Deck 14: Time-Series Forecasting and Index Numbers

Question 1

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

Answer 1

False

Question 2

Based on the following scatter plot,which of the time-series components is not present in this quarterly time series?

A) Irregular
B) Trend
C) Cyclical
D) Seasonal

Answer 2

C

Question 3

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

A) the cyclical component has not been accounted for.
B) the irregular component has not been accounted for.
C) the trend component has not been accounted for.
D) the seasonal component has not been accounted for.

Answer 3

C

Question 4

Leading indicator forecasting is an example of

A) casual forecasting.
B) qualitative forecasting.
C) econometric forecasting.
D) historical forecasting.

Question 5

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

A) Casual forecasting
B) Qualitative forecasting
C) Historical forecasting
D) Quantitative forecasting

Question 6

Which of the following terms describes the up and down movements of a time series that vary both in length and intensity?

A) Trend
B) Seasonal component
C) Cyclical component
D) Irregular component

Question 7

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

A) trend
B) cyclical
C) irregular
D) seasonal

Question 8

The effect of an unpredictable,rare event will be contained in the _______ component.

A) trend
B) cyclical
C) irregular
D) seasonal

Question 9

The cyclical component of a time series

A) represents periodic fluctuations which reoccur within one year.
B) is obtained by adjusting for calendar variation.
C) represents periodic fluctuations which usually occur in two or more years.
D) is obtained by adding up the seasonal indexes.

Question 10

Which of the following terms describes the overall long-term tendency of a time series?

A) Seasonal component
B) Cyclical component
C) Trend
D) Irregular component

Question 11

Instruction 14-1
The number of cases of chardonnay wine sold by a Barossa Valley Winery in an eight-year period follows.
$$\begin{array} { c c } \text { Year } &\text { Coses of }\\& \text { Wine } \\\hline 1991 &270\\1992 & 356 \\1993 & 398 \\1994 & 456 \\1995 & 438 \\1996 & 478 \\1997 & 460 \\1998 & 480\end{array}$$

-Referring to Instruction 14-1,does there appear to be a relationship between year and the number of cases of wine sold?

A) No, there appears to be no relationship between the year and the number of cases of wine sold by the vintner.
B) Yes, there appears to be a negative nonlinear relationship between the year and the number of cases of wine sold by the vintner.
C) Yes, there appears to be a slight negative linear relationship between the year and the number of cases of wine sold by the vintner.
D) Yes, there appears to be a slight positive relationship between the year and the number of cases of wine sold by the vintner.

Question 12

A trend is a persistent pattern in annual time-series data that has to be followed for several years.

Question 13

The monthly publication of the quarterly GDP of a country is an example of a(n)_______.

Question 14

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

A) the cyclical component has not been accounted for.
B) the seasonal component has not been accounted for.
C) the irregular component has not been accounted for.
D) the trend component has not been accounted for.

Question 15

The fairly regular fluctuations that occur within each year would be contained in the _______ component.

A) trend
B) cyclical
C) irregular
D) seasonal

Question 16

The annual multiplicative time-series model does not possess_______ component.

A) a trend
B) a cyclical
C) an irregular
D) a seasonal

Question 17

_______methods are primarily based on the subjective opinion of the forecaster rather than the analysis of numerical data.

A) Casual forecasting
B) Qualitative forecasting
C) Time-series forecasting
D) Quantitative forecasting

Question 18

Quantitative forecasting methods are highly subjective and judgmental.

Question 19

The method of moving averages is used

A) in regression analysis.
B) to exponentiate a series.
C) to smooth a series.
D) to plot a series.

Question 20

What type of forecasting is based entirely on the past and present values of a variable?

A) Economic forecasting
B) Time-series forecasting
C) Casual forecasting
D) Qualitative forecasting

Question 21

Instruction 14-2
The following table contains the number of complaints received in a department store for the first six months of last year.
$$\begin{array} { c c } \text { Month } & \text { Complaints } \\\text { January } & 36 \\\text { February } & 45 \\\text { March } & 81 \\\text { April } & 50 \\\text { May } & 108 \\\text { June } & 144\end{array}$$

-Referring to Instruction 14-2,if a three-term moving average is used to smooth this series,what would be the second calculated value?

A) 36
B) 72
C) 54
D) 40.5

Question 22

Which of the following statements about moving averages is NOT true?

A) It gives equal weight to all values in the computation.
B) It is simpler than the method of exponential smoothing.
C) It gives greater weight to more recent data.
D) It can be used to smooth a series.

Question 23

Instruction 14-3
The number of cases of merlot wine sold by a Barossa Valley Winery in an eight-year period follows.
$\begin{array}{ll}\text { Year } &\text { Coses of }\\& \text { Wine } \\2003 & 270 \\2004 & 356 \\2005 & 398 \\2006 & 456 \\2007 & 358 \\2008 & 500 \\2009 & 410 \\2010 & 376\end{array}$



-Referring to Instruction 14-3,a centred three-year moving average is to be constructed for the wine sales.The result of this process will lead to a total of _______ moving averages.

Question 24

Instruction 14-2
The following table contains the number of complaints received in a department store for the first six months of last year.
$$\begin{array} { c c } \text { Month } & \text { Complaints } \\\text { January } & 36 \\\text { February } & 45 \\\text { March } & 81 \\\text { April } & 50 \\\text { May } & 108 \\\text { June } & 144\end{array}$$

-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?

A) 53
B) 39
C) 45
D) 42

Question 25

Instruction 14-3
The number of cases of merlot wine sold by a Barossa Valley Winery in an eight-year period follows.
$\begin{array}{ll}\text { Year } &\text { Coses of }\\& \text { Wine } \\2003 & 270 \\2004 & 356 \\2005 & 398 \\2006 & 456 \\2007 & 358 \\2008 & 500 \\2009 & 410 \\2010 & 376\end{array}$



-Referring to Instruction 14-3,a centred three-year moving average is to be constructed for the wine sales.The moving average for 2004 is _______.

Question 26

Instruction 14-2
The following table contains the number of complaints received in a department store for the first six months of last year.
$$\begin{array} { c c } \text { Month } & \text { Complaints } \\\text { January } & 36 \\\text { February } & 45 \\\text { March } & 81 \\\text { April } & 50 \\\text { May } & 108 \\\text { June } & 144\end{array}$$

-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?

A) 68
B) 81
C) 65.33
D) 53

Question 27

Instruction 14-2
The following table contains the number of complaints received in a department store for the first six months of last year.
$$\begin{array} { c c } \text { Month } & \text { Complaints } \\\text { January } & 36 \\\text { February } & 45 \\\text { March } & 81 \\\text { April } & 50 \\\text { May } & 108 \\\text { June } & 144\end{array}$$

-Referring to Instruction 14-2,suppose the last two smoothed values are 81 and 96 (Note: They are not).What would you forecast as the value of the time series for July?

A) 86
B) 91
C) 96
D) 81

Question 28

When using the exponentially weighted moving average for purposes of forecasting rather than smoothing,

A) the previous smoothed value becomes the forecast.
B) the next smoothed value becomes the forecast.
C) the current smoothed value becomes the forecast.
D) None of the above.

Question 29

Instruction 14-2
The following table contains the number of complaints received in a department store for the first six months of last year.
$$\begin{array} { c c } \text { Month } & \text { Complaints } \\\text { January } & 36 \\\text { February } & 45 \\\text { March } & 81 \\\text { April } & 50 \\\text { May } & 108 \\\text { June } & 144\end{array}$$

-Referring to Instruction 14-2,if a three-term moving average is used to smooth this series,what would be the last calculated value?

A) 93
B) 72
C) 114
D) 126

Question 30

Which of the following methods should not be used for short-term forecasts into the future?

A) Exponential smoothing
B) Linear trend model
C) Moving averages
D) Autoregressive modelling

Question 31

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

A) It enables us to smooth out cyclical components.
B) It enables us to perform more than one-period ahead forecasting.
C) It enables us to perform one-period ahead forecasting.
D) It enables us to smooth out seasonal components.

Question 32

Given a data set with 15 yearly observations,a three-year moving average will have fewer observations than a five-year moving average.

Question 33

Instruction 14-2
The following table contains the number of complaints received in a department store for the first six months of last year.
$$\begin{array} { c c } \text { Month } & \text { Complaints } \\\text { January } & 36 \\\text { February } & 45 \\\text { March } & 81 \\\text { April } & 50 \\\text { May } & 108 \\\text { June } & 144\end{array}$$

-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) Three
B) Six
C) Four
D) Five

Question 34

Given a data set with 15 yearly observations,there are only 13 three-year moving averages.

Question 35

Given a data set with 15 yearly observations,there are only seven nine-year moving averages.

Question 36

Instruction 14-2
The following table contains the number of complaints received in a department store for the first six months of last year.
$$\begin{array} { c c } \text { Month } & \text { Complaints } \\\text { January } & 36 \\\text { February } & 45 \\\text { March } & 81 \\\text { April } & 50 \\\text { May } & 108 \\\text { June } & 144\end{array}$$

-Referring to Instruction 14-2,if a three-term moving average is used to smooth this series,how many values would it have?

A) Five
B) Three
C) Two
D) Four

Question 37

Which of the following statements about the method of exponential smoothing is NOT true?

A) It can be used for forecasting.
B) It gives greater weight to the earlier observations in the series.
C) It gives greater weight to more recent data.
D) It uses all earlier observations in each smoothing calculation.

Question 38

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

A) [0.2, 0.4].
B) [0.6, 0.8].
C) [0.8, 1.0].
D) [0, 0.2].

Question 39

Instruction 14-2
The following table contains the number of complaints received in a department store for the first six months of last year.
$$\begin{array} { c c } \text { Month } & \text { Complaints } \\\text { January } & 36 \\\text { February } & 45 \\\text { March } & 81 \\\text { April } & 50 \\\text { May } & 108 \\\text { June } & 144\end{array}$$

-Referring to Instruction 14-2,suppose the last two smoothed values are 81 and 96 (Note: They are not).What would you forecast as the value of the time series for September?

A) 91
B) 86
C) 96
D) 81

Question 40

Instruction 14-2
The following table contains the number of complaints received in a department store for the first six months of last year.
$$\begin{array} { c c } \text { Month } & \text { Complaints } \\\text { January } & 36 \\\text { February } & 45 \\\text { March } & 81 \\\text { April } & 50 \\\text { May } & 108 \\\text { June } & 144\end{array}$$

-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?

A) 39
B) 42
C) 45
D) 36

Question 41

Instruction 14-3
The number of cases of merlot wine sold by a Barossa Valley Winery in an eight-year period follows.
$\begin{array}{ll}\text { Year } &\text { Coses of }\\& \text { Wine } \\2003 & 270 \\2004 & 356 \\2005 & 398 \\2006 & 456 \\2007 & 358 \\2008 & 500 \\2009 & 410 \\2010 & 376\end{array}$



-Referring to Instruction 14-3,a centred five-year moving average is to be constructed for the wine sales.The number of moving averages that will be calculated is_______.

Question 42

Instruction 14-3
The number of cases of merlot wine sold by a Barossa Valley Winery in an eight-year period follows.
$\begin{array}{ll}\text { Year } &\text { Coses of }\\& \text { Wine } \\2003 & 270 \\2004 & 356 \\2005 & 398 \\2006 & 456 \\2007 & 358 \\2008 & 500 \\2009 & 410 \\2010 & 376\end{array}$



-Referring to Instruction 14-3,a centred five-year moving average is to be constructed for the wine sales.The moving average for 2005 is _______.

Question 43

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 five-term moving average.The last smoothed value will be_______.

Question 44

Instruction 14-3
The number of cases of merlot wine sold by a Barossa Valley Winery in an eight-year period follows.
$\begin{array}{ll}\text { Year } &\text { Coses of }\\& \text { Wine } \\2003 & 270 \\2004 & 356 \\2005 & 398 \\2006 & 456 \\2007 & 358 \\2008 & 500 \\2009 & 410 \\2010 & 376\end{array}$



-Referring to Instruction 14-3,a centred five-year moving average is to be constructed for the wine sales.The moving average for 2008 is_______.

Question 45

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 five-term moving average.The first smoothed value will be _______.

Question 46

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.The first smoothed value will be _______.

Question 47

Instruction 14-3
The number of cases of merlot wine sold by a Barossa Valley Winery in an eight-year period follows.
$\begin{array}{ll}\text { Year } &\text { Coses of }\\& \text { Wine } \\2003 & 270 \\2004 & 356 \\2005 & 398 \\2006 & 456 \\2007 & 358 \\2008 & 500 \\2009 & 410 \\2010 & 376\end{array}$



-Referring to Instruction 14-3,exponential smoothing with a weight or smoothing constant of 0.2 will be used to smooth the wine sales.The value of E₂,the smoothed value for 2004 is _______.

Question 48

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_______.

Question 49

Instruction 14-3
The number of cases of merlot wine sold by a Barossa Valley Winery in an eight-year period follows.
$\begin{array}{ll}\text { Year } &\text { Coses of }\\& \text { Wine } \\2003 & 270 \\2004 & 356 \\2005 & 398 \\2006 & 456 \\2007 & 358 \\2008 & 500 \\2009 & 410 \\2010 & 376\end{array}$



-Referring to Instruction 14-3,exponentially smooth the wine sales with a weight or smoothing constant of 0.4.

Question 50

Instruction 14-3
The number of cases of merlot wine sold by a Barossa Valley Winery in an eight-year period follows.
$\begin{array}{ll}\text { Year } &\text { Coses of }\\& \text { Wine } \\2003 & 270 \\2004 & 356 \\2005 & 398 \\2006 & 456 \\2007 & 358 \\2008 & 500 \\2009 & 410 \\2010 & 376\end{array}$



-Referring to Instruction 14-3,exponentially smooth the wine sales with a weight or smoothing constant of 0.2.

Question 51

Instruction 14-3
The number of cases of merlot wine sold by a Barossa Valley Winery in an eight-year period follows.
$\begin{array}{ll}\text { Year } &\text { Coses of }\\& \text { Wine } \\2003 & 270 \\2004 & 356 \\2005 & 398 \\2006 & 456 \\2007 & 358 \\2008 & 500 \\2009 & 410 \\2010 & 376\end{array}$



-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 _______.

Question 52

Instruction 14-3
The number of cases of merlot wine sold by a Barossa Valley Winery in an eight-year period follows.
$\begin{array}{ll}\text { Year } &\text { Coses of }\\& \text { Wine } \\2003 & 270 \\2004 & 356 \\2005 & 398 \\2006 & 456 \\2007 & 358 \\2008 & 500 \\2009 & 410 \\2010 & 376\end{array}$



-Referring to Instruction 14-3,a centred three-year moving average is to be constructed for the wine sales.The moving average for 2007 is _______.

Question 53

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.

Question 54

Instruction 14-3
The number of cases of merlot wine sold by a Barossa Valley Winery in an eight-year period follows.
$\begin{array}{ll}\text { Year } &\text { Coses of }\\& \text { Wine } \\2003 & 270 \\2004 & 356 \\2005 & 398 \\2006 & 456 \\2007 & 358 \\2008 & 500 \\2009 & 410 \\2010 & 376\end{array}$



-Referring to Instruction 14-3,exponential smoothing with a weight or smoothing constant of 0.2 will be used to forecast wine sales.The forecast for 2011 is _______.

Question 55

Instruction 14-3
The number of cases of merlot wine sold by a Barossa Valley Winery in an eight-year period follows.
$\begin{array}{ll}\text { Year } &\text { Coses of }\\& \text { Wine } \\2003 & 270 \\2004 & 356 \\2005 & 398 \\2006 & 456 \\2007 & 358 \\2008 & 500 \\2009 & 410 \\2010 & 376\end{array}$



-Referring to Instruction 14-3,exponential smoothing with a weight or smoothing constant of 0.4 will be used to forecast wine sales.The forecast for 2011 is _______.

Question 56

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.Then the forecast for the seventh Monday will be_______

Question 57

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 _______.

Question 58

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.The last smoothed value will be _______.

Question 59

Instruction 14-3
The number of cases of merlot wine sold by a Barossa Valley Winery in an eight-year period follows.
$\begin{array}{ll}\text { Year } &\text { Coses of }\\& \text { Wine } \\2003 & 270 \\2004 & 356 \\2005 & 398 \\2006 & 456 \\2007 & 358 \\2008 & 500 \\2009 & 410 \\2010 & 376\end{array}$



-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 E₂,the smoothed value for 2004 is _______.

Question 60

Instruction 14-3
The number of cases of merlot wine sold by a Barossa Valley Winery in an eight-year period follows.
$\begin{array}{ll}\text { Year } &\text { Coses of }\\& \text { Wine } \\2003 & 270 \\2004 & 356 \\2005 & 398 \\2006 & 456 \\2007 & 358 \\2008 & 500 \\2009 & 410 \\2010 & 376\end{array}$



-Referring to Instruction 14-3,exponential smoothing with a weight or smoothing constant of 0.2 will be used to smooth the wine sales.The value of E₄,the smoothed value for 2006 is _______.

Question 61

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:

A) The fitted value for the first quarter of 2005, after seasonal adjustment, is log₁₀(6.102).
B) The fitted value for the first quarter of 2005, after seasonal adjustment, is 10^6.102.
C) The fitted value for the first quarter of 2005, prior to seasonal adjustment, is log₁₀(6.102).
D) The fitted value for the first quarter of 2005, prior to seasonal adjustment, is 10^6.102.

Question 62

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 _______.

Question 63

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?

A) 391,742
B) 1,238,797
C) 4,355,119
D) 144,212

Question 64

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?

A) The number of contracts in the first quarter of the year is not significantly different than the number of contracts in an average quarter ( $\alpha$ = 0.05).
B) The number of contracts in the first quarter of the year is not significantly different than the number of contracts in the fourth quarter for a given coded quarterly value of X ( $\alpha$ = 0.05).
C) The number of contracts in the first quarter of the year is significantly different than the number of contracts in the fourth quarter for a given coded quarterly value of X ( $\alpha$ = 0.05).
D) The number of contracts in the first quarter of the year is significantly different than the number of contracts in an average quarter ( $\alpha$ = 0.05).

Question 65

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:

A) The fitted value for the first quarter of 2008, prior to seasonal adjustment, is log₁₀ 3.37.
B) The fitted value for the first quarter of 2008, after seasonal adjustment, is 10^3.37.
C) The fitted value for the first quarter of 2008, after seasonal adjustment, is log₁₀ 3.37.
D) The fitted value for the first quarter of 2008, prior to seasonal adjustment, is 10^3.37.

Question 66

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 of X in the regression equation (0.117),the results were a t-statistic of 9.08 and an associated p-value of 0.0000.Which of the following is the best interpretation of this result?

A) The quarterly growth rate in the number of contracts is not significantly different than 100% ( $\alpha$ = 0.05).
B) The quarterly growth rate in the number of contracts is significantly different than 100% ( $\alpha$ = 0.05).
C) The quarterly growth rate in the number of contracts is significantly different than 0% ( $\alpha$ = 0.05).
D) The quarterly growth rate in the number of contracts is not significantly different than 0% ( $\alpha$ = 0.05).

Question 67

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:

A) The quarterly compound growth rate in contracts is around 30.92%.
B) The quarterly compound growth rate in contracts is around 11.7%.
C) The annually compound growth rate in contracts is around 30.92%.
D) The annually compound growth rate in contracts is around 11.7%.

Question 68

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 X (0.012)in the regression equation is:

A) The annual growth rate in revenues is around 1.2%.
B) The quarterly growth rate in revenues is around 1.2%.
C) The quarterly compound growth rate in revenues is around 2.8%.
D) The annual growth rate in revenues is around 2.8%.

Question 69

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

A) compute moving averages.
B) estimate a least square trend model.
C) perform exponential smoothing.
D) compute the MAD statistic.

Question 70

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 third quarter of 2011?

A) 133,352
B) 421,697
C) 49,091
D) 1,482,518

Question 71

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 _______.

Question 72

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

A) exponential trend.
B) quadratic trend.
C) linear trend.
D) None of the above.

Question 73

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:

A) The number of contracts in the third quarter of a year is approximately 314% higher than the average over all four quarters.
B) The number of contracts in the third quarter of a year is approximately 62% higher than it would be during the fourth quarter.
C) The number of contracts in the third quarter of a year is approximately 62% higher than the average over all four quarters.
D) The number of contracts in the third quarter of a year is approximately 314% higher than it would be during the fourth quarter.

Question 74

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?

A) X = 13, Q₁ = 1, Q₂ = 0, Q₃ = 0
B) X = 12, Q₁ = 1, Q₂ = 0, Q₃ = 0
C) X = 12, Q₁ = 0, Q₂ = 0, Q₃ = 0
D) X = 13, Q₁ = 0, Q₂ = 0, Q₃ = 0

Question 75

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

A) 2.8%.
B) 12%.
C) 1.2%.
D) 28%.

Question 76

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

A) quadratic trend.
B) exponential trend.
C) linear trend.
D) All of the above.

Question 77

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 Q₂ (-0.054)in the regression equation is:

A) The revenues in the second quarter of a year is approximately 11.69% lower than the average over all 4 quarters.
B) The revenues in the second quarter of a year is approximately 11.69% lower than it would be during the fourth quarter.
C) The revenues in the second quarter of a year is approximately 5.4% lower than it would be during the fourth quarter.
D) The revenues in the second quarter of a year is approximately 5.4% lower than the average over all four quarters.

Question 78

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?

A) X = 15, Q₁ = 1, Q₂ = 0, Q₃ = 0
B) X = 16, Q₁ = 0, Q₂ = 0, Q₃ = 0
C) X = 16, Q₁ = 1, Q₂ = 0, Q₃ = 0
D) X = 15, Q₁ = 0, Q₂ = 0, Q₃ = 0

Question 79

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 _______.

Question 80

The method of least squares is used on time-series data for

A) deseasonalising the data.
B) exponentially smoothing a series.
C) obtaining the trend equation.
D) eliminating irregular movements.