Very useful answer Dr. Kumar Roy. I recommend it.

Any autoregressive process is necessarily invertible but a stationarity condition must be imposed to ensure uniqueness of model for a particular autocorrelation structure. A moving average process on the other hand is stationary but in order for there to be a unique model for a particular autocorrelation structure an invertbility condition must be imposed. This invertibility condition is usually built into a software to ensure uniqueness of model fitting. The root of the characteristic equation should lie outside the unit circle for such a moving average model.

thank you prof. Ajit kumar Roy and Ette Etuk for your valuable answer to my query.

what do you mean by current and past innovations?

How do we derive this variable in compuation of MA?

thanks in advance

A moving average model is a linear combination of innovations ei's. That is Xt = et+a1*et-1+a2*et-2+ ... + aq*et-q is a moving average model of order q (MA(q)). The current innovation is et and the et-i's are the past innovations. For invertibility of an MA(1), a1 < 1.

The following discussion in stackexchange should give you an intuitive explanation of the invertibility of moving average processes (see the comment by Rob Hyndman): https://stats.stackexchange.com/questions/50682/what-is-the-intuition-of-invertible-process-in-time-series

Invertibility refers to linear stationary process which behaves like infinite representation of autoregressive. In other word, this is the property that possessed by a moving average process. Invertibility solves non-uniqueness of autocorrelation function of moving average.