What is the m a Process?

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The m Process, denoted by MA(q) is believed to be the general finite order process that is an autoegressive version of a stationary series that has covariance. It is stationary in the sense that the current conditional expectations are solely dependent on the lagged and current shocks. This function is the partial autocorrelation function.

The MA(q) does not possess a unique MA polynomial, unlike AR processes. In fact, there are numerous possibilities for MA(q) lag operator polynomials that could be stationary and possess the same asymptotic properties.

It is therefore conventional to place invertibility constraints on the MA polynomial to ensure that the process is causal. This ensures that only past events (not future ones) predict current events.