Exercise

# AR vs MA models

As you've seen, autoregressive (AR) and simple moving average (MA) are two useful approaches to modeling time series. But how can you determine whether an AR or MA model is more appropriate in practice?

To determine model fit, you can measure the Akaike information criterion (AIC) and Bayesian information criterion (BIC) for each model. While the math underlying the AIC and BIC is beyond the scope of this course, for your purposes the main idea is these these indicators penalize models with more estimated parameters, to avoid overfitting, and smaller values are preferred. All factors being equal, a model that produces a lower AIC or BIC than another model is considered a better fit.

To estimate these indicators, you can use the AIC() and BIC() commands, both of which require a single argument to specify the model in question.

In this exercise, you'll return to the `Nile`

data and the `AR`

and `MA`

models you fitted to this data. These models and their predictions for the 1970s (`AR_fit`

) and (`MA_fit`

) are depicted in the plot on the right.

Instructions

**100 XP**

- As a first step in comparing these models, use
`cor()`

to measure the correlation between`AR_fit`

and`MA_fit`

. - Use two calls to
`AIC()`

to calculate the AIC for`AR`

and`MA`

, respectively. - Use two calls to
`BIC()`

to calculate the BIC for`AR`

and`MA`

, respectively.