Question 1

Which of the following components of a time-series reflects the overall general movement of the data?

Accepted Answer

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

Question 2

To measure the seasonal variation, we compute seasonal indexes, which gauge the degree to which the seasons differ from one another.

Accepted Answer

A) True 
 B)False

Question 3

The mean absolute deviation averages the absolute differences between the actual values of the time series at time t and the forecast values at time:

Accepted Answer

A)  t + 1. 
B)  t. 
C)  t - 1. 
D)  t - 2. 
A)  t + 1. 
B)  t. 
C)  t - 1. 
D)  t - 2.

Question 4

The following trend line and seasonal indexes were computed from five years of quarterly observations:    $ = 1800 + 75 t - 2 t ^ { 2 }$ . $$\begin{array} { | c c | } 
\hline \text { Quarter } & S I _ { t } \
\hline 1 & 0.575 \
2 & 0.825 \
3 & 1.225 \
4 & 1.375 \
\hline
\end{array}$$ Forecast the four quarterly values for next year.

Accepted Answer

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

Question 5

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 6

The quarterly earnings of a large microcomputer company have been recorded for the years
1993-1996. These data (in millions of dollars) are shown in the accompanying table. $$\begin{array}{l}
\text { Year }\
\begin{array} { | c | c c c c | } 
\hline \text { Quarter } & 1993 & 1994 & 1995 & 1996 \
\hline 1 & 60 & 65 & 68 & 74 \
2 & 75 & 83 & 85 & 90 \
3 & 93 & 98 & 102 & 106 \
4 & 62 & 69 & 71 & 75 \
\hline
\end{array}
\end{array}$$ Using an appropriate moving average, measure the quarterly variation by computing the seasonal (quarterly) indexes.

Accepted Answer

@#IMG-DLM& \[\begin{array} { | c | c c c c | c | }

Question 7

Which of the following will be reflected by a deseasonalised time series?

Accepted Answer

A)  Trend effects. 
B)  Cyclical effects. 
C)  Random variation. 
D)  All of these choices are correct. 
A)  Trend effects. 
B)  Cyclical effects. 
C)  Random variation. 
D)  All of these choices are correct.

Question 8

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 9

The time-series component that reflects a long-term, relatively smooth pattern or direction exhibited by a time series over a long time period is called trend.

Accepted Answer

A) True 
 B)False

Question 10

a. The seasonally adjusted US quarterly Industrial Production Index from the first quarter of 2001 to the fourth quarter of 2005 (yt, 2002 = 100) is shown in the table below. Would the linear or quadratic model fit better? $\begin{array} { | c r | } 
\hline \text { Time period } & y _ { t } \
\hline \text { Mar-01 } & 136.7 \
\text { Jun-01 } & 124.1 \
\text { Sep-01 } & 120.5 \
\text { Dec-01 } & 117.4 \
\text { Mar-02 } & 101.1 \
\text { Jun-02 } & 102.5 \
\text { Sep-02 } & 98.5 \
\text { Dec-02 } & 97.9 \
\text { Mar-03 } & 94.0 \
\text { Jun-03 } & 86.7 \
\text { Sep-03 } & 89.8 \
\text { Dec-03 } & 92.3 \
\text { Mar-04 } & 95.9 \
\text { Jun-04 } & 89.6 \
\text { Sep-04 } & 86.3 \
\text { Dec-04 } & 84.5 \
\text { Mar-05 } & 88.7 \
\text { Jun-05 } & 109.9 \
\text { Sep-05 } & 100.9 \
\text { Dec-05 } & 108.4 \
\hline
\end{array}$ b. Use Excel and the regression technique to calculate the linear trend line and the quadratic trend line. Which model fits better?

Accepted Answer

a. @#IMG-DLM& The quadratic model appear

Question 11

Monthly sales (in $1000s) of a computer store are shown below. $$\begin{array} { | l | c c c c c c | } 
\hline \text { Month } & \text { Jan } & \text { Feb } & \text { Mar } & \text { Apr } & \text { May } & \text { Jun } \
\hline \text { Sales } & 73 & 65 & 72 & 82 & 86 & 90 \
\hline
\end{array}$$ a. Compute the three-month and five-month moving averages.
b. Compute the exponentially smoothed sales with w = 0.3 and w = 0.5
c. Calculate the four-month moving average, and four-month centred moving average.

Accepted Answer

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

Question 12

The table below shows the number of pizzas sold daily during a four-week period at King Pizza in Melbourne. $$\begin{array}{l}
\text { Week }\
\begin{array} { | l | c r r c | } 
\hline \text { Day } & 1 & 2 & 3 & 4 \
\hline \text { Sunday } & 253 & 234 & 248 & 232 \
\text { Monday } & 98 & 93 & 99 & 104 \
\text { Tuesday } & 106 & 88 & 87 & 115 \
\text { Wednesday } & 119 & 134 & 113 & 102 \
\text { Thursday } & 138 & 123 & 130 & 118 \
\text { Friday } & 201 & 215 & 218 & 205 \
\text { Saturday } & 327 & 399 & 415 & 390 \
\hline
\end{array}
\end{array}$$ a. Calculate the seasonal (daily) indexes, using a seven-day moving average.
b. Use regression analysis to find the linear trend line.
c. Calculate the seasonal (daily) indexes, using the trend line developed in (b).

Accepted Answer

None

Question 13

The most commonly used measures of forecast accuracy are the mean absolute deviation (MAD) and the sum of squares for forecast error (SSE).

Accepted Answer

A) True 
 B)False

Question 14

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 15

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: $\hat { T _ { t } }$ = 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 16

The trend equation for quarterly sales data (in millions of dollars) for 2001-2005 is $\ddot { y } _ { t } = 6.8 + 1.2 t$ , where t = 1 for the first quarter of 2001. The seasonal index for the third quarter of 2006 is 1.25. The forecast sales for the third quarter of 2006 is:

Accepted Answer

A)  34.40. 
B)  27.52. 
C)  43.00. 
D)  35.65. 
A)  34.40. 
B)  27.52. 
C)  43.00. 
D)  35.65.

Question 17

The actual and forecast values of a time series are shown below. $$\begin{array} { | c c | } 
\hline \text { Actual values } y _ { t } & \text { Forecast values } F _ { t } \
\hline 2325 & 2330 \
2555 & 2595 \
2835 & 2860 \
3185 & 3125 \
3510 & 3390 \
\hline
\end{array}$$ a. Calculate the mean absolute deviation (MAD).
b. Calculate the sum of squares for forecast error (SSE).

Accepted Answer

a. MAD = @#LAT-DLM&

Question 18

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 19

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 20

Random variation is one of the four different components of a time series. It is caused by irregular and unpredictable changes in a time series that are not caused by any other component. It tends to mask the existence of the other, more predictable components.

Accepted Answer

A) True 
 B)False

Which of the following components of a time-series reflects the overall general movement of the data?

To measure the seasonal variation, we compute seasonal indexes, which gauge the degree to which the seasons differ from one another.

The mean absolute deviation averages the absolute differences between the actual values of the time series at time t and the forecast values at time:

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

Which of the following will be reflected by a deseasonalised time series?

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

The time-series component that reflects a long-term, relatively smooth pattern or direction exhibited by a time series over a long time period is called trend.

The most commonly used measures of forecast accuracy are the mean absolute deviation (MAD) and the sum of squares for forecast error (SSE).

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 trend equation for quarterly sales data (in millions of dollars) for 2001-2005 is $\ddot { y } _ { t } = 6.8 + 1.2 t$ , where t = 1 for the first quarter of 2001. The seasonal index for the third quarter of 2006 is 1.25. The forecast sales for the third quarter of 2006 is:

The actual and forecast values of a time series are shown below. Actual values Forecast values 2325 2330 2555 2595 2835 2860 3185 3125 3510 3390 a. Calculate the mean absolute deviation (MAD). b. Calculate the sum of squares for forecast error (SSE).

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.

Random variation is one of the four different components of a time series. It is caused by irregular and unpredictable changes in a time series that are not caused by any other component. It tends to mask the existence of the other, more predictable components.

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

Which of the following components of a time-series reflects the overall general movement of the data?

To measure the seasonal variation, we compute seasonal indexes, which gauge the degree to which the seasons differ from one another.

The mean absolute deviation averages the absolute differences between the actual values of the time series at time t and the forecast values at time:

The following trend line and seasonal indexes were computed from five years of quarterly observations: =1800+75t−2t2 = 1800 + 75 t - 2 t ^ { 2 }=1800+75t−2t2 . Quarter S 1 0.575 2 0.825 3 1.225 4 1.375 Forecast the four quarterly values for next year.

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

Which of the following will be reflected by a deseasonalised time series?

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

The time-series component that reflects a long-term, relatively smooth pattern or direction exhibited by a time series over a long time period is called trend.

The most commonly used measures of forecast accuracy are the mean absolute deviation (MAD) and the sum of squares for forecast error (SSE).

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 actual and forecast values of a time series are shown below. Actual values Forecast values 2325 2330 2555 2595 2835 2860 3185 3125 3510 3390 a. Calculate the mean absolute deviation (MAD). b. Calculate the sum of squares for forecast error (SSE).

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.

Random variation is one of the four different components of a time series. It is caused by irregular and unpredictable changes in a time series that are not caused by any other component. It tends to mask the existence of the other, more predictable components.

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