# MA process formula explained

I'm currently reading about moving average processes. According to my textbook, the following applies:

$$y_t=\mu + \epsilon_t -\theta_1\epsilon_{t-1}-...-\theta_q \epsilon_{t-q}$$

Questions on formula:

-Does this presuppose a constant process, since we only have $\mu$ and error terms in the formula?

-Is this in any way related to the simple moving average ($M_T=\frac {y_T + y_{T-1}+...+y_{T-N+1}}{N}$)?

-Why do we subtract the weighted values, instead of adding everything up and dividing with the number of time points (as shown above)?

• 1. What do you mean by "constant process"? Stationary process, maybe. In which case this is correct: the marginal distribution of $y_t$ does not depend on $t$. – Xi'an Jan 2 '16 at 20:38
• The weighted and lagged error terms are there to create correlation between the $y_t$'s. Up to lag $q$. – Xi'an Jan 2 '16 at 20:53
• I definitely suggest you to read an introductory book on times series, like Brockwell and Davis' Introduction to Times Series and Forecasting. Or an equivalent on-line introduction. Like [Davis' notes](www.stat.columbia.edu/~rdavis/lectures/Session6.pdf). – Xi'an Jan 2 '16 at 21:23
• On closer inspection, my course book (though sharing the same name) is written by Montgomery/Jennings/Kulachi. I'll try a peek at the ones you suggested. – Magnus Jan 2 '16 at 21:38
• The subtraction is simply a matter of convention that goes back to the book by Box and Jenkins. – Brian Borchers Jan 3 '16 at 0:13