CFA Institute CFA-Level-II Exam - Topic 1 Question 72 Discussion

Ernie Smith and Jama! Sims are analysts with the firm of Madison Consultants. Madison provides statistical modeling and advice to portfolio managers throughout the United States and Canada.

In an effort to estimate future cash flows and value the Canadian stock market. Smith has been examining* the country's aggregate retail sales. He runs two autoregressive regression models in an attempt to determine whether there are any patterns in the data, utilizing nine years of unadjusted monthly retail sales data. One model uses a lag one variable and the other adds a lag twelve variable. The results of both regressions are shown in Exhibits 1 and 2.

Sims has been assigned the task of valuing the U .S . stock market and uses data similar to the data that Smith uses for Canada. He decides, however, that the data should be transformed. He takes the natural log of the data and uses it in the following model:

Smith and Sims are concerned that the data for Canadian retail sales may be more appropriately modeled with an ARCH process. Smith states, that in order to find out, he would take the residuals from the original autoregressive model for Canadian retail sales and then square them.

Sims states that these residuals would then be regressed against the Canadian retail sales data using the

where e represents the residual terms from the original regression and X represents the Canadian retail sales data. If is statistically different from zero, then the regression model contains an ARCH process.

Smith also examines the quarterly inflation data for an emerging market over the past nine years. He models the data using an autoregressive model with a lag one independent variable which he finds is statistically different from zero. He wonders whether he should also include lag two and lag four terms, given the magnitude of the autocorrelations of the residuals shown in Exhibit 4, assuming a 5% significance level. The critical t-values, assuming a 5% significance level and 35 degrees of freedom, are 2.03 for a two-tail test and 1.69 for a one-tail test.

where: FF is the Federal Funds rate in the United States (US), and BY is the bond yield in the European Union (E) and Great Britain (B).

Before he runs this regression, he investigates the characteristics of the dependent and independent variables. He finds that the Federal Funds rate in the United States and the bond yield in Great Britain have a unit root but that the bond yield in the European Union does not. Furthermore, the Federal Funds rate in the United States and the bond yield in Great Britain are cointegrated but the Federal Funds rate in the United States and the bond yield in the European Union are not.

Which of the following models would be the best formulation for the Canadian retail sales data?