# Why use ARMA (1,0,0) when AR (1) could work

I'm confused because I thought $$ARMA(p,q)$$, has elements of autoregression $$AR(p)$$ and moving average $$MA(q)$$.

I know a series is $$ARIMA$$ if the differenced data is an $$ARMA$$.

The authors of something I'm reading say that this model:

$$Y_t=0.9Y_{t-1}+W_t$$ is an $$ARIMA (1,1,0)$$ because the differenced data are an autoregression of order one:

$$Y_t=X_t-X_{t-1}$$

I agree with the differenced data being an autoregression of order 1 but if a series is a $$ARIMA$$ if the differenced data is an $$ARMA$$, then where's the moving average part?.

In other words, why say that a series is a $$ARIMA$$ if the differenced data is an $$ARMA$$, why not just say that a series is a $$ARIMA$$ if the differenced data is an autoregression.

• Why ever use a general word instead of the most specific word possible? Nov 29, 2018 at 21:41

## 1 Answer

There is no MA part .. thus it could be referred to as an ARI model . In a similar vein if there is no AR structure but differencing and an MA then it could be called an IMA model. The usage of the term ARIMA is a collective one not necessarily as precise as you wish but it is in common parlance.

Your example is an ARIMA in X and an ARMA in Y .... or more precisely ARI in X and AR in Y