# Estimate the autoregressive (AR) model

For a given time series `x`

we can fit the autoregressive (AR) model using the `arima()`

command and setting `order`

equal to `c(1, 0, 0)`

. Note for reference that an AR model is an **ARIMA(1, 0, 0)** model.

In this exercise, you'll explore additional qualities of the AR model by practicing the `arima()`

command on a simulated time series `x`

as well as the `AirPassengers`

data. This command allows you to identify the estimated slope (`ar1`

), mean (`intercept`

), and innovation variance (`sigma^2`

) of the model.

Both `x`

and the `AirPassengers`

data are preloaded in your environment. The time series `x`

is shown in the figure on the right.

This is a part of the course

## “Time Series Analysis in R”

### Exercise instructions

- Use
`arima()`

to fit the AR model to the series`x`

. Closely examine the output from this command. - What are the slope (
`ar1`

), mean (`intercept`

), and innovation variance (`sigma^2`

) estimates from your previous command? Type them into your R workspace. - Now, fit the AR model to
`AirPassengers`

, saving the results as`AR`

. Use`print()`

to display the fitted model`AR`

. - Finally, use the commands provided to plot the
`AirPassengers`

, calculate the fitted values, and add them to the figure.

### Hands-on interactive exercise

Have a go at this exercise by completing this sample code.

```
# Fit the AR model to x
arima(___, order = ___)
# Copy and paste the slope (ar1) estimate
# Copy and paste the slope mean (intercept) estimate
# Copy and paste the innovation variance (sigma^2) estimate
# Fit the AR model to AirPassengers
AR <-
print(AR)
# Run the following commands to plot the series and fitted values
ts.plot(AirPassengers)
AR_fitted <- AirPassengers - residuals(AR)
points(AR_fitted, type = "l", col = 2, lty = 2)
```

This exercise is part of the course

## Time Series Analysis in R

Learn the core techniques necessary to extract meaningful insights from time series data.

In this chapter, you will learn the autoregressive (AR) model and several of its basic properties. You will also practice simulating and estimating the AR model in R, and compare the AR model with the random walk (RW) model.

Exercise 1: The autoregressive modelExercise 2: Simulate the autoregressive modelExercise 3: Estimate the autocorrelation function (ACF) for an autoregressionExercise 4: Persistence and anti-persistenceExercise 5: Compare the random walk (RW) and autoregressive (AR) modelsExercise 6: AR model estimation and forecastingExercise 7: Estimate the autoregressive (AR) modelExercise 8: Simple forecasts from an estimated AR model### What is DataCamp?

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