A New Approach to Modeling Multivariate Time Series on Multiple Temporal Scales

In certain situations, observations are collected on a multivariate time series at a certain temporal scale. However, there may also exist underlying time series behavior on a larger temporal scale that is of interest. Often times, identifying the behavior of the data over the course of the larger scale is the key objective. Because this large scale trend is not being directly observed, describing the trends of the data on this scale can be more difficult. To further complicate matters, the observed data on the smaller time scale may be unevenly spaced from one larger scale time point to the next. The existence of these multiple time scales means that it may be more appropriate to view the observations as coming from multiple, shorter multivariate time series occurring at each large scale time point as opposed to a single, long multivariate time series. Approaching the problem by examining the smaller scale time series separately, and then modeling the resulting estimates over the larger time scale, will provide an alternative to previous methods of dealing with similar situations while also producing additional information on the behavior of the data on the smaller observable time scale.