Exam 14: Time-Series Forecasting and Index Numbers

Some computer models for forecasting include factors such as changing habits and needs.

The method of least squares may be used to estimate both linear and curvilinear trends.

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 a three-term moving average is used to smooth this series,what would be the last calculated value?

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 0.9 for both level and trend will be used to forecast the number of arrivals.The forecast for the twelfth Monday 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 14-13,exponentially smooth the number of arrivals using a smoothing constant of 0.25.

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 second-order autoregressive model is _______.

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 first value?

Each forecast using the method of exponential smoothing depends on all the previous observations in the time series.

Instruction 14-8 The number of cases of merlot wine sold by a Barossa Valley Winery in an eight-year period follows. Year Cases of Wine 2003 270 2004 356 2005 398 2006 456 2007 358 2008 500 2009 410 2010 376 -Referring to Instruction 14-8,construct a centred five-year moving average for the wine sales.

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 sixth 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 forecast for profits in 2015 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,plot both the number of arrivals series and the series of Holt-Winters forecast for the seventh through twelfth Mondays using 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,what would be the second value?

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 X (0.117)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,using the regression equation,what is the forecast for the revenues in the third quarter of 2003?

The MAD is a measure of the mean of the absolute discrepancies between the actual and the fitted values in a given time series.

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 0.9 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.

A price index that includes consumption quantities is a(n)

To convert actual dollars to real dollars,multiple each dollar value in a time series by _______.

Instruction 14-7 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 14-7,advertising expenditures appear to be increasing in a linear rather than curvilinear manner over time.