In Example 13.10, a bivariate AR(1) model was fit to (Δcpi, Δip) and
The mean of (Δcpi, Δip) is (0.0052, 0.0021) and the last observation of (Δcpi, Δip) is (0.0017, 0.0059) . Forecast the next two values of Δip. (The forecasts are shown in Fig. 13.15, but you should compute numerical values.)
Example 13.10.
A bivariate AR model for Δ cpi and Δ ip
This example uses the CPI and IP data sets discussed in earlier examples (cpi and ip denote the log transformed series). Bivariate AR processes were fit to (Δcpi, Δip) using R’s function ar(). AIC as a function of p is shown
below. The two best-fitting models are AR(1) and AR(5), with the latter being slightly better by AIC. Although BIC is not part of ar()’s output, it can be calculated easily since BIC = AIC + {log(n)−2}p. Because {log(n)−2} = 2.9 in this example, it is clear that BIC is much smaller for the AR(1) model than for the AR(5) model. For this reason and because the AR(1) model is so much simpler to analyze, we will use the AR(1) model.