Exam 14: Time-Series Forecasting and Index Numbers

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 for Q₁ in the regression equation (-0.129)which has a p-value of 0.492,which of the following is the best interpretation of this result?

The overall upward or downward pattern of the data in an annual time series will be contained in the_______ component.

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,in testing the coefficient for Q₁ in the regression equation (-0.083),the results were a t-statistic of-0.66 and an associated p-value of 0.530.Which of the following is the best interpretation of this result?

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 2010 are _______ and_______,respectively.

The manager of a company believed that her company's profits were following an exponential trend.She used Microsoft Excel to obtain a prediction equation for the logarithm (base 10)of profits: log₁₀(Profits)= 2 + 0.3X The data she used were from 2003 through 2008,coded 0 to 5.The forecast for 2009 profits 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 are the simple price indexes for electricity,natural gas and fuel oil,respectively,in 2008 using 2010 as the base year?

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,to obtain a forecast for the fourth quarter of 2011 using the model,which of the following sets of values should be used in the regression equation?

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 2009 for a family that consumed 13 units of electricity,26 units of natural gas and 235 units of fuel oil in 2009 using 2006 as the base year?

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 estimated quarterly compound growth rate in revenues is around

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 first quarter of 2005?

_______ methods use time-series data in a mathematical process to forecast future values of the series.

Instruction 14-19 Business closures in Perth from 2005 to 2010 were: 2005 10 2005 11 2007 13 2008 19 2009 24 2010 35 Microsoft Excel was used to fit both first-order and second-order autoregressive models, resulting in the following partial outputs: SIMMARY OUTIPU - Second-Order Mode Coefficients Intercept -5.77 X Variable 1 0.80 X Variable 2 1.14 SIMMARY OUTPUT - Fist-Order Model Coefficients Intercept -4.16 X Variable 1 1.59 -Referring to Instruction 14-19,the value of the MAD for the first-order autoregressive model is _______.

The principle of parsimony indicates that the simplest model that gets the job done adequately should be used.

Instruction 14-20 The manager of a health fitness club has recorded average attendance in newly introduced Zumba classes over the last 15 months: 32.1, 39.5, 40.3, 46.0, 65.2, 73.1, 83.7, 106.8, 118.0, 133.1, 163.3, 182.8, 205.6, 249.1 and 263.5. She then used Microsoft Excel to obtain the following partial output for both first- and second-order autoregressive model. -Referring to Instruction 14-20,using the second-order model,the forecast of mean attendance for month 17 is _______

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 second Monday will be _______.

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 1990 is _______.

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 2005 are _______ and _______,respectively.

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,using the regression equation,which of the following values is the best forecast for the number of contracts in the second quarter of 2012?

Which of the following is NOT an advantage of exponential smoothing?

In the Holt-Winters method of forecasting,to give more weight to recent levels of the time series,you would use_______.