Question 1

Forecasts based on trend and seasonality are generated by:

Accepted Answer

A)  identifying and removing the seasonal effect. 
B)  extrapolating the linear trend. 
C)  adjusting the forecasts to the seasonal effect. 
D)  All of these choices are correct. 
A)  identifying and removing the seasonal effect. 
B)  extrapolating the linear trend. 
C)  adjusting the forecasts to the seasonal effect. 
D)  All of these choices are correct.

Question 2

Which of the following best describes a time series?

Accepted Answer

A)  A time series is a set of measurements on a variable collected at the same time. 
B)  A time series is a set of measurements on a variable taken over some time period in sequential order. 
C)  A time series is a model that attempts to analyze the relationship between a dependent variable and one or more independent variables. 
D)  A time series is a model that attempts to forecast the future value of a variable. 
A)  A time series is a set of measurements on a variable collected at the same time. 
B)  A time series is a set of measurements on a variable taken over some time period in sequential order. 
C)  A time series is a model that attempts to analyze the relationship between a dependent variable and one or more independent variables. 
D)  A time series is a model that attempts to forecast the future value of a variable.

Question 3

The results of a quadratic model fit to time-series data were ?t = 7.5 - 0.2t + 2.8t2, where t = 1 for 2002. The forecast value for 2011 is:

Accepted Answer

A)  289.5. 
B)  285.5. 
C)  236.1. 
D)  232.5. 
A)  289.5. 
B)  285.5. 
C)  236.1. 
D)  232.5.

Question 4

The cyclical variation component of a time series is a wave like movement, showing peaks and troughs.

Accepted Answer

A) True 
 B)False

Question 5

The mean absolute deviation (MAD) and the sum of squares for forecast error (SSE) are the most commonly used measures of forecast accuracy. The model that forecasts the data best will usually have the:

Accepted Answer

A)  lowest MAD and highest SSE. 
B)  highest MAD and lowest SSE. 
C)  lowest MAD and SSE. 
D)  highest MAD and SSE. 
A)  lowest MAD and highest SSE. 
B)  highest MAD and lowest SSE. 
C)  lowest MAD and SSE. 
D)  highest MAD and SSE.

Question 6

A company selling swimming goggles wants to analyze its Australian sales figures.
Time series forecasting with regression was used to generate Excel output to estimate trend and seasonal effects of the time series of Swimming goggle sales (in thousands of dollars) where the origin is the March Quarter 2000 and Q₁ denotes sales in the March quarter, Q₃ denotes sales in the September quarter and Q₄ denotes sales in the December quarter. SUMMARY OUTPUT
$\begin{array}{l}
\text { Regression Statistios }\
\begin{array}{lc}
\hline \text { Multiple R } & 0.9460 \
\text { R Square } & 0.8950 \
\text { Adjusted R Square } & 0.8864 \
\text { Standard Error } & 3.7394 \
\text { Obserwations } & 54 \
\hline
\end{array}
\end{array}$
ANOVA
$\begin{array}{lccccc}
\hline & d f & S S & \text { MS } & F & \text { Significance } \
\hline \text { Regression } & 4 & 5837.596003 & 1459.4 & 104.3701 & 2.41949 \mathrm{E}-23 \
\text { Residual } & 49 & 685.1632564 & 13.9829 & & \
\text { Total } & 53 & 6522.759259 & & & \
\hline
\end{array}$

$\begin{array}{lcccccr} && \text {Standard }&&&& \text {Upper }\
& \text { Coeffcients } & \text { Error } & \text { t Stat } & \text { P-value } & \text { Lower } 95 \% & 95 \% \
\hline \text { Intercept } & 3.0588 & 1.3331 & 2.2944 & 0.0261 & 0.3797 & 5.7378 \
\mathrm{t} & 0.2518 & 0.0327 & 7.7052 & 0.0000 & 0.1861 & 0.3175 \
\mathrm{Q} 1 & 12.4604 & 1.3897 & 8.9664 & 0.0000 & 9.6677 & 15.2530 \
\mathrm{Q} 3 & 1.1458 & 1.4721 & 0.7784 & 0.4401 & -1.8124 & 4.1041 \
\mathrm{Q4} & 23.9121 & 1.4403 & 16.6025 & 0.0000 & 21.0177 & 26.8064
\end{array}$
 (a) Using p-values test the significance of the independent variables.
(b) Test the significance of the overall regression equation.

Accepted Answer

(a) Ho: β_t = 0 H_A: β_t ≠ 0 p-value = 0, so t

Question 7

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, 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 is the correct value of the estimate for the number of surfboards sold by this manufacturing company in March 2015?

Accepted Answer

A)  86 
B)  90 
C)  93 
D)  51 
A)  86 
B)  90 
C)  93 
D)  51

Question 8

For which of the following values of the smoothing constant w will the smoothed series catch up most quickly whenever the original time series changes direction?

Accepted Answer

A)  0.10. 
B)  0.50. 
C)  0.30. 
D)  0.70. 
A)  0.10. 
B)  0.50. 
C)  0.30. 
D)  0.70.

Question 9

Which of the following is not true in regard to the weights used in exponential smoothing?

Accepted Answer

A)  The last weight is always the smallest. 
B)  They are all positive. 
C)  They add up to 1. 
D)  They decrease exponentially into the past. 
A)  The last weight is always the smallest. 
B)  They are all positive. 
C)  They add up to 1. 
D)  They decrease exponentially into the past.

Question 10

Which of the four time-series components is most likely to exhibit the changes in a stock market crash?

Accepted Answer

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

Question 11

In forecasting, we use data from the past in predicting the future value of the variable of interest.

Accepted Answer

A) True 
 B)False

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

We compute the three-period moving averages for all time periods except the first and last.

Accepted Answer

A) True 
 B)False

Question 14

The Pyramids of Giza are one of the most visited monuments in Egypt. The number of visitors per quarter has been recorded (in thousands) as shown in the accompanying table: $$\begin{array}{l}
\text { Year }\
\begin{array} { | l | c c c c | } 
\hline \text { Quarter } & 1995 & 1996 & 1997 & 1998 \
\hline \text { WTinter } & 210 & 215 & 218 & 220 \
\text { Spring } & 260 & 275 & 282 & 290 \
\text { Summer } & 480 & 490 & 505 & 525 \
\text { Autumn } & 250 & 255 & 265 & 270 \
\hline
\end{array}
\end{array}$$ a. Plot the time series.
b. Discuss why exponential smoothing is not recommended as a forecasting method in this case.
c. Calculate the four-quarter centred moving averages.
d. Use the moving averages computed in (c) to calculate the seasonal (quarterly) indexes.
e. Use the seasonal indexes computed in (d) to deseasonalise the original time-series data, and plot the deseasonalised time series.
f. Use regression analysis to develop the trend line.
g. Use the seasonal indexes calculated in (d) and the linear trend calculated in (f) to forecast the number of visitors in the next four quarters and describe the seasonal fluctuations in the number of visitors.

Accepted Answer

a. @#IMG-DLM& b. There is a distinct pattern of se

Question 15

A time series is shown in the table below: $$\begin{array} { | c | c | } 
\hline \text { Time period } & y _ { t } \
\hline 1 & 48 \
2 & 50 \
3 & 46 \
4 & 42 \
5 & 40 \
6 & 32 \
7 & 34 \
8 & 26 \
9 & 21 \
10 & 13 \
\hline
\end{array}$$ a. Plot the time series to determine which of the trend models appears to fit better.
b. Use the regression technique to calculate the linear trend line and the quadratic trend line. Which line fits better? Use the best model to forecast the value of y for time period 7.

Accepted Answer

a. @#IMG-DLM& The linear trend model app

Question 16

A company selling swimming goggles wants to analyze its Australian sales figures.
Time series forecasting with regression was used to generate Excel output to estimate trend and seasonal effects of the time series of Swimming goggle sales (in thousands of dollars) where the origin is the March Quarter 2000 and Q₁ denotes sales in the March quarter, Q₃ denotes sales in the September quarter and Q₄ denotes sales in the December quarter. SUMMARY OUTPUT
$\begin{array}{l}
\text { Regression Statistios }\
\begin{array}{lc}
\hline \text { Multiple R } & 0.9460 \
\text { R Square } & 0.8950 \
\text { Adjusted R Square } & 0.8864 \
\text { Standard Error } & 3.7394 \
\text { Observations } & 54 \
\hline
\end{array}
\end{array}$

ANOVA
$\begin{array}{lccccc} 
& & & & & \text { Significance } \
& d f & S S & \text { MS } & F & F \
\hline \text { Regression } & 4 & 5837.596003 & 1459.4 & 104.3701 & 2.41949 \mathrm{E}-23 \
\text { Residual } & 49 & 685.1632564 & 13.9829 & & \
\text { Total } & 53 & 6522.759259 & & & \
\hline
\end{array}$

$\begin{array}{lcccccr} && \text {Standard }&&&& \text {Upper }\
& \text { Coeffcients } & \text { Error } & \text { t Stat } & \text { P-value } & \text { Lower } 95 \% & 95 \% \
\hline \text { Intercept } & 3.0588 & 1.3331 & 2.2944 & 0.0261 & 0.3797 & 5.7378 \
\mathrm{t} & 0.2518 & 0.0327 & 7.7052 & 0.0000 & 0.1861 & 0.3175 \
\mathrm{Q} 1 & 12.4604 & 1.3897 & 8.9664 & 0.0000 & 9.6677 & 15.2530 \
\mathrm{Q} 3 & 1.1458 & 1.4721 & 0.7784 & 0.4401 & -1.8124 & 4.1041 \
\mathrm{Q4} & 23.9121 & 1.4403 & 16.6025 & 0.0000 & 21.0177 & 26.8064
\end{array}$

(a) Forecast swimming goggle sales for all four quarters of 2016.
(b) Are these good forecasts? Explain.
(c) Separate the difference in your forecasts for June 2016 and December 2016 between seasonal and trend.

Accepted Answer

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

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

Which of the following models might be appropriate to describe a new product that has experienced a rapid early growth rate followed by the inevitable levelling-off?

Accepted Answer

A)  The autoregressive model. 
B)  The linear model for long-term trend. 
C)  The quadratic model for long-term trend. 
D)  All of these choices are correct. 
A)  The autoregressive model. 
B)  The linear model for long-term trend. 
C)  The quadratic model for long-term trend. 
D)  All of these choices are correct.

Question 19

If summer 2010 sales were $26 800 and the summer seasonal index was 1.15, the deseasonalised 2010 summer sales value is $30 820.

Accepted Answer

A) True 
 B)False

Question 20

A time series regression equation measuring the number of surfboards sold by 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 trend component?

Accepted Answer

A)  There were 43 surfboards sold in December 2010, and this increases by 3 surfboards per quarter, irrespective of the season of the year. 
B)  There were 35 surfboard sold in December 2010, and this increases by 15.5 surfboards per quarter, irrespective of the season of the year. 
C)  There were 35 surfboard sold in December 2010, and this increases by 3 surfboards per quarter, irrespective of the season of the year. 
D)  None of these choices are correct. 
A)  There were 43 surfboards sold in December 2010, and this increases by 3 surfboards per quarter, irrespective of the season of the year. 
B)  There were 35 surfboard sold in December 2010, and this increases by 15.5 surfboards per quarter, irrespective of the season of the year. 
C)  There were 35 surfboard sold in December 2010, and this increases by 3 surfboards per quarter, irrespective of the season of the year. 
D)  None of these choices are correct.

Forecasts based on trend and seasonality are generated by:

Which of the following best describes a time series?

The results of a quadratic model fit to time-series data were ?_t = 7.5 - 0.2t + 2.8t², where t = 1 for 2002. The forecast value for 2011 is:

The cyclical variation component of a time series is a wave like movement, showing peaks and troughs.

The mean absolute deviation (MAD) and the sum of squares for forecast error (SSE) are the most commonly used measures of forecast accuracy. The model that forecasts the data best will usually have the:

For which of the following values of the smoothing constant w will the smoothed series catch up most quickly whenever the original time series changes direction?

Which of the following is not true in regard to the weights used in exponential smoothing?

Which of the four time-series components is most likely to exhibit the changes in a stock market crash?

In forecasting, we use data from the past in predicting the future value of the variable of interest.

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

We compute the three-period moving averages for all time periods except the first and last.

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.

Which of the following models might be appropriate to describe a new product that has experienced a rapid early growth rate followed by the inevitable levelling-off?

If summer 2010 sales were $26 800 and the summer seasonal index was 1.15, the deseasonalised 2010 summer sales value is $30 820.

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

Forecasts based on trend and seasonality are generated by:

Which of the following best describes a time series?

The results of a quadratic model fit to time-series data were ?t = 7.5 - 0.2t + 2.8t2, where t = 1 for 2002. The forecast value for 2011 is:

The cyclical variation component of a time series is a wave like movement, showing peaks and troughs.

The mean absolute deviation (MAD) and the sum of squares for forecast error (SSE) are the most commonly used measures of forecast accuracy. The model that forecasts the data best will usually have the:

For which of the following values of the smoothing constant w will the smoothed series catch up most quickly whenever the original time series changes direction?

Which of the following is not true in regard to the weights used in exponential smoothing?

Which of the four time-series components is most likely to exhibit the changes in a stock market crash?

In forecasting, we use data from the past in predicting the future value of the variable of interest.

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

We compute the three-period moving averages for all time periods except the first and last.

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.

Which of the following models might be appropriate to describe a new product that has experienced a rapid early growth rate followed by the inevitable levelling-off?

If summer 2010 sales were $26 800 and the summer seasonal index was 1.15, the deseasonalised 2010 summer sales value is $30 820.

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 results of a quadratic model fit to time-series data were ?_t = 7.5 - 0.2t + 2.8t², where t = 1 for 2002. The forecast value for 2011 is: