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.
This exercise is part of the course
Time Series Analysis in R
Exercise instructions
- Use
arima()to estimate the WN model fory. Be sure to include theorder = c(0, 0, 0)argument after specifying your data. - Calculate the mean and variance of
yusingmean()andvar(), respectively. Compare the results with the output of yourarima()command.
Hands-on interactive exercise
Have a go at this exercise by completing this sample code.
# Fit the WN model to y using the arima command
# Calculate the sample mean and sample variance of y