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问题如下：

Thomas Knight Case Scenario

Thomas Knight, an analyst with Wanjarri Investment Management, is tasked with forecasting future sales for Rudall Hardware, a publicly traded retail business specializing in home improvements. Using 25 quarters of sales data ending with the most recent quarter-end date, Knight estimates a log-linear trend with an intercept of 9.464 million and a trend coefficient of 0.003 million. Based on this model, he creates a forecast of sales for the next four quarters to discuss with his supervisor, Rory Johnson.

Johnson reviews Knight's forecast and states:

• Statement 1: As long as the R² is high, we can be comfortable that the model is a good fit for our analysis.
• Statement 2: A statistically meaningful low Durbin-Watson statistic indicates that the errors in the model may exhibit positive serial correlation.
• Statement 3: If Rudall Hardware's sales are growing at a constant rate, a linear trend model may be a better fit than a log-linear model.

Next, Johnson asks Knight to forecast Rudall Hardware's net margin (net income/sales) for the next four quarters. Knight agrees and explains that he will use a first-order autoregressive model since each quarter's net margin appears related to the prior quarter's net margin. Knight also mentions that he will use an intercept of 0.0415 and a coefficient on the first lag of the net margin of 0.8295.

When applying the first-order autoregressive model, Knight wants to conduct some tests to ensure the model is producing meaningful results. In order to do this, Knight comments that he must test whether the:

• Test 1: Durbin-Watson statistic differs significantly from 2.
• Test 2: residual autocorrelations differ significantly from 0.
• Test 3: intercept and coefficient on the first lag differ significantly from 0.

In reviewing the quarterly net margin forecast, Johnson points out that the autocorrelation of the residuals for the 4^th lag is significantly different than 0, while lags 1 through 3 are not significantly different than 0, indicating an issue with seasonality. Johnson asks Knight to build a first-order autoregressive model to forecast earnings per share for the next four quarters, but to account for seasonality in this model.

Knight reviews the company's earnings per share data and determines that he can create a first-order autoregressive model to account for the seasonality using the information in Exhibit 1.

Exhibit 1:

After the models Knight created are in use for several quarters, Johnson asks Knight to put together a report assessing the accuracy of the models in forecasting out-of-sample forecasts. Knight reports to Johnson that the root mean squared error for each model is:

Exhibit 2:

Which of Johnson's statements relating to Knight's forecasted future sales for Rudall Hardware is most likely correct?

选项：

A.A.Statement 1 B.B.Statement 2 C.C.Statement 3

解释：

• A is Incorrect. Even if the R² is high, this trend model is not appropriate if the errors are serially correlated.

• B is Correct. A statistically significant low Durbin-Watson statistic indicates that the errors in the model may exhibit positive serial correlation.

• C is Incorrect. If sales were growing at a constant dollar amount a linear trend model would be more appropriate, but with a constant rate of growth a log-linear model is a better fit.