econometrics has long employed "points" to measure time series data. In real life situations, however, it suffers the loss of volatility information, since many variables are bounded by intervals in a given period. To address this issue, this paper provides a new methodology for interval time series analysis. The concept of "interval stochastic process" is formally defined as a counterpart of "stochastic process" in point-based econometrics. The authors introduce the concepts of interval stationarity, interval statistics (including interval mean, interval variance, etc.) and propose an interval linear model to investigate the dynamic relationships between interval processes. A new interval-based optimization approach for estimation is proposed, and corresponding evaluation criteria are derived. To demonstrate that the new interval method provides valid results, an empirical example on the sterling-dollar exchange rate is presented.