I was wondering how his "second-order stationary process" is defined in Brockwell and Davis' Introduction to Time Series and Forecasting:
The class of linear time series models, which includes the class of autoregressive moving-average (ARMA) models, provides a general framework for studying stationary processes. In fact, every second-order stationary process is either a linear process or can be transformed to a linear process by subtracting a deterministic com- ponent. This result is known as Wold's decomposition and is discussed in Section 2.6.
The case of second-order stationarity arises when the requirements of strict stationarity are only applied to pairs of random variables from the time-series.
But I think the book has a different definition from Wikipedia's, because the book uses stationarity short for wide-sense stationarity, while Wikipedia uses stationarity short for strict stationarity.
Thanks and regards!