Time Series Analysis of Intervals

Abstract

Time series data are ubiquitous. Time series observations recorded as intervals are also ubiquitous; e.g., financial data recorded by the high and low daily stock market prices, or daily temperatures reported as minimum and maximum temperatures, are interval-valued observations. Analyses frequently proceed by using the interval endpoints (minimum and maximum) values or the midpoint values. Using such classical surrogates, while certainly producing answers, typically give inaccurate answers since the complete information contained within the intervals is ignored. The autoregressive model of order p for interval-valued time series observations is presented, whereby all the interval information is used. Model parameters are estimated, asymptotic properties are briefly discussed. The results are studied and compared with other methods through simulations and applied to a Dow Jones Index data set.