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10Further Topics
10.1 Transfer Function Models
10.1 Transfer Function Models
10.2 Intervention Analysis
10.3 Nonlinear Models
10.4 Continuous-Time Models
10.5 Long-Memory Models
In this final chapter we touch on a variety of topics of special interest. In Section 10.1
we consider transfer function models, designed to exploit for predictive purposes the
relationship between two time series when one acts as a leading indicator for the other.
Section 10.2 deals with intervention analysis, which allows for possible changes in
the mechanism generating a time series, causing it to have different properties over
different time intervals. In Section 10.3 we introduce the very fast growing area of
nonlinear time series analysis, and in Section 10.4 we briefly discuss continuous-time
ARMA processes, which, besides being of interest in their own right, are very useful
also for modeling irregularly spaced data. In Section 10.5 we discuss fractionally
integrated ARMA processes, sometimes called “long-memory” processes on account
of the slow rate of convergence of their autocorrelation functions to zero as the lag
increases.
In this section we consider the problem of estimating the transfer function of a linear
filter when the output includes added uncorrelated noise. Suppose that {Xt1} and {Xt2}