ABSTRACT
Records of real-world phenomena can mostly be categorized as nonsta-
tionary time series. The simplest approach to modeling nonstationary
time series is, firstly, to partition the time interval into several subin-
tervals of appropriate size, on the assumption that the time series are
stationary on each subinterval. Secondly, by fitting an AR model to each
subinterval, we can obtain a series of models that approximate nonsta-
tionary time series. In this chapter, two modeling methods are shown for
analysis of nonstationary time series, namely, a model for roughly de-
ciding on the number of subintervals and the locations of their endpoints
and a model for precisely estimating a change point. A more sophisti-
cated time-varying coefficient AR model will be considered in Chapter
8.1 Locally Stationary AR Model
It is assumed that the given time series y1, · · · ,yN is nonstationary as a whole, but that we can consider it to be stationary on each subinterval
of an appropriately constructed partition. Such a time series that satisfies
piecewise stationarity is called a locally stationary time series (Ozaki
and Tong (1975), Kitagawa and Akaike (1978), Kitagawa and Gersch
(1996)). To be specific, k and Ni are assumed to denote the number of
subintervals, and the number of observations in the i-th subinterval (N1+ · · ·+Nk = N), respectively. Actually, k and Ni are unknown in practical modeling. Therefore, in the analysis of locally stationary time series, it
is necessary to estimate the number of subintervals, k, the locations of
the dividing points and appropriate models for subintervals.
