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m a processThe m a process, denoted as MA(q), is the general finite order process that is an autoregressive representation of a stationary series. It is a stationary process in the sense that the current conditional expectation depends solely on a function of the lagged and current unknown shocks. This function is called the partial autocorrelation.
The MA(q) is not a unique MA polynomial, which is different from AR processes. There are a variety of MA(q), lag operator polynomials, which could be stationary, and share the same asymptotic property.
It is therefore normal to impose invertibility constraints on the MA polynomial to ensure that the process is causal. This guarantees that only past events (not future ones) predict current events.
