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11
Dependent Stochastic
Processes and Time Series
In this chapter, we continue the study of random processes initiated in Chapter 7. As you recall
in that chapter, we assumed that the values at any time t are independent of the values at previous
times. In this chapter, we will relax this assumption to allow for the value at time t to be depen-
dent on values at previous times. Therefore, the value at time t is conditioned on the history of
the process.
11.1 MARKOV
11.1.1 DepenDent MoDels: Markov chain
In many cases we can assume that the random value depends only on recent past values, instead
of the entire history. For example, the rainfal