Explain the Box-Jenkins approach to building ARMA models.

1.   
Explain the Box-Jenkins approach to building ARMA models.

[25%]

2.   
Open the workfile “cpi.wf1”. The file contains quarterly data of the U.S. Consumer Price Index (CPI) over the period 1960Q1 to 2012Q4. Calculate the logarithmic change of the series, i.e.:

                                                                                 △ cpi_t = cpi_{t  −}  cpi_{t –1}

where cpi_t=ln(cpi_t) (Note: Use the natural logarithm)

(a)       
Use the full sample period to obtain a graph of the △cpi_t series. Based on the graph, does the series appear to be stationary? Comment on the behaviour of the series over time.

[10%]

(b)      
Read Chapter 6 in Brooks (2014) and briefly explain the terms autocorrelation function (ACF) and partial autocorrelation function (PACF). What shape would these two functions take for a stationary autoregressive process, a moving average process, and a combination autoregressive moving average process?

[10%]

(c)       
Obtain the ACF and PACF for △cpi_t in Eviews (specify the number of autocorrelations to be 12) using data from 1960Q1 to 2009Q4 (Note that this is not the full sample). Discuss the significance of the ACF and PACF coefficients. Based on your answer to Question 2(b), try to identify the tentative models that you would want to estimate.