8Time Series
Throughout this chapter we shall focus on time series in discrete time; those whose time index 
is integer valued; that is, 
. We shall typically label the observed values of time series as 
or 
, and so on.
We shall assume that our time series is either stationary in some sense or may be reduced to stationarity by a combination of elementary differencing operations and regression trend removal. Two types of stationarity are in common use, second‐order stationarity and strict stationarity. The sequence is said to be second‐order (or wide‐sense) stationary if the first‐ and second‐order moments 
and 
exist and are finite, with 
a constant independent of 
, and the covariance of and ...
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