  To reduce operational costs, gas distribution networks require accurate
forecasts of the demand for gas. Amongst domestic and commercial customers,
demand relates primarily to the weather and patterns of life and work. Public
holidays have a pronounced effect which often spreads into neighbouring days.
We call this spread the "proximity effect". Traditionally, the days over which
the proximity effect is felt are pre-specified in fixed windows around each
holiday, allowing no uncertainty in their identification. We are motivated by
an application to modelling daily gas demand in two large British regions. We
introduce a novel model which does not fix the days on which the proximity
effect is felt. Our approach uses a four-state, non-homogeneous hidden Markov
model, with cyclic dynamics, where the classification of days as public
holidays is observed, but the assignment of days as "pre-holiday",
"post-holiday" or "normal" is unknown. The number of days to the preceding and
succeeding holidays guide transitions between states. We apply Bayesian
inference and illustrate the benefit of our modelling approach. A preliminary
version of the model is now being used by one of the UK's regional distribution
networks.
