  Given an integral hyperplane arrangement, Kamiya-Takemura-Terao (2008 & 2011)
introduced the notion of characteristic quasi-polynomial, which enumerates the
cardinality of the complement of the arrangement modulo a positive integer. The
most popular candidate for period of the characteristic quasi-polynomials is
the lcm period. In this paper, we initiate a study of period collapse in
characteristic quasi-polynomials stemming from the concept of period collapse
in the theory of Ehrhart quasi-polynomials. We say that period collapse occurs
in a characteristic quasi-polynomial when the minimum period is strictly less
than the lcm period. Our first main result is that in the non-central case,
with regard to period collapse anything is possible: period collapse occurs in
any dimension $\ge 1$, occurs for any value of the lcm period $\ge 2$, and the
minimum period when it is not the lcm period can be any proper divisor of the
lcm period. Our second main result states that in the central case, however, no
period collapse is possible in any dimension, that is, the lcm period is always
the minimum period.
