THEME: Regression analysis and model selection

Here, we will consider choosing an ARMA model for GDP growth (denoted growt). In particular, we will choose between a model that lets growth be related to two lags of itself (called an AR(2)) and a model that lets growth be related to two lags of itself and two lags of the residuals (called an ARMA(2,2) model). Throughout this question, the sample size for every model is 242. You are also given the following information (the mean of GDP growth is 2.788%)

(2.788)2242=1=4237.861

The more general ARMA(2,2) model can be denoted as follows:

growt = m + f1growt1 +f2growt-2 + t+q1t-1 +q2t-2

a. Output for the above model, denoted MODEL #1, is found here:

Series: grow

ARIMA(2,0,2) with non-zero mean

Coefficients:

ar1 ar2 ma1 ma2 mean

-0.3523 0.6058 0.7591 -0.1540 2.6059

s.e. 0.1411 0.1397 0.1637 0.1601 0.5381

AIC=1354.84 BIC=1375.77 R2 =0.14284

MODEL #1

(ar1 simply refers to growt-1 with the estimated coefficient for f1 appearing immediately below the heading ar1. Similar meaning is ascribed to ma1 as it relates to t-1). Please note that the AIC and BIC are shown.

Question:

Unfortunately, real GDP growth in the second quarter reached historically low numbers. The models analyzed above are entirely backward looking. The preferred model generates a forecast of -13.7% and -10.3% for the last two quarters of 2020. Fortunately, there is little to no chance this will occur. In fact, Bank of America recently released forecasts for Q3:2020 and Q4:2020 to be 27% and 3%, respectively.

Assume that the forecasts for Bank of America are correct. Calculate the root mean squared error that would result for the two-step ahead forecast our model generated (e.g. -13.7% for Q3 and -10.3% for Q4 against 27% and 3%).