这题的理解

问题如下：

Eduardo DeMolay Case Scenario

Eduardo DeMolay, a research analyst at Mumbai Securities, is studying the time-series behavior of price-to-earnings ratios (P/Es) computed with trailing 12-month earnings (E_trailing). He and his assistant, Deepa Kamini, are reviewing the results of the ordinary least squares time series regression shown in Exhibit 1.

Exhibit 1

Results of Regression of P/E on Lagged P/E (P/E_t = b₀ + b₁P/E_t–1 + ε_t)

DeMolay states: “This regression is a special case of a first-order autoregressive [AR(1)] model in which the value for b₀ is close to zero and the value of b₁ is close to 1. These values suggest that the time series is a random walk.”

Kamini replies: “I’m convinced the P/E series based on trailing earnings truly is a random walk.”

Kamini and DeMolay next examine the behavior of P/Es calculated using forward 12-month earnings (E_forward). Kamini estimates another AR(1) model but uses the forward P/E values this time. She denotes the errors from this second regression as η_t. She states: “The presence of first-order autoregressive conditional heteroskedasticity [ARCH(1)] errors in this regression is highly likely given the results reported in Exhibit 2.”

Exhibit 2

Results of Regression of Squared Residuals, ${}_{}^{}$ , on Lagged Squared Residuals,

After further discussion, DeMolay proposes that he and Kamini incorporate more variables into the analysis. He suggests they use a variation of the Fed model, in which the earnings-to-price ratio (E/P) is regressed on long-term interest rates.

DeMolay cautions Kamini: “Remember that when we analyze two time series in regression analysis, we need to ensure that

1. neither the dependent variable series nor the independent variable series has a unit root, or

2. that both series have a unit root and are not cointegrated.

Unless Condition 1 or Condition 2 holds, we cannot rely on the validity of the estimated regression coefficients.”

Question

Based on the results depicted in Exhibit 2, DeMolay and Kamini should most likely model the forward P/E data using a(n):

选项：

A.generalized least squares model. B.AR(1) model. C.random walk model.

解释：

If ARCH exists, the standard errors for the regression parameters will not be correct. In the case that ARCH exists, you will need to use generalized least squares or other methods that correct for heteroskedasticity to correctly estimate the standard error of the parameters in the time series model.