Exam 14: Time-Series Forecasting and Index Numbers

Instruction 14-5 A contractor developed a multiplicative time-series model to forecast the number of contracts in future quarters, using quarterly data on number of contracts during the three-year period from 2008 to 2010. The following is the resulting regression equation: $\log _ { 10 } \hat { Y } = 3.37 + 0.117 X - 0.083 Q _ { 1 } + 1.28 Q _ { 2 } + 0.617 Q _ { 3 }$ Where $\hat { Y }$ is the estimated number of contracts in a quarter. $X$ is the coded quarterly value with $X = 0$ in the first quarter of 2008 . $Q _ { 1 }$ 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 14-5,the best interpretation of the coefficient of Q₃ (0.617)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 0.3 for both level and trend.

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 smooth the wine sales.The smoothed values of the level and trend for 2005 are _______ and_______,respectively.

The base period should be recent so that a price index is not severely affected by change in technology,and consumer attitudes and habits.

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 are the simple price indexes for electricity,natural gas and fuel oil,respectively,in 2007 using 2010 as the base year?

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 estimate of the amount by which sales (in millions of dollars)is increasing each year 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,in testing the significance of the coefficient of X in the regression equation (0.012)which has a p-value of 0.0000,which of the following is the best interpretation of this result?

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 Laspeyres price index for the group of three energy items in 2008 for a family that consumed 15 units of electricity,24 units of natural gas and 200 units of fuel oil in 2006 using 2006 as the base year?

The Laspeyres price index uses the initial consumption quantities as the weights.

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,what would be the third value?

When a time series appears to be increasing at an increasing rate,such that percentage difference from observation to observation is constant,the appropriate model to fit is the

Instruction 14-4 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 14-4,the number of arrivals will be exponentially smoothed with a smoothing constant of 0.25.The smoothed value for the third Monday will be _______.

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,the Holt-Winters method for forecasting with smoothing constant of 0.3 for both level and trend will be used to smooth the number of arrivals.The smoothed values of the level and trend for the sixth Monday are _______ and _______,respectively.

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,exponentially smooth the wine sales with a weight or smoothing constant of 0.4.

After estimating a trend model for annual time-series data,you obtain the following residual plot against time. The problem with your model is that

Instruction 14-11 The manager of a marketing consulting firm has been examining his company's yearly profits. He believes that these profits have been showing a quadratic trend since 1990. He uses Microsoft Excel to obtain the partial output below. The dependent variable is profit (in thousands of dollars), while the independent variables are coded years and squared of coded years, where 1990 is coded as 0, 1991 is coded as 1, etc. $\text { SUMMAROUTPUT }$ $\text { Regression Statistics }$ MultipleR 0.998 R Square 0.996 Adjusted R Square 0.996 StandardError 4.996 Observations 17 Coefficients Intercept 35.5 Coded Year 0.45 Year Squared 1.00 -Referring to Instruction 14-11,the fitted value for 1995 is _______

The Paasche price index reflects more accurately the consumption cost at a point in time because it uses the consumption quantities in the initial year as the base.

The method of moving averages is used

If you want to recover the trend using exponential smoothing,you will choose a weight (W)that falls in the range

Instruction 14-4 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 14-4,the number of arrivals will be smoothed with a three-term moving average.There will be a total of _______ smoothed values.