Keywords: Symbolic Data, Interval Time Series, Internal Variation
While many series record a single value for each time point, many other series record the observations as intervals. This is particularly so with financial data, where, e.g., assets have two prices (bid and ask prices) and the interval between them represents all possible prices at which the asset can be traded. There are countless examples. Therefore, in comparison with standard classical data, they are more complex and can have structures (especially internal structures) that impose complications that are not evident in classical data. As a result of dependency in time series observations, it is difficult to deal with symbolic interval-valued time series data and take into account their complex structure and internal variability. In the literature, the proposed procedures for analyzing interval time series data used either midpoint or radius that are inappropriate surrogates for symbolic interval variables. All previously available methods in the literature fail in some way to use all the variations inherent in the interval-valued data; there is a loss of information. We develop a methodology using the information contained in the complete intervals (and not just on the two point values represented by the end points and/or the center-range values) to analyze interval time series data.