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.