Question 1

Which of the following represents the fluctuations up to a twelve month time period?

Accepted Answer

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

Question 2

The actual and forecast values of a time series are shown below. $$\begin{array} { | c c | } 
\hline \text { Actual values } y _ { t } & \text { Forecast values } F _ { t } \
\hline 135 & 140 \
162 & 165 \
155 & 150 \
182 & 191 \
174 & 168 \
194 & 190 \
233 & 220 \
280 & 240 \
\hline
\end{array}$$ a. Calculate the mean absolute deviation (MAD).
b. Calculate the sum of squares for forecast error (SSE).

Accepted Answer

a. 11ec93ce_01b9_004a_8afc_e16

Question 3

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
$\begin{array}{l}
\hline\text { Regression Statistios }\
\begin{array}{lc}
\hline\text { Multiple R } & 0.9460 \
\text { R Square } & 0.8950 \
\text { Adjusted R Square } & 0.8864 \
\text { Standard Error } & 3.7394 \
\text { Obserwations } & 54 \
\hline
\end{array}
\end{array}$

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

$\begin{array}{lcrrrrrr} 
& \text { Coeffients } & \text { Standard Error } & \text { tStat } & \text { P-value } & \text { Lower } 95 \% & \text { Upper } 95 \% \
\hline \text { Intercept } & 3.0588 & 1.3331 & 2.2944 & 0.0261 & 0.3797 & 5.7378 \
\mathrm{t} & 0.2518 & 0.0327 & 7.7052 & 0.0000 & 0.1861 & 0.3175 \
\mathrm{Q} 1 & 12.4604 & 1.3897 & 89664 & 0.0000 & 9.6677 & 15.2530 \
\mathrm{Q}3 & 1.1458 & 1.4721 & 0.7784 & 0.4401 & -1.8124 & 4.1041 \
\mathrm{Q}4 & 23.9121 & 1.4403 & 16.6025 & 0.0000 & 21.0177 & 26.8064 \
\hline
\end{array}$ (a) Write out the regression equations for each of the four quarters.
(b) Sketch the four equations from part (a) on the same set of axes.
(c) Interpret the coefficients on all the indicator variables.
(c) All the indicator variables have positive coefficients. Is this surprising? Explain.

Accepted Answer

(a) March: Swimming goggle sales = 15.52

Question 4

Of the four different components of a time series, cyclical variation is the one most likely to exhibit the long-term direction of the data.

Accepted Answer

A) True 
 B)False

Question 5

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?

Accepted Answer

A) The coefficients of the indicator variables are all positive because the June Quarter has the lowest sales of surfboards. 
B) The coefficients of the indicator variables are all positive because sales of surfboards in the March, September and December quarter are all above June. 
C) The coefficients of the indicator variables are all positive indicating that the June quarter is seasonally disadvantaged for selling surfboards due to winter in Australia in this quarter. 
D) All of these choices are correct. 
A) The coefficients of the indicator variables are all positive because the June Quarter has the lowest sales of surfboards. 
B) The coefficients of the indicator variables are all positive because sales of surfboards in the March, September and December quarter are all above June. 
C) The coefficients of the indicator variables are all positive indicating that the June quarter is seasonally disadvantaged for selling surfboards due to winter in Australia in this quarter. 
D) All of these choices are correct.

Question 6

The time-series component that reflects the irregular changes in a time series that are not caused by any other component, and tends to hide the existence of the other, more predictable components, is called random variation.

Accepted Answer

A) True 
 B)False

Question 7

If autumn 2013 sales were $20 500 and the summer seasonal index was 1.17, then the deseasonalised 2010 autumn sales value would be:

Accepted Answer

A) $19 422. 
B) $13 675. 
C) $14 188. 
D) $18 720. 
A) $19 422. 
B) $13 675. 
C) $14 188. 
D) $18 720.

Question 8

Regression analysis was used to develop the following equation from 60 observations of quarterly data:
ŷt = 2500 - 3t - 3Q1 + 2Q2 + 5Q3,
where: $$Q _ { i }$$ = 1, if quarter i (i = 1, 2, 3)
= 0, otherwise
Forecast the next four quarters.

Accepted Answer

Question 9

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.

Question 10

The following trend line and seasonal indexes were computed from four weeks of daily observations. $\hat { y } _ { t }$ = 145 + 1.66t. $$\begin{array} { | l | c | } 
\hline \text { Day } & S I _ { t } \
\hline \text { Sunday } & 1.403 \
\text { Monday } & 0.517 \
\text { Tuesday } & 0.515 \
\text { Wednesday } & 0.621 \
\text { Thursday } & 0.675 \
\text { Friday } & 1.145 \
\text { Saturday } & 2.124 \
\hline
\end{array}$$ Forecast the seven values for the next week.

Accepted Answer

The answer of The following trend line and seasonal indexes...

Question 11

Which of the following methods is appropriate for forecasting a time series when the trend, cyclical and seasonal components of the series are not significant?

Accepted Answer

A) Moving averages. 
B) Exponential smoothing. 
C) Mean absolute deviation. 
D) Seasonal indexes. 
A) Moving averages. 
B) Exponential smoothing. 
C) Mean absolute deviation. 
D) Seasonal indexes.

Question 12

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 13

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:

Accepted Answer

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

Question 14

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?

Accepted Answer

A) There is a mistake with this regression model because all the coefficients of the indicator variables are positive. 
B) There is no indicator variable for the June quarter in this model because there is no seasonal effect in June due to winter in Australia. 
C) There is a mistake with this model because the indicator variable for the June quarter has been left out. 
D) There is no indicator variable for the June quarter in this model because we need one less indicator variable than number of categories to use indicator variables with regression for a time series. 
A) There is a mistake with this regression model because all the coefficients of the indicator variables are positive. 
B) There is no indicator variable for the June quarter in this model because there is no seasonal effect in June due to winter in Australia. 
C) There is a mistake with this model because the indicator variable for the June quarter has been left out. 
D) There is no indicator variable for the June quarter in this model because we need one less indicator variable than number of categories to use indicator variables with regression for a time series.

Question 15

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 16

The time-series multiplicative model is used for forecasting, where $T _ { t } , C _ { t } , S _ { t },$ and $R _ { t }$ are respectively the trend, cyclical, seasonal and random variation components of the time series, and $y _ { t }$ is the value of the time series at time t. The following estimates are obtained: $\hat { T _ { 1 } }$ = 125, $\hat { C } _ { t }$ = 1.03, $\hat { S } _ { t }$ = 1.02, $\hat { R } _ { t }$ = 0.97. The model will produce a forecast of:

Accepted Answer

A) 122.659. 
B) 131.325. 
C) 118.980. 
D) 127.385. 
A) 122.659. 
B) 131.325. 
C) 118.980. 
D) 127.385.

Question 17

In determining weekly seasonal indexes for natural gas consumption, the sum of the 52 means for gas consumption as a percentage of the moving average is 5195. To get the seasonal indexes, each monthly mean is to be multiplied by (5200 / 5195).

Accepted Answer

A) True 
 B)False

Question 18

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 19

One measure of the accuracy of a forecasting model is the:

Accepted Answer

A) deseasonalised time series. 
B) four-period moving average. 
C) mean absolute deviation. 
D) smoothing constant. 
A) deseasonalised time series. 
B) four-period moving average. 
C) mean absolute deviation. 
D) smoothing constant.

Question 20

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. @#IMG-DLM& b. @#IMG-DLM& There appear

Which of the following represents the fluctuations up to a twelve month time period?

The actual and forecast values of a time series are shown below. Actual values Forecast values 135 140 162 165 155 150 182 191 174 168 194 190 233 220 280 240 a. Calculate the mean absolute deviation (MAD). b. Calculate the sum of squares for forecast error (SSE).

Of the four different components of a time series, cyclical variation is the one most likely to exhibit the long-term direction of the data.

The time-series component that reflects the irregular changes in a time series that are not caused by any other component, and tends to hide the existence of the other, more predictable components, is called random variation.

If autumn 2013 sales were $20 500 and the summer seasonal index was 1.17, then the deseasonalised 2010 autumn sales value would be:

Regression analysis was used to develop the following equation from 60 observations of quarterly data: ŷt = 2500 - 3t - 3Q₁ + 2Q₂ + 5Q₃, where: $Q _ { i }$ = 1, if quarter i (i = 1, 2, 3) = 0, otherwise Forecast the next four quarters.

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:

The following trend line and seasonal indexes were computed from four weeks of daily observations. $\hat { y } _ { t }$ = 145 + 1.66t. Day S Sunday 1.403 Monday 0.517 Tuesday 0.515 Wednesday 0.621 Thursday 0.675 Friday 1.145 Saturday 2.124 Forecast the seven values for the next week.

Which of the following methods is appropriate for forecasting a time series when the trend, cyclical and seasonal components of the series are not significant?

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).

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:

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?

In determining weekly seasonal indexes for natural gas consumption, the sum of the 52 means for gas consumption as a percentage of the moving average is 5195. To get the seasonal indexes, each monthly mean is to be multiplied by (5200 / 5195).

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.

One measure of the accuracy of a forecasting model is the:

What Is Statistics

Types of Data, Data Collection and Sampling

Graphical Descriptive Techniques Nominal Data

Graphical Descriptive Techniques Numerical Data

Numerical Descriptive Measures

Probability

Random Variables and Discrete Probability Distributions

Continuous Probability Distributions

Statistical Inference and Sampling Distributions

Estimation: Describing a Single Population

Estimation: Comparing Two Populations

Hypothesis Testing: Describing a Single Population

Hypothesis Testing: Comparing Two Populations

Additional Tests for Nominal Data: Chi-Squared Tests

Simple Linear Regression and Correlation

Multiple Regression

Index Numbers

Filters

Exam 17: Time-Series Analysis and Forecasting

Which of the following represents the fluctuations up to a twelve month time period?

The actual and forecast values of a time series are shown below. Actual values Forecast values 135 140 162 165 155 150 182 191 174 168 194 190 233 220 280 240 a. Calculate the mean absolute deviation (MAD). b. Calculate the sum of squares for forecast error (SSE).

Of the four different components of a time series, cyclical variation is the one most likely to exhibit the long-term direction of the data.

The time-series component that reflects the irregular changes in a time series that are not caused by any other component, and tends to hide the existence of the other, more predictable components, is called random variation.

If autumn 2013 sales were $20 500 and the summer seasonal index was 1.17, then the deseasonalised 2010 autumn sales value would be:

Regression analysis was used to develop the following equation from 60 observations of quarterly data: ŷt = 2500 - 3t - 3Q1 + 2Q2 + 5Q3, where: QiQ _ { i }Qi​ = 1, if quarter i (i = 1, 2, 3) = 0, otherwise Forecast the next four quarters.

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:

The following trend line and seasonal indexes were computed from four weeks of daily observations. y^t\hat { y } _ { t }y^​t​ = 145 + 1.66t. Day S Sunday 1.403 Monday 0.517 Tuesday 0.515 Wednesday 0.621 Thursday 0.675 Friday 1.145 Saturday 2.124 Forecast the seven values for the next week.

Which of the following methods is appropriate for forecasting a time series when the trend, cyclical and seasonal components of the series are not significant?

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).

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:

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?

In determining weekly seasonal indexes for natural gas consumption, the sum of the 52 means for gas consumption as a percentage of the moving average is 5195. To get the seasonal indexes, each monthly mean is to be multiplied by (5200 / 5195).

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.

One measure of the accuracy of a forecasting model is the:

What Is Statistics

Types of Data, Data Collection and Sampling

Graphical Descriptive Techniques Nominal Data

Graphical Descriptive Techniques Numerical Data

Numerical Descriptive Measures

Probability

Random Variables and Discrete Probability Distributions

Continuous Probability Distributions

Statistical Inference and Sampling Distributions

Estimation: Describing a Single Population

Estimation: Comparing Two Populations

Hypothesis Testing: Describing a Single Population

Hypothesis Testing: Comparing Two Populations

Additional Tests for Nominal Data: Chi-Squared Tests

Simple Linear Regression and Correlation

Multiple Regression

Index Numbers

Filters

Regression analysis was used to develop the following equation from 60 observations of quarterly data: ŷt = 2500 - 3t - 3Q₁ + 2Q₂ + 5Q₃, where: $Q _ { i }$ = 1, if quarter i (i = 1, 2, 3) = 0, otherwise Forecast the next four quarters.

The following trend line and seasonal indexes were computed from four weeks of daily observations. $\hat { y } _ { t }$ = 145 + 1.66t. Day S Sunday 1.403 Monday 0.517 Tuesday 0.515 Wednesday 0.621 Thursday 0.675 Friday 1.145 Saturday 2.124 Forecast the seven values for the next week.