When speaking of time series, one usually has in mind a series of data points with a constant temporal interval. An example is the series of daily closing prices, where the interval between two data points of the time series is exactly one day. In the analysis of time-dependent data, however, it is not always possible to fit the measurements into such a uniform grid.
Let us consider as an example the intraday price development of a stock. Every concluded contract is contained in the intraday history as a so-called tick. The date, the time of day and the price at which the relevant security was traded are all known. The intervals between the concluded transactions, however, are not constant.
The modelling of such a time series requires the use of interpolation methods. Thus, for example, the average price of the past 30 minutes can constitute a data point for the time series. Such procedures, however, are not without problems. Within the said 30 minutes, two, 200 or no transaction might be concluded. Aside from the fact that in such a time series the price following a single transaction would weigh just as much as the average value of 200 transactions in another 30 minute time period, much information regarding the actual price movement is lost in this type of interpolation. In order to conserve all of this information, a modelling method is required, which is able to represent »fuzzy« time series with varying intervals between the data points.