NO.PZ201709270100000405
问题如下:
Angela Martinez, an energy sector analyst at an investment bank, is concerned about the future level of oil prices and how it might affect portfolio values. She is considering whether to recommend a hedge for the bank portfolio’s exposure to changes in oil prices. Martinez examines West Texas Intermediate (WTI) monthly crude oil price data, expressed in US dollars per barrel, for the 181-month period from August 2000 through August 2015. The end-of-month WTI oil price was $51.16 in July 2015 and $42.86 in August 2015 (Month 181). After reviewing the time-series data, Martinez determines that the mean and variance of the time series of oil prices are not constant over time. She then runs the following four regressions using the WTI time-series data.
Linear trend model: Oil pricet = b0 + b1t+ et
Log-linear trend model: ln Oil pricet = b0 + b1t+ et
AR(1) model: Oil pricet = b0 + b1Oil pricet–1 + et
AR(2) model: Oil pricet = b0 + b1Oil pricet–1 + b2Oil pricet–2 + et
Exhibit 1 presents selected data from all four regressions, and Exhibit 2 presents selected autocorrelation data from the AR(1) models.
In Exhibit 1, at the 5% significance level, the lower critical value for the Durbin–Watson test statistic is 1.75 for both the linear and log-linear regressions.
After reviewing the data and regression results, Martinez draws the following conclusions.
Conclusion 1: The time series for WTI oil prices is covariance stationary.
Conclusion 2: Out-of-sample forecasting using the AR(1) model appears to be more accurate than that of the AR(2) model.
5. Based on Exhibit 1, the forecasted oil price in September 2015 based on the AR(2) model is closest to:
选项:
A. $38.03.
B. $40.04.
C. $61.77.
解释:
B is correct. The last two observations in the WTI time series are July and August 2015, when the WTI oil price was $51.16 and $42.86, respectively. Therefore, September 2015 represents a one-period-ahead forecast. The one-period- ahead forecast from an AR(2) model is calculated as
So, the one-period-ahead (September 2015) forecast is calculated as
Therefore, the September 2015 forecast based on the AR(2) model is $40.04.
请问按照题目里给的公式,最后一项残差项et为何没有加上,我是按照stand error那一项数字5·2799给加上了。谢谢老师啦,辛苦