Box, Jenkins, and Reinsel [1994] fit a transfer function model to data from a gas furnace. The input variable is the volume of methane entering the chamber in cubic feet per minute and the output is...

Box, Jenkins, and Reinsel [1994] fit a transfer function model to data from a gas furnace. The input variable is the volume of methane entering the chamber in cubic feet per minute and the output is the concentration of carbon dioxide emitted. The transfer function model is

where the input and output variables are measured every nine seconds.

a. What are the values of b, s, and r for this model?

b. What is the form of the ARIMA model for the errors?

c. If the methane input was increased, how long would it take before the carbon dioxide concentration in the output is impacted?