Question 1

Seasonal variations will be present in a deseasonalised time series.

Accepted Answer

A) True 
 B)False

Question 2

In an exponentially smoothed time series, the smoothing constant w is chosen on the basis of how much smoothing is required. In general, a small value of w such as 0.1 results in a great deal of smoothing, while a large value of w, such as 0.9, results in very little smoothing.

Accepted Answer

A) True 
 B)False

Question 3

The high level of airline ticket sales that travel agencies experience during summer is an example of which component of a time series?

Accepted Answer

A)  Trend. 
B)  Cyclical. 
C)  Seasonal. 
D)  Random variation. 
A)  Trend. 
B)  Cyclical. 
C)  Seasonal. 
D)  Random variation.

Question 4

Which of the following smoothing constants causes the most rapid reaction to a change in the current time-series value?

Accepted Answer

A)  0.40. 
B)  0.48. 
C)  0.43. 
D)  0.37. 
A)  0.40. 
B)  0.48. 
C)  0.43. 
D)  0.37.

Question 5

The model that assumes the time-series value at time t is the sum of the four time-series components is referred to as the:

Accepted Answer

A)  additive model. 
B)  multiplicative model. 
C)  moving averages model. 
D)  forecast model. 
A)  additive model. 
B)  multiplicative model. 
C)  moving averages model. 
D)  forecast model.

Question 6

Which of the following equations will deseasonalise a time series, where T, C, S and R are respectively the trend, cyclical, seasonal and random variation components of the time series?

Accepted Answer

A)  (T $\times$ C $\times$ S $\times$ R) / T = C $\times$ S $\times$ R. 
B)  (T $\times$ C $\times$ S $\times$ R) / C = T $\times$ S $\times$ R. 
C)  (T $\times$ C $\times$ S $\times$ R) / S = T $\times$ C $\times$ R. 
D)  (T $\times$ C $\times$ S $\times$ R) / R = T $\times$ C $\times$ S. 
A)  (T $\times$ C $\times$ S $\times$ R) / T = C $\times$ S $\times$ R. 
B)  (T $\times$ C $\times$ S $\times$ R) / C = T $\times$ S $\times$ R. 
C)  (T $\times$ C $\times$ S $\times$ R) / S = T $\times$ C $\times$ R. 
D)  (T $\times$ C $\times$ S $\times$ R) / R = T $\times$ C $\times$ S.

Question 7

The term $b _ { 1 }$ in the equation  $\ = b _ { 0 } + b _ { 1 } t + b _ { 2 } Q _ { 1 } + b _ { 3 } Q _ { 2 } + b _ { 4 } Q _ { 3 }$ , where ?t represents the predicted value of y at time t, is:

Accepted Answer

A)  the time trend. 
B)  the seasonal trend. 
C)  an indicator variable. 
D)  a value between 0 and 4. 
A)  the time trend. 
B)  the seasonal trend. 
C)  an indicator variable. 
D)  a value between 0 and 4.

Question 8

Quarterly sales revenue (in $millions) for a particular company has been modelled using linear regression with indicator variables:
Y = 132 + 2Q1 + 3Q2 - 5Q4 + 2t
Where t is time in quarters, with origin March 2006 and Q1, Q2 and Q4 are the indicator variables for March, June and December quarters, respectively.
(a) What is the estimate for December quarter of 2011?
(b) What is the estimate for March 2011?
(c) Separate the differences from your two estimates in parts (a) and (b) into the trend component and the seasonal component.

Accepted Answer

(a) Y = 132 - 5(1) +2(23) = $173 million

Question 9

Which of the four time-series components is most likely to exhibit the steady growth of the population of Australia from 1945 to 1995?

Accepted Answer

A)  Trend. 
B)  Cyclical. 
C)  Seasonal. 
D)  Random variation. 
A)  Trend. 
B)  Cyclical. 
C)  Seasonal. 
D)  Random variation.

Question 10

In determining monthly seasonal indexes for natural gas consumption, the sum of the 12 means for gas consumption as a percentage of the moving average is 1195. To get the seasonal indexes, each monthly mean is to be multiplied by (1195 / 1200).

Accepted Answer

A) True 
 B)False

Question 11

Smoothing time-series data by the moving average method or exponential smoothing method is an attempt to remove the effect of the:

Accepted Answer

A)  trend component. 
B)  cyclical component. 
C)  seasonal component. 
D)  random variation component. 
A)  trend component. 
B)  cyclical component. 
C)  seasonal component. 
D)  random variation component.

Question 12

Share prices at the end of trading for 10 selected stocks is an example of a time series.

Accepted Answer

A) True 
 B)False

Question 13

Which of the following will not be present in a deseasonalised time series?

Accepted Answer

A)  Trend effects. 
B)  Cyclical variation. 
C)  Seasonal variation. 
D)  Random variation. 
A)  Trend effects. 
B)  Cyclical variation. 
C)  Seasonal variation. 
D)  Random variation.

Question 14

In determining monthly seasonal indexes for petrol consumption, the sum of the 12 means for petrol consumption as a percentage of the moving average is 1230. To get the seasonal indexes, each of the 12 monthly means is to be multiplied by:

Accepted Answer

A)  1200 / 1230. 
B)  1230 / 1200. 
C)  (1230 + 1200) / 2. 
D)  (1230 + 1200) / 12. 
A)  1200 / 1230. 
B)  1230 / 1200. 
C)  (1230 + 1200) / 2. 
D)  (1230 + 1200) / 12.

Question 15

A time series regression equation for a surfboard manufacturing company in Australia is given below: Y = 35 + 4Q1 + 0.5Q3 + 8Q4 + 3t
With t in quarters and the origin is December 2010 and Q1 is the indicator variable for March, Q3 is the indicator variable for September and Q4 is the indicator variable for December.
Which of the following statements is correct regarding the coefficient of Q4?

Accepted Answer

A)  This company expects to sell 8 more surfboards in the December quarter than in the March quarter or the September quarter. 
B)  This company expects to sell 8 more surfboards in the December quarter than in the June quarter. 
C)  This company expects to sell 8 more surfboards in the June quarter than in the December quarter. 
D)  None of these choices are correct. 
A)  This company expects to sell 8 more surfboards in the December quarter than in the March quarter or the September quarter. 
B)  This company expects to sell 8 more surfboards in the December quarter than in the June quarter. 
C)  This company expects to sell 8 more surfboards in the June quarter than in the December quarter. 
D)  None of these choices are correct.

Question 16

A retailing outlet has been keeping daily sales records over the past four weeks, as shown below. $$\begin{array}{l}
\quad\quad\quad\quad\quad\quad\quad\text { Week }\
\begin{array} { | l | c c c c | } 
\hline \text { Dox } & 1 & 2 & 3 & 4 \
\hline \text { Monday } & 20 & 25 & 22 & 27 \
\text { Tuesday } & 26 & 30 & 26 & 28 \
\text { Wednesday } & 28 & 29 & 29 & 26 \
\text { Thursday } & 34 & 32 & 34 & 31 \
\text { Friday } & 38 & 35 & 37 & 36 \
\hline
\end{array}
\end{array}$$ a. Use the regression technique to calculate the linear trend line.
b. Calculate the daily indexes based on the regression trend line in part (a).
c. What do the daily indexes tell us?

Accepted Answer

a. ŷ_t = 27.558 + 0.199t. b. Use Excel to

Question 17

Cycle is one of the four different components of a time series. It has a wavelike pattern over short, repetitive calendar periods and, by definition, has duration of less than one year.

Accepted Answer

A) True 
 B)False

Question 18

The following are the values of a time series for the first four time periods: $$\begin{array} { | c | c c c c | } 
\hline t & 1 & 2 & 3 & 4 \
\hline y _ { t } & 23 & 25 & 28 & 24 \
\hline
\end{array}$$ Using exponential smoothing, with w = 0.25, the forecast value for time period 5 is:

Accepted Answer

A)  18.352. 
B)  23.500. 
C)  24.469. 
D)  23.000. 
A)  18.352. 
B)  23.500. 
C)  24.469. 
D)  23.000.

Question 19

Of the four different components of a time series, the trend component is the one most likely to exhibit the relatively steady growth of the population of the Australian from about 10 million in 1960 to about 20 million in 2000.

Accepted Answer

A) True 
 B)False

Question 20

Consider the time series shown in the following table. $$\begin{array} { | c c | c c | } 
\hline \text { Time period } & y & \text { Time period } & y \
\hline 1 & 35 & 9 & 46 \
2 & 32 & 10 & 43 \
3 & 29 & 11 & 48 \
4 & 26 & 12 & 41 \
5 & 28 & 13 & 34 \
6 & 32 & 14 & 29 \
7 & 38 & 15 & 25 \
8 & 43 & 16 & 23 \
\hline
\end{array}$$ a. Calculate the percentage of trend for each time period.
b. Plot the percentage of trend.
c. Describe the cyclical effect (if there is one).

Accepted Answer

a. @#IMG-DLM& b. @#IMG-DLM& c. There app

Seasonal variations will be present in a deseasonalised time series.

In an exponentially smoothed time series, the smoothing constant w is chosen on the basis of how much smoothing is required. In general, a small value of w such as 0.1 results in a great deal of smoothing, while a large value of w, such as 0.9, results in very little smoothing.

The high level of airline ticket sales that travel agencies experience during summer is an example of which component of a time series?

Which of the following smoothing constants causes the most rapid reaction to a change in the current time-series value?

The model that assumes the time-series value at time t is the sum of the four time-series components is referred to as the:

Which of the following equations will deseasonalise a time series, where T, C, S and R are respectively the trend, cyclical, seasonal and random variation components of the time series?

Which of the four time-series components is most likely to exhibit the steady growth of the population of Australia from 1945 to 1995?

In determining monthly seasonal indexes for natural gas consumption, the sum of the 12 means for gas consumption as a percentage of the moving average is 1195. To get the seasonal indexes, each monthly mean is to be multiplied by (1195 / 1200).

Smoothing time-series data by the moving average method or exponential smoothing method is an attempt to remove the effect of the:

Share prices at the end of trading for 10 selected stocks is an example of a time series.

Which of the following will not be present in a deseasonalised time series?

In determining monthly seasonal indexes for petrol consumption, the sum of the 12 means for petrol consumption as a percentage of the moving average is 1230. To get the seasonal indexes, each of the 12 monthly means is to be multiplied by:

Cycle is one of the four different components of a time series. It has a wavelike pattern over short, repetitive calendar periods and, by definition, has duration of less than one year.

The following are the values of a time series for the first four time periods: t 1 2 3 4 23 25 28 24 Using exponential smoothing, with w = 0.25, the forecast value for time period 5 is:

Of the four different components of a time series, the trend component is the one most likely to exhibit the relatively steady growth of the population of the Australian from about 10 million in 1960 to about 20 million in 2000.

What Is Statistics

Types of Data, Data Collection and Sampling

Graphical Descriptive Methods Nominal Data

Graphical Descriptive Techniques Numerical Data

Numerical Descriptive Measures

Probability

Random Variables and Discrete Probability Distributions

Continuous Probability Distributions

Statistical Inference: Introduction

Sampling Distributions

Estimation: Describing a Single Population

Estimation: Comparing Two Populations

Hypothesis Testing: Describing a Single Population

Hypothesis Testing: Comparing Two Populations

Inference About Population Variances

Analysis of Variance

Additional Tests for Nominal Data: Chi-Squared Tests

Simple Linear Regression and Correlation

Multiple Regression

Model Building

Nonparametric Techniques

Statistical Inference: Conclusion

Index Numbers

Decision Analysis

Filters

Exam 23: Time-Series Analysis and Forecasting

Seasonal variations will be present in a deseasonalised time series.

In an exponentially smoothed time series, the smoothing constant w is chosen on the basis of how much smoothing is required. In general, a small value of w such as 0.1 results in a great deal of smoothing, while a large value of w, such as 0.9, results in very little smoothing.

The high level of airline ticket sales that travel agencies experience during summer is an example of which component of a time series?

Which of the following smoothing constants causes the most rapid reaction to a change in the current time-series value?

The model that assumes the time-series value at time t is the sum of the four time-series components is referred to as the:

Which of the following equations will deseasonalise a time series, where T, C, S and R are respectively the trend, cyclical, seasonal and random variation components of the time series?

The term b1b _ { 1 }b1​ in the equation =b0+b1t+b2Q1+b3Q2+b4Q3\ = b _ { 0 } + b _ { 1 } t + b _ { 2 } Q _ { 1 } + b _ { 3 } Q _ { 2 } + b _ { 4 } Q _ { 3 } =b0​+b1​t+b2​Q1​+b3​Q2​+b4​Q3​ , where ?t represents the predicted value of y at time t, is:

Which of the four time-series components is most likely to exhibit the steady growth of the population of Australia from 1945 to 1995?

In determining monthly seasonal indexes for natural gas consumption, the sum of the 12 means for gas consumption as a percentage of the moving average is 1195. To get the seasonal indexes, each monthly mean is to be multiplied by (1195 / 1200).

Smoothing time-series data by the moving average method or exponential smoothing method is an attempt to remove the effect of the:

Share prices at the end of trading for 10 selected stocks is an example of a time series.

Which of the following will not be present in a deseasonalised time series?

In determining monthly seasonal indexes for petrol consumption, the sum of the 12 means for petrol consumption as a percentage of the moving average is 1230. To get the seasonal indexes, each of the 12 monthly means is to be multiplied by:

Cycle is one of the four different components of a time series. It has a wavelike pattern over short, repetitive calendar periods and, by definition, has duration of less than one year.

The following are the values of a time series for the first four time periods: t 1 2 3 4 23 25 28 24 Using exponential smoothing, with w = 0.25, the forecast value for time period 5 is:

Of the four different components of a time series, the trend component is the one most likely to exhibit the relatively steady growth of the population of the Australian from about 10 million in 1960 to about 20 million in 2000.

What Is Statistics

Types of Data, Data Collection and Sampling

Graphical Descriptive Methods Nominal Data

Graphical Descriptive Techniques Numerical Data

Numerical Descriptive Measures

Probability

Random Variables and Discrete Probability Distributions

Continuous Probability Distributions

Statistical Inference: Introduction

Sampling Distributions

Estimation: Describing a Single Population

Estimation: Comparing Two Populations

Hypothesis Testing: Describing a Single Population

Hypothesis Testing: Comparing Two Populations

Inference About Population Variances

Analysis of Variance

Additional Tests for Nominal Data: Chi-Squared Tests

Simple Linear Regression and Correlation

Multiple Regression

Model Building

Nonparametric Techniques

Statistical Inference: Conclusion

Index Numbers

Decision Analysis

Filters