Question 1

If data for a time-series analysis are collected on a monthly basis only, which component of the time series may be ignored?

Accepted Answer

A)  Long-term trend. 
B)  Cyclical variation. 
C)  Seasonal variation. 
D)  Random variation. 
A)  Long-term trend. 
B)  Cyclical variation. 
C)  Seasonal variation. 
D)  Random variation.

Question 2

The purpose of using the moving average is to take away the short-term seasonal and random variation, leaving behind a combined trend and cyclical movement.

Accepted Answer

A) True 
 B)False

Question 3

The time-series component that reflects a wavelike pattern describing a long-term trend that is generally apparent over a number of years is called seasonal.

Accepted Answer

A) True 
 B)False

Question 4

A time series is shown in the table below: $$\begin{array} { | c c | } 
\hline \text { Period } t & \
\hline 1 & 40 \
2 & 45 \
3 & 44 \
4 & 47 \
5 & 48 \
6 & 50 \
7 & 52 \
8 & 51 \
9 & 48 \
10 & 47 \
\hline
\end{array}$$ a. Apply exponential smoothing with w = 0.1 and w = 0.8 to help detect the components of the time series.
b. Draw the time series and the two sets of exponentially smoothed values. Does there appear to be a trend component in the time series?

Accepted Answer

a. \[\begin{array} { | c | c | c  c | }

Question 5

Of the four components of the multiplicative time-series model, the ratio of the time series to the moving average isolates the:

Accepted Answer

A)  trend and cyclical components. 
B)  cyclical and seasonal components. 
C)  seasonal and random variation components. 
D)  four components. 
A)  trend and cyclical components. 
B)  cyclical and seasonal components. 
C)  seasonal and random variation components. 
D)  four components.

Question 6

A time series can consist of four different components: long-term trend, cyclical variation, seasonal variation, and random variation.

Accepted Answer

A) True 
 B)False

Question 7

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 8

Which of the following best describes what may be used when measuring the seasonal and random variation of a time series with no cyclical effect?

Accepted Answer

A)  The trend value ŷ. 
B)  The ratio of the time series divided by the predicted values. 
C)  The ratio of the time series divided by the moving average and the ratio of the time series divided by the predicted values. 
D)  The ratio of the time series divided by the moving average. 
A)  The trend value ŷ. 
B)  The ratio of the time series divided by the predicted values. 
C)  The ratio of the time series divided by the moving average and the ratio of the time series divided by the predicted values. 
D)  The ratio of the time series divided by the moving average.

Question 9

The trend line  $=125+2 t$ and seasonal indexes shown below were computed from 10 years of quarterly data. Forecast the values for the next four quarters. $$\begin{array} { | c c | } 
\hline \text { Quarter } & S T _ { t } \
\hline 1 & 0.6 \
2 & 1.3 \
3 & 1.6 \
4 & 0.5 \
\hline
\end{array}$$

Accepted Answer

The answer of The trend line  $=125+2 t$ and...

Question 10

The equation Ft+1 = wyt + (1-w)St-1 (for t $\ge$ 2) refers to a time series forecast prepared by exponential smoothing.

Accepted Answer

A) True 
 B)False

Question 11

A company selling swimming goggles wants to analyze the company's Australian sales figures.
Time series forecasting with regression was used to generate Excel output to estimate trend of the time series of Swimming goggle sales (in thousands of dollars) where the origin is the March Quarter 2000. $\text { SUMMARY OUTPUT }$
$\begin{array}{lr}
{\text { Regression Statistics }} \
\hline \text { Multiple R } & 0.37281 \
\text { R Square } & 0.13899 \
\text { Adjusted R } & \
\text { Square } & 0.12243 \
\text { StandardError } & 10.3925 \
\text { Observations } & 54 \
\hline
\end{array}$

$\begin{array}{l}
A N O V A\
\begin{array}{lrcccr}
\hline & d f & S S & M S & F & \text { Significance } F \
\hline \text { Regression } & 1 & 906.5867925 & 906.59 & 839406 & 0.005497292 \
\text { Residual } & 52 & 5616.172467 & 108 & & \
\text { Total } & 53 & 6522.759259 & & &
\end{array}
\end{array}$

$\begin{array}{lrrrrrr} 
& {\text { Standard }} & \
& \text { Coefficients } & \text { Error } & \text { tStat } & \text { P-value } & \text { Lower } 95 \% & \text { Upper } 95 \% \
\hline \text { Interoept } & 12.237 & 2.789633876 & 4.3866 & 5.6 \mathrm{E}-05 & 6.639227133 & 17.8348469 \
\mathrm{t} & 0.26289 & 0.090738795 & 2.8973 & 0.0055 & 0.080812368 & 0.4449738
\end{array}$ (a) Forecast goggles sales for each quarter of 2016.
(b) Are these good predictions? Explain.

Accepted Answer

(a) \[\begin{array} { | l | c | c | } 
\

Question 12

We calculate the three-period moving average for a time series for all time periods except the first.

Accepted Answer

A) True 
 B)False

Question 13

Which of the following is the time-series component that reflects the irregular changes in a time series?

Accepted Answer

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

Question 14

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) = $1

Question 15

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

Question 16

The following trend line was calculated from quarterly data for 2006-2010: ŷ = 2.35 + 0.12t, where t = 1 for the first quarter of 2006. The trend value for the third quarter of the year 2011 is:

Accepted Answer

A)  5.110. 
B)  4.990. 
C)  5.230. 
D)  None of these choices are correct. 
A)  5.110. 
B)  4.990. 
C)  5.230. 
D)  None of these choices are correct.

Question 17

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 18

A retailing outlet has been keeping daily sales records over the past four weeks, as shown below. $$\begin{array}{l}
\quad\quad\quad\quad\quad\quad\quad\quad\quad\text { Week }\
\begin{array} { | l | c c c c | } 
\hline \text { Day } & 1 & 2 & 3 & 4 \
\hline \text { Monday } & 20 & 25 & 22 & 27 \
\text { Tuesday } & 26 & 30 & 26 & 28 \
\text { Wednesday } & 28 & 29 & 29 & 26 \
\text { Thursday } & 34 & 32 & 34 & 31 \
\text { Friday } & 38 & 35 & 37 & 36 \
\hline
\end{array}
\end{array}$$ 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 19

Any variable that is measured over time in sequential order is called a time series.

Accepted Answer

A) True 
 B)False

Question 20

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

Accepted Answer

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

If data for a time-series analysis are collected on a monthly basis only, which component of the time series may be ignored?

The purpose of using the moving average is to take away the short-term seasonal and random variation, leaving behind a combined trend and cyclical movement.

The time-series component that reflects a wavelike pattern describing a long-term trend that is generally apparent over a number of years is called seasonal.

Of the four components of the multiplicative time-series model, the ratio of the time series to the moving average isolates the:

A time series can consist of four different components: long-term trend, cyclical variation, seasonal variation, and random variation.

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.

Which of the following best describes what may be used when measuring the seasonal and random variation of a time series with no cyclical effect?

The equation F_t₊₁ = wy_t + (1-w)S_t_-1 (for t $\ge$ 2) refers to a time series forecast prepared by exponential smoothing.

We calculate the three-period moving average for a time series for all time periods except the first.

Which of the following is the time-series component that reflects the irregular changes in a time series?

The following trend line was calculated from quarterly data for 2006-2010: ŷ = 2.35 + 0.12t, where t = 1 for the first quarter of 2006. The trend value for the third quarter of the year 2011 is:

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?

Any variable that is measured over time in sequential order is called a time series.

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

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

If data for a time-series analysis are collected on a monthly basis only, which component of the time series may be ignored?

The purpose of using the moving average is to take away the short-term seasonal and random variation, leaving behind a combined trend and cyclical movement.

The time-series component that reflects a wavelike pattern describing a long-term trend that is generally apparent over a number of years is called seasonal.

Of the four components of the multiplicative time-series model, the ratio of the time series to the moving average isolates the:

A time series can consist of four different components: long-term trend, cyclical variation, seasonal variation, and random variation.

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.

Which of the following best describes what may be used when measuring the seasonal and random variation of a time series with no cyclical effect?

The trend line =125+2t=125+2 t=125+2t and seasonal indexes shown below were computed from 10 years of quarterly data. Forecast the values for the next four quarters. Quarter S 1 0.6 2 1.3 3 1.6 4 0.5

The equation Ft+1 = wyt + (1-w)St-1 (for t ≥\ge≥ 2) refers to a time series forecast prepared by exponential smoothing.

We calculate the three-period moving average for a time series for all time periods except the first.

Which of the following is the time-series component that reflects the irregular changes in a time series?

The following trend line was calculated from quarterly data for 2006-2010: ŷ = 2.35 + 0.12t, where t = 1 for the first quarter of 2006. The trend value for the third quarter of the year 2011 is:

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?

Any variable that is measured over time in sequential order is called a time series.

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

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

The equation F_t₊₁ = wy_t + (1-w)S_t_-1 (for t $\ge$ 2) refers to a time series forecast prepared by exponential smoothing.