Before we talking about the ARMA models (frequently seen in economic literatures), let's begin with the basic concepts where all these time series models are built. Things being reviewed include autocovariance, autocorrelation, partial autocorrelation, moving average, and autoregressive representations of time series. I will also give brief introduction on stationarity and ergodicity.
A stochastic process is a family of random variables that describes the evolution through time of some process. We can see stochastic process as a process described by statistical properties, opposed to a deterministic process such as sin(t). A stochastic time series is a realization from a certain stochastic process.
completely stationarity: any time series distribution function is time-invariant. Why should we worry about stationarity? We need to remove stationarity before we do most of the time series analysis, so we have a lot of preprocessing.
