Exercise

# Estimate the white noise model

For a given time series `y`

we can fit the white noise (WN) model using the `arima(..., order = c(0, 0, 0))`

function. Recall that the WN model is an ARIMA(0,0,0) model. Applying the arima() function returns information or output about the estimated model. For the WN model this includes the estimated mean, labeled `intercept`

, and the estimated variance, labeled `sigma^2`

.

In this exercise, you'll explore the qualities of the WN model. What is the estimated mean? Compare this with the sample mean using the mean() function. What is the estimated variance? Compare this with the sample variance using the var() function.

The time series `y`

has already been loaded, and is shown in the adjoining figure.

Instructions

**100 XP**

- Use
`arima()`

to estimate the WN model for`y`

. Be sure to include the`order = c(0, 0, 0)`

argument after specifying your data. - Calculate the mean and variance of
`y`

using`mean()`

and`var()`

, respectively. Compare the results with the output of your`arima()`

command.