Number of MA(q) terms - Eviews Manual vs Practice

[SEbert]

Dear all, I am refering to your online Eviews tutorial, specifically "Time Series Estimation - SERIAL CORRELATION AND ARMA MODELLING". On page 29 you mention that a MA(2) process has to be modeled as MA(1) MA(2) in eviews...I conclude, this applies as well for higher ordered MA(q) processes, e.g. MA(4) needs to be modeled as MA(1to4)? However, from various source/examples i can see that in practice once several of those terms found to be insignificant (e.g. MA(1), MA(2), MA(3), they are dropped (remaining just a MA(4) term). It seems unclear to me, whether this right. Can i omit this non significant MA terms? This would violate the restriction posed in the manual/tutorial. Moreover, on p26 you address this issue with AR(p) terms, lower ordered terms singled non-contiguous terms are OK, but for higher ordered all of them need (all lower AR terms) to be entered. What is "higher ordered" and "lower ordered"? What are the thresholds? Thanks for clarification.

[EViews Glenn]

All that the tutorial is indicating is that what is commonly termed an MA(2) is a process with unrestricted coefficients on both the first and second lags of the residuals. To specify this model in EViews you must include both an "MA(1)" and an "MA(2)" term.

You can certainly estimate restricted forms of this model if you wish by omitting a term. Likewise for higher order models.

So the bottom line is that you can add any MA, AR, SAR, SMA terms that you like. EViews will only use the ones that are listed explicitly.

[SEbert]

Thanks. Could you please shortly indicate what is understood as "higher ordered" and "lower ordered"? What are the "thresholds"? I am basically referring to the notion that "higher ordered MA terms are extremely difficult to estimate". Thanks for clarification.

[EViews Glenn]

Higher order - models with larger MA lags
Lower order - models with only lower MA lags

Note that people usually mean a model with all relevant terms when they speak of higher order MA processes (e.g., an unrestricted MA(12) process with non-zero coefficients on all lags from 1 to 12). But it can also mean a model with just a high lag (as in seasonal models). It depends on the context.

[SEbert]

Dear Glenn, thank you very much. I assume a MA(4) process is still considered rather "low ordered" then? Thanks as well for clarification on the notion "process".