ABSTRACT
When we speak of a complete data set we mean a data set whose constituent series have known values at every timing point defined over a given interval. For example, if we have a data set comprising monthly series for sales and price from January 1985 to August 1991, then if the monthly sales and price values are recorded for all of these months, the data set is complete. The data sets that we have utilised in previous chapters are complete in this sense. It is now fairly clear what we mean by an incomplete data set: a data set in which there is at least one component series for which one or more of the ‘observations’ are unknown. In the context of the foregoing example, this could be a missing sales value for September 1987 say. Such ‘missing values’ may be missing for any number of reasons; indeed a value may not be missing at all, merely regarded as rather unreliable. The reasons do not concern us directly at this point, but whatever they may be, the fact is the values are not known and our modelling and analysis must be capable of dealing with the situation. Data series with values unavailable for certain times pose no particular problems for a Bayesian analysis. At any time for which there is no ob servation on the series of interest, one’s posterior distribution on model parameters is straightforwardly one’s prior for that time. With no new information becoming available, estimates and uncertainties remain unal tered. This is the basic situation. Irregularly observed time series can be handled in the same way by defining an equally spaced underlying time scale, placing the known observations appropriately on that scale, and treating the unfilled times as missing values. BATS is quite capable of
dealing with missing observations: this chapter explains and demonstrates the mechanics.
