  We demonstrate on a case study with two competing products at a bank how one
can use a Hidden Markov Chain (HMC) to estimate missing information on a
competitor's marketing activity. The idea is that given time series with sales
volumes for products A and B and marketing expenditures for product A, as well
as suitable predictors of sales for products A and B, we can infer at each
point in time whether it is likely or not that marketing activities took place
for product B. The method is successful in identifying the presence or absence
of marketing activity for product B about 84% of the time. We allude to the
issue of whether, if one can infer marketing activity about product B from
knowledge of marketing activity for product A and of sales volumes of both
products, the reverse might be possible and one might be able to impute
marketing activity for product A from knowledge of that of product B. This
leads to a concept of symmetric imputation of competing marketing activity. The
exposition in this paper aims to be accessible and relevant to practitioners.
