Question #64

of 101 David Brice, CFA, has used an AR(1) model to forecast the next period's interest rate to be 0.08. The AR(1) has a positive slope coefficient. If the interest rate is a mean reverting process with an unconditional mean, a.k.a., mean reverting level, equal to 0.09, then which of the following could be his forecast for two periods ahead? A) 0.072. B) 0.113. C) 0.081. Yolanda Seerveld is an analyst studying the growth of sales of a new restaurant chain called Very Vegan. The increase in the public's awareness of healthful eating habits has had a very positive effect on Very Vegan's business. Seerveld has gathered quarterly data for the restaurant's sales for the past three years. Over the twelve periods, sales grew from $17.2 million in the first quarter to $106.3 million in the last quarter. Because Very Vegan has experienced growth of more than 500% over the three years, the Seerveld suspects an exponential growth model may be more appropriate than a simple linear trend model. However, she begins by estimating the simple linear trend model: (sales)t = α + β × (Trend)t + εt Where the Trend is 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12. Regression Statistics Multiple R 0.952640 R2 0.907523 Adjusted R2 0.898275 Standard Error 8.135514 Observations 12 1st order autocorrelation coefficient of the residuals: −0.075 ANOVA df SS Regression 1 6495.203 Residual 10 661.8659 Total 11 7157.069 Coefficients Standard Error Intercept 10.0015 5.0071 Trend 6.7400 0.6803 The analyst then estimates the following model: (natural logarithm of sales)t = α + β × (Trend)t + εt Regression Statistics Multiple R 0.952028 R2 0.906357 Adjusted R2 0.896992 Standard Error 0.166686 Observations 12 1st order autocorrelation coefficient of the residuals: −0.348 ANOVA df SS Regression 1 2.6892 Residual 10 0.2778 Total 11 2.9670 Coefficients Standard Error Intercept 2.9803 0.1026 Trend 0.1371 0.0140 Seerveld compares the results based upon the output statistics and conducts two-tailed tests at a 5% level of significance. One concern is the possible problem of autocorrelation, and Seerveld makes an assessment based upon the first-order autocorrelation coefficient of the residuals that is listed in each set of output. Another concern is the stationarity of the data. Finally, the analyst composes a forecast based on each equation for the quarter following the end of the sample.