Exam 14: Time-Series Forecasting and Index Numbers

Instruction 14-9 The president of a chain of department stores believes that her stores' total sales have been showing a linear trend since 1980. She uses Microsoft Excel to obtain the partial output below. The dependent variable is sales (in millions of dollars), while the independent variable is coded years, where 1990 is coded as 0, 1991 is coded as 1, etc. SUMMAROUIPUT Regression Statistics MultipleR 0.604 R Square 0.365 Adjusted R Square 0.316 standard Error 4.800 Observations 17 Coeflients Intercept 31.2 Coded Year 0.78 -Referring to Instruction 14-9,the fitted trend value (in millions of dollars)for 1990 is_______.

Instruction 14-6 A local store developed a multiplicative time-series model to forecast its revenues in future quarters, using quarterly data on its revenues during the four-year period from 2005 to 2009. The following is the resulting regression equation: $\log _ { 10 } \hat { Y } = 6.102 + 0.012 X - 0.129 Q _ { 1 } - 0.054 Q _ { 2 } + 0.098 Q _ { 3 }$ Where $X$ is the coded quarterly value with $X = 0$ in the first quarter of 2005 . $Q _ { 1 }$ is a dummy variable equal to 1 in the first quarter of a year and 0 otherwise. $Q _ { 2 }$ is a dummy variable equal to 1 in the second quarter of a year and 0 otherwise. $Q _ { 3 }$ is a dummy variable equal to 1 in the third quarter of a year and 0 otherwise. -Referring to Instruction 14-6,using the regression equation,what is the forecast for the revenues in the fourth quarter of 2004?

One reason to use quantitative forecasting methods is if historical data are not available.

Instruction 14-19 The number of train passengers arriving in Adelaide on the Overland on six successive Mondays were: 60, 72, 96, 84, 36 and 48. -Referring to Instruction 14-14,the Holt-Winters method for forecasting with smoothing constant of 0.2 for both level and trend will be used to forecast the wine sales.The forecast for 2011 is _______.

In the Holt-Winters method of forecasting,the term U refers to the

Instruction 14-6 A local store developed a multiplicative time-series model to forecast its revenues in future quarters, using quarterly data on its revenues during the four-year period from 2005 to 2009. The following is the resulting regression equation: $\log _ { 10 } \hat { Y } = 6.102 + 0.012 X - 0.129 Q _ { 1 } - 0.054 Q _ { 2 } + 0.098 Q _ { 3 }$ Where $X$ is the coded quarterly value with $X = 0$ in the first quarter of 2005 . $Q _ { 1 }$ is a dummy variable equal to 1 in the first quarter of a year and 0 otherwise. $Q _ { 2 }$ is a dummy variable equal to 1 in the second quarter of a year and 0 otherwise. $Q _ { 3 }$ is a dummy variable equal to 1 in the third quarter of a year and 0 otherwise. -Referring to Instruction 14-6,the best interpretation of the constant 6.102 in the regression equation is:

Instruction 14-15 The number of train passengers arriving in Adelaide on the Overland on six successive Mondays were: 60, 72, 96, 84, 36 and 48. -Referring to Instruction 14-15,use the Holt-Winters method of fitting number of arrivals to compute the smoothed level and trend with a smoothing constant of 0.9 for both level and trend.

Instruction 14-2 The following table contains the number of complaints received in a department store for the first six months of last year. Month Complaints January 36 February 45 March 81 April 50 May 108 June 144 -Referring to Instruction 14-2,if this series is smoothed using exponential smoothing with a smoothing constant of 1/3,how many values would it have?

A second-order autoregressive model for average mortgage rate is: Rate_i = -2.0 + 1.8(Rate)_i-1 -0.5 (Rate)_i-2 If the average mortgage rate in 2008 was 7.0,and in 2007 was 6.4,the forecast for 2010 is _______.

A simple price index tracks the price of a group of commodities at a given period of time to the price paid for that group of commodities at a particular point of time in the past.

Instruction 14-13 The monthly advertising expenditures of a department store chain (in $1,000,000s) were collected over the last decade. The last 14 months of this time series follows: $\begin{array}{cc}\text { Month } &\text { Expenditures }\\&(\$)\\1 & 1.4 \\2 & 1.8 \\3 & 1.6 \\4 & 1.5 \\5 & 1.8 \\6 & 1.7 \\7 & 1.9 \\8 & 2.2 \\9 & 1.9 \\10 & 1.9 \\11 & 2.1 \\12 & 2.4 \\13 & 2.8 \\14 & 3.1\end{array}$ -Referring to Instruction 14-13,set up a scatter diagram (i.e.,time-series plot)with months on the horizontal X-axis.

One disadvantage of time-series forecasting is that it requires knowledge of a future cause in order to predict change in an independent variable.

Instruction 14-19 The number of train passengers arriving in Adelaide on the Overland on six successive Mondays were: 60, 72, 96, 84, 36 and 48. -Referring to Instruction 14-14,the Holt-Winters method for forecasting with smoothing constant of 0.8 for both level and trend will be used to smooth the wine sales.The smoothed values of the level and trend for 2010 are_______ and _______,respectively.

Instruction 14-16 Given below are Microsoft Excel outputs for various estimated autoregressive (AR) models for a company’s real operating revenues (in billions of dollars) from 1985 to 2008. From the data, you also know that the real operating revenues for 2006, 2007 and 2008 are 11.7909, 11.7757 and 11.5537, respectively. AR (1) Model: Coefficients Standard Error t Stat p -value Intercept 0.1802 0.3980 0.4528 0.6553 XLag1 1.0112 0.0497 20.3526 0.0000 AR (2) Model: Coefficients Standard Error t Stat p -value Intercept 0.3005 0.4408 0.6817 0.5036 X Lag 1 1.1732 0.2347 4.9980 0.0001 X Lag 2 -0.1830 0.2507 -0.7300 0.4743 AR (3) Model: Coefficients Standard Error t Stat p -value Intercept 0.3130 0.5144 0.6085 0.5509 XLag1 1.1737 0.2465 4.7617 0.0002 XLag2 -0.0694 0.3731 -0.1860 0.8547 XLag3 -0.1221 0.2820 -0.4330 0.6704 -Referring to Instruction 14-16 and using a 5% level of significance,what is the appropriate AR model for the company's real operating revenue?

A model that can be used to make predictions about long-term future values of a time series is

Instruction 14-21 Given below are the average prices for three types of energy products in Australia from 2006 to 2010. Year Electricity Natural Gas Fuel Oil 2006 43.205 25.893 0.892 2007 16.959 28.749 0.969 2008 47.202 28.933 1.034 2009 48.874 29.872 0.913 2010 48.693 28.384 0.983 -Referring to Instruction 14-21,what is the Paasche price index for the group of three energy items in 2010 for a family that consumed 13 units of electricity,26 units of natural gas and 235 units of fuel oil in 2010 using 2006 as the base year?

Instruction 14-16 Given below are Microsoft Excel outputs for various estimated autoregressive (AR) models for a company’s real operating revenues (in billions of dollars) from 1985 to 2008. From the data, you also know that the real operating revenues for 2006, 2007 and 2008 are 11.7909, 11.7757 and 11.5537, respectively. AR (1) Model: Coefficients Standard Error t Stat p -value Intercept 0.1802 0.3980 0.4528 0.6553 XLag1 1.0112 0.0497 20.3526 0.0000 AR (2) Model: Coefficients Standard Error t Stat p -value Intercept 0.3005 0.4408 0.6817 0.5036 X Lag 1 1.1732 0.2347 4.9980 0.0001 X Lag 2 -0.1830 0.2507 -0.7300 0.4743 AR (3) Model: Coefficients Standard Error t Stat p -value Intercept 0.3130 0.5144 0.6085 0.5509 XLag1 1.1737 0.2465 4.7617 0.0002 XLag2 -0.0694 0.3731 -0.1860 0.8547 XLag3 -0.1221 0.2820 -0.4330 0.6704 -Referring to Instruction 14-16,if you decide to use AR(3),what will the predicted real operating revenue for the company be in 2011?

Instruction 14-3 The number of cases of merlot wine sold by a Barossa Valley Winery in an eight-year period follows. Year Coses of Wine 2003 270 2004 356 2005 398 2006 456 2007 358 2008 500 2009 410 2010 376 -Referring to Instruction 14-3,exponential smoothing with a weight or smoothing constant of 0.4 will be used to smooth the wine sales.The value of E₅,the smoothed value for 2007 is _______.

Microsoft Excel was used to obtain the following quadratic trend equation: Sales = 100 -10X + 15X² The data used was from 1999 through 2008,coded 0 to 9.The forecast for 2009 is_______.

You need to decide whether you should invest in a particular stock.You would like to invest if the price is likely to rise in the long run.You have data on the daily mean price of this stock over the past 12 months.Your best action is to