Exam 14: Time-Series Forecasting and Index Numbers

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 first-order model,the forecast of mean attendance for month 17 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 2010 using 2006 as the base year?

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 forecast for profits in 2010 is _______.

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 16 is _______.

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 residuals for the second-order autoregressive model are _______,_______,_______and _______.

MAD is the summation of the residuals divided by the sample size.

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 first 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 are the simple price indexes for electricity,natural gas and fuel oil,respectively,in 2006 using 2010 as the base year?

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 0.1.The smoothed value for the second Monday will be_______.

The Paasche price index uses the consumption quantities in the year of interest as the weights.

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 forecast of the number of arrivals on the seventh Monday will be _______.

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 forecast the wine sales.The forecast for 2011 is _______.

Instruction 14-10 The executive vice president of a drug manufacturing firm believes that the demand for the firm's most popular drug has been evidencing an exponential trend since 1995. She uses Microsoft Excel to obtain the partial output below. The dependent variable is the log base 10 of the demand for the drug, while the independent variable is years, where 1995 is coded as 0, 1996 is coded as 1, etc. PuMMaression Statistics MultipleR 0.996 R Square 0.992 Adjusted R Square 0.991 Standard Error 0.02831 Observations 12 Coefiients Intercept 1.44 Coded Year 0.068 -Referring to Instruction 14-10,the fitted exponential trend equation to predict Y 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 2009 using 2006 as the base year?

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 2006 as the base year?

Instruction 14-10 The executive vice president of a drug manufacturing firm believes that the demand for the firm's most popular drug has been evidencing an exponential trend since 1995. She uses Microsoft Excel to obtain the partial output below. The dependent variable is the log base 10 of the demand for the drug, while the independent variable is years, where 1995 is coded as 0, 1996 is coded as 1, etc. PuMMaression Statistics MultipleR 0.996 R Square 0.992 Adjusted R Square 0.991 Standard Error 0.02831 Observations 12 Coefiients Intercept 1.44 Coded Year 0.068 -Referring to Instruction 14-10,the forecast for the demand in 2009 is_______

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 constant 3.37 in the regression equation 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,the best interpretation of the coefficient of Q₃ (0.098)in the regression equation is:

The consumer price index is a Paasche price index.

The cyclical component of a time series