Exam 11: Forecasting Models

Cycles,one of the components of time series,is a pattern that repeats itself during the exact same time period.

Use this information to answer the following questions. The following data,provided by the U.S.Bureau of Citizenship and Immigration Services,represent the number of immigrants admitted to the United States,in thousands,from 1990-2001. Year No. of Immigrants (in 000s) 1990 1536 1991 1827 1992 974 1993 904 1994 804 1995 720 1996 916 1997 798 1998 654 1999 647 2000 850 2001 1064 -Refer to the table above. a.What is the linear trend equation that best fits the data? b.What is the forecast of the number of immigrants in 2002 using the linear trend equation? c.What is the MAPE for this method?

The time series component random variation usually shows a discernible pattern and is easy to forecast.

Removing the seasonal component from a data series (i.e. ,unseasonalization)can be accomplished by multiplying each data point by its appropriate seasonal index.

The following data were collected on the number of study hours per week,and the current GPA of 6 students at a local college. GPA No. of Study Hours/Week 3.95 35 3.00 28 2.20 10 2.5 15 3.5 30 2.00 7 a.Develop a regression model to predict GPA based on the number of study hours. b.What percent of the total variation in GPA has been explained by study hours? c.If a student studies 20 hours per week,what would you estimate the GPA to be?

The basic exponential smoothing formula is:

In an exponential smoothing forecast,the value of the smoothing constant alpha can range between -1 and +1.

Time series models usually incorporate variables or factors that are perceived to influence the variable being forecasted.

A farmer develops a simple regression model to determine if there is a relationship between the amount of crop that he will harvest and the amount of rainfall.In this example,the variable "rainfall" would be the dependent variable.

Use this information to answer the following questions. The following time series,provided by the Federal Loan Home Mortgage Corporation,represents weekly 30-year fixed mortgage rates. Date Mortgage Rate (\%) October 14, 2005 6.03 October 21, 2005 6.10 October 28, 2005 6.15 November 4, 2005 6.31 November 11, 2005 6.36 November 18, 2005 6.37 November 25, 2005 6.28 December 2, 2005 6.26 December 9, 2005 6.32 December 16,2005 6.30 December 23, 2005 6.26 December 30,2005 6.22 January 6, 2006 6.21 January 13, 2005 6.15 -Refer to the table above.a.Use exponential smoothing with a smoothing constant of 0.5 to forecast the next weekly mortgage rate. b.Use exponential smoothing with a smoothing constant of 0.9 to forecast the next weekly mortgage rate. c.Which of the two methods provides a more accurate forecast based on the MAD criterion?

Use this information to answer the following questions. The following time series,provided by the Federal Loan Home Mortgage Corporation,represents weekly 30-year fixed mortgage rates. Date Mortgage Rate (\%) October 14, 2005 6.03 October 21, 2005 6.10 October 28, 2005 6.15 November 4, 2005 6.31 November 11, 2005 6.36 November 18, 2005 6.37 November 25, 2005 6.28 December 2, 2005 6.26 December 9, 2005 6.32 December 16,2005 6.30 December 23, 2005 6.26 December 30,2005 6.22 January 6, 2006 6.21 January 13, 2005 6.15 -Refer to the table above. a.What is the linear trend equation that best fits the data? b.What is the forecast of the next weekly mortgage rate? c.What is the MAPE for this method?

Use this information to answer the following questions. The following data were collected on annual revenues (millions)and the number of slot machines in a Las Vegas casino from 1995 to 2005. Year Annual Revenues Number of SlotMachines 1995 4 35 1996 6 40 1997 7 45 1998 8 50 1999 6.8 55 2000 8.8 60 2001 9 65 2002 10 70 2003 13 75 2004 12 75 2005 13 75 -Refer to the table above.Suppose that the casino manager believes that warmer weather attracts more gamblers.The data on average yearly temperatures from 1995 to 2005 are shown as follows. Year Average Temperature () 1995 60 1996 65 1997 68 1998 69 1999 63 2000 70 2001 72 2002 71 2003 74 2004 73 2005 72 a.Develop a regression model to predict annual revenue based on the number of slot machines and average temperature. b.What percent of the total variation in revenue is explained by the regression model? c.Predict annual revenue if the casino has 75 slot machines and the average temperature is 74 degrees.

A smoothing constant of .1 will cause an exponential smoothing forecast to react less quickly to a sudden change than a value of .3 will.

Use this information to answer the following questions. The following time series represent the total population of the United States,in thousands,over the last 12 years. Year Population (in 000s) 1991 253,493 1992 256,894 1993 260,255 1994 263,436 1995 266,557 1996 269,667 1997 272,912 1998 276,115 1999 279,295 2000 282,434 2001 285,545 2002 288,600 -Refer to the table above.Use a 3-period weighted moving average to forecast the population of the United States in 2003.Use Solver to determine the optimal weights based on minimizing the MAD criterion.

The smaller the value of the standard error of the regression estimate,the better the fit of the regression model.

Use this information to answer the following questions. The following time series,provided by the Federal Loan Home Mortgage Corporation,represents weekly 30-year fixed mortgage rates. Date Mortgage Rate (\%) October 14, 2005 6.03 October 21, 2005 6.10 October 28, 2005 6.15 November 4, 2005 6.31 November 11, 2005 6.36 November 18, 2005 6.37 November 25, 2005 6.28 December 2, 2005 6.26 December 9, 2005 6.32 December 16,2005 6.30 December 23, 2005 6.26 December 30,2005 6.22 January 6, 2006 6.21 January 13, 2005 6.15 -Refer to the table above. a.Use a 2-period moving average to forecast the next weekly mortgage rate. b.Use a 3-period moving average to forecast the next weekly mortgage rate. c.Use a 4-period moving average to forecast the next weekly mortgage rate. d.Which averaging period provides a better historical fit based on the MAD criterion?

A moving average forecast tends to be more responsive to recent changes in the data series when more data points are included in the average.

Consider the following data and its associated Excel output for a simple linear regression model.How would you describe the linear relationship between Y and X? Period Y X Period 1 10 1 Period 2 11 2 Period 3 9 3 Period 4 12 4 Period 5 13 5 Period 6 12 6 Period 7 15 7 Intercept 2.267 Slope 0.843 SE 1.810 Correlation 0.890 r-squared 0.791

Use this information to answer the following questions. The following data,provided by the U.S.Bureau of Citizenship and Immigration Services,represent the number of immigrants admitted to the United States,in thousands,from 1990-2001. Year No. of Immigrants (in 000s) 1990 1536 1991 1827 1992 974 1993 904 1994 804 1995 720 1996 916 1997 798 1998 654 1999 647 2000 850 2001 1064 -Refer to the table above.Use a 3-period weighted moving average to forecast the number of immigrants in 2002.Use Solver to determine the optimal weights based on minimizing the MAD criterion.

Use this information to answer the following questions. The following time series represent the total population of the United States,in thousands,over the last 12 years. Year Population (in 000s) 1991 253,493 1992 256,894 1993 260,255 1994 263,436 1995 266,557 1996 269,667 1997 272,912 1998 276,115 1999 279,295 2000 282,434 2001 285,545 2002 288,600 -Refer to the table above. a.Use a 2-period moving average to forecast the population of the United States in 2003. b.Use a 3-period moving average to forecast the population of the United States in 2003. c.Which averaging period provides a better historical fit based on the MAD criterion?