Exam 14: Time Series: Descriptive Analyses, Models, and Forecasting Available on CD

Consider the table below which displays the price of a commodity for six consecutive years. Year Price (dollars) 1 250 2 255 3 253 4 255 5 259 6 261 a. Use the method of least squares to fit the model $E \left( Y _ { t } \right) = \beta _ { 0 } + \beta _ { 1 } t$ to the data. Write the prediction equation. b. Use the prediction equation to obtain forecasts of the prices in years 7 and 8 . c. Find $95 \%$ prediction intervals for years 7 and 8 .

The _______ generally describes fluctuations of the time series that are attributable to business and economic conditions.

(Situation J) The table lists the number (in millions) of Chevrolet passenger cars sold to dealers in the U.S. and Canada from 1980 to 1985. Year Sales 1980 1.740 1981 1.444 1982 0.896 1983 1.289 1984 1.455 1985 4.882 -Using the exponential smoothing technique to the data from 1980 to 1985, forecast the number of Chevrolet passenger cars sold to U.S. and Canadian dealers in 1986 using $\mathrm { w } = 0.3$

(Situation N) An economist wishes to study the monthly trend in the Dow Jones Industrial Average (DJIA). Data collected over the past 40 months were used to fit the model $E \left( Y _ { t } \right) = \beta _ { 0 } + \beta _ { 1 } t _ { \text {, where } }$ , monthly close of the DJIA and $t =$ month $( 1,2,3 , \ldots , 40 )$ . The regression results appear below: $\hat { y } = 88 + 0.25 t \quad R ^ { 2 } = 0.37 \quad \text { MSE } = 144 \quad F = 4.25 \quad \text { Durbin-Watson } \mathrm { d } = 0.96$ -Since the data are recorded over time (months), there is a strong possibility that the residuals are positively correlated. How could you check for residual correlation using a graphical technique?

Price indexes measure changes in the price of a commodity or group of commodities over time.

(Situation G) The number of industrial and construction failures in the United States by the type of firm for the years 1985-1996 is given in the table. Year Commercial Service Construction Manufacturing and Mining Retail Trade Wholesale Trade 1985 1637 2262 1645 4799 1089 1986 1331 1770 1360 4139 1028 1987 1041 1463 1122 3406 887 1988 773 1204 1013 2889 740 1989 930 1378 1165 3183 908 1990 1594 2355 1599 4910 1284 1991 2366 3614 2223 6882 1709 1992 3840 4872 3683 9730 2783 1993 8627 5247 4433 11,429 3598 1994 12,787 6936 5759 13,787 4882 1995 16,647 7004 5662 13,501 4835 1996 20,911 7035 5641 13,509 4808 -Using 1985 as the base year and using all five types of firms, calculate the simple composite index for 1995.

(Situation J) The table lists the number (in millions) of Chevrolet passenger cars sold to dealers in the U.S. and Canada from 1980 to 1985. Year Sales 1980 1.740 1981 1.444 1982 0.896 1983 1.289 1984 1.455 1985 4.882 -Using a smoothing constant of $w = 0.30$ 0.30, calculate the value of the exponentially smoothed series in 1982.

(Situation M) Fast food chains are closely watching what proposed legislation will do to consumption of "huge meals" in the United States. Researchers have accumulated statistics on the annual consumption of "huge for the past 25 years. The goal of the analysis is to use the past data to predict future consumption and then compare the predicted consumption to the actual consumption in those years. -Propose a straight-line model that includes both a long-term trend and a seasonal component for the time series. Let $t =$ the year in which the data was collected $( t = 1,2 , \ldots , 25 )$ and let $Q _ { 1 } , Q _ { 2 }$ , and $Q _ { 3 }$ be dummy variables used to model a seasonal effect.

The Laspeyres index is a weighted index while the Paasche index is not weighted.

Smaller choices of the exponential smoothing constant w assign more weight to the current value of the series and yield a smoother series.

The _______ of a time series can account for fluctuations that recur during specific time periods.

Consider the monthly time series shown in the table. Month January 1 185 February 2 192 March 3 189 April 4 201 May 5 195 June 6 199 July 7 206 August 8 203 September 9 208 October 10 209 November 11 218 December 12 216 a. Use the values of $Y$ in the table to forecast the values of $Y$ for the next two months, using simple exponential smoothing with $\mathrm { w } = 0.7$ . b. Use the Holt model with $w = 0.7$ and $v = 0.7$ to forecast the values of $Y$ for the next two months.

(Situation J) The table lists the number (in millions) of Chevrolet passenger cars sold to dealers in the U.S. and Canada from 1980 to 1985. Year Sales 1980 1.740 1981 1.444 1982 0.896 1983 1.289 1984 1.455 1985 4.882 -Use the Holt forecasting model with trend to forecast the number of Chevrolet passenger cars sold to U.S. and Canadian dealers in 1990 using $w = 0.6 \text { and } v = 0.5$