Deck 9: Forecasting Techniques

Question 1

Answer the following questions) using exponential smoothing after having optimized α at 0.1 increments.
What is the forecasted value for the 7^th week?

A) 53 phones
B) 82 phones
C) 71 phones
D) 49 phones

Answer 1

82 phones

Question 2

Answer the following questions) using exponential smoothing after having optimized α at 0.1 increments.
What is the formula used to calculate the value of at in the linear trend equation Ft+k = at + btk while using double exponential smoothing?

A) at = βbt - bt-1) + 1 -β)bt-1
B) at = αFt-1 + 1 - α)at +1 + bt+1)
C) at = αFt + 1 - α)at -1 + bt-1)
D) at = βbt + bt-1) + 1 + γ)bt-1

Answer 2

at = αFt + 1 - α)at -1 + bt-1)

Question 3

Use the data given below to answer the following questions).
The table provided below gives the sales details of the number of android smart phones at an electronic retail store for the past 6 weeks. The time series appears to be relatively stable, without trend, seasonal, or cyclical effects. The simple moving average value of k is set at 2. $$\begin{array} { | c | c | } \hline \text { Week } & \text { Units sold } \\\hline 1 & 88 \\\hline 2 & 44 \\\hline 3 & 54 \\\hline 4 & 65 \\\hline 5 & 72 \\\hline 6 & 85 \\\hline\end{array}$$

-For the given data, what is the value of the simple moving average mean square error?

A) 0.21
B) 20.12
C) 14.25
D) 207.13

Answer 3

207.13

Question 4

What is a stream of historical data known as?

A) a time series
B) an index
C) a complex number
D) an orthopole

Question 5

Before launching a new line of toys, Toys Inc. used the method of historical analogy to obtain a forecast. In this scenario, Toys Inc.:

A) noted the behavior of its current customers while they use their products.
B) used a panel of experts, whose identities were kept confidential from one another, to respond to a sequence of questionnaires.
C) noted the consumer response to similar previous products to marketing campaigns and used the responses as a basis to predict how the new marketing campaign might fare.
D) used a brainstorming session among a group of experts to draw new ideas.

Question 6

Use the data given below to answer the following questions).
The table provided below gives the sales details of the number of android smart phones at an electronic retail store for the past 6 weeks. The time series appears to be relatively stable, without trend, seasonal, or cyclical effects. The simple moving average value of k is set at 2. $$\begin{array} { | c | c | } \hline \text { Week } & \text { Units sold } \\\hline 1 & 88 \\\hline 2 & 44 \\\hline 3 & 54 \\\hline 4 & 65 \\\hline 5 & 72 \\\hline 6 & 85 \\\hline\end{array}$$

-For the given data, calculate the value of the simple moving average mean absolute percentage error.

A) 20.90
B) 23.45
C) 14.39
D) 25.56

Question 7

What is the formula used to calculate the value of bt in the linear trend equation Ft+k = at + btk while using double exponential smoothing?

A) bt = βbt - bt-1) + 1 -β)bt-1
B) bt = αFt-1 + 1 - α)at +1 + bt+1)
C) bt = αFt + 1 - α)at -1 + bt-1)
D) bt = βat - at-1) + 1 -β)bt-1

Question 8

The Delphi method used for forecasting:

A) obtains forecasts through a comparative analysis with a previous situation.
B) uses measures that are believed to influence the behavior of a variable that the researcher wishes to forecast.
C) uses a single measure that weights multiple indicators and provides a measure of overall expectation.
D) uses a panel of experts, whose identities are typically kept confidential from one another, to respond to a sequence of questionnaires.

Question 9

Use the data given below to answer the following questions).
The worldwide sales of cars from 1981-1990 are shown in the table below. Given: ? = 0.2 and
? = 0.15 Hint: Use XLMiner) $$\begin{array} { | c | c| } \hline \text { Year } & \begin{array} { c } \text { Units sold in } \\\text { thousands }\end{array} \\\hline 1981 & 888 \\\hline 1982 & 900 \\\hline 1983 & 1000 \\\hline 1984 & 1200 \\\hline 1985 & 1100 \\\hline 1986 & 1300 \\\hline 1987 & 1250 \\\hline 1988 & 1150 \\\hline 1989 & 1100 \\\hline 1990 & 1200 \\\hline\end{array}$$

-Calculate the value of the mean absolute percentage error using double exponential smoothing for the given data.

A) 1.80
B) 8.10
C) 91.27
D) 11976.17

Question 10

Answer the following questions) using exponential smoothing after having optimized α at 0.1 increments.
In the linear trend equation, Ft+k = at + btk, at is known as the .

A) level
B) trend
C) slope
D) forecast

Question 11

Answer the following questions) using exponential smoothing after having optimized α at 0.1 increments.
In the linear trend equation Ft+k = at + btk, identify the term that signifies the trend.

A) bt
B) k
C) at
D) Ft + k

Question 12

Answer the following questions) using exponential smoothing after having optimized α at 0.1 increments.
Which of the following is the value of the root mean square error for the given data?

A) 11.56
B) 21.77
C) 13.87
D) 20.13

Question 13

In forecasting, what is an index?

A) It is a single measure that weights multiple indicators and provides a measure of overall expectation.
B) It is a stream of historical data, such as weekly sales.
C) It is a time series that does not have trend, seasonal, or cyclical effects but is relatively constant and only exhibits random behavior.
D) It is a measure that provides a complete forecast.

Question 14

Answer the following questions) using exponential smoothing after having optimized α at 0.1 increments.
What is the forecasted value for the 3rd week?

A) 53 phones
B) 64 phones
C) 71 phones
D) 49 phones

Question 15

Answer the following questions) using exponential smoothing after having optimized α at 0.1 increments.
Calculate the value of the mean absolute percentage error for the given data.

A) 20.90
B) 16.60
C) 21.72
D) 29.97

Question 16

The data for the number of hand-held gaming devices sold for the past 5 weeks are 15 units, 20 units, 25 units, 30 units, and 17 units respectively. The time series appears to be relatively stable, without trend, seasonal, or cyclical effects; thus, a moving average model would be appropriate. Setting k = 3 the three-period moving average forecast for week 6 is .

A) 20 units
B) 24 units
C) 30 units
D) 17 units

Question 17

Use the data given below to answer the following questions).
The table provided below gives the sales details of the number of android smart phones at an electronic retail store for the past 6 weeks. The time series appears to be relatively stable, without trend, seasonal, or cyclical effects. The simple moving average value of k is set at 2. $$\begin{array} { | c | c | } \hline \text { Week } & \text { Units sold } \\\hline 1 & 88 \\\hline 2 & 44 \\\hline 3 & 54 \\\hline 4 & 65 \\\hline 5 & 72 \\\hline 6 & 85 \\\hline\end{array}$$

-Using the data, determine the value of the simple moving average root mean square error.

A) 0.21
B) 14.39
C) 20.12
D) 207.13

Question 18

Answer the following questions) using exponential smoothing after having optimized α at 0.1 increments.
What is the difference between the forecasted and the actual value for the 3rd week?

A) 1 phones
B) 6 phones
C) 4 phones
D) 3 phones

Question 19

Time-series models may exhibit seasonal effects or cyclical effects. A seasonal effect differs from a cyclical effect in that a seasonal effect:

A) has no trend, is relatively constant, and only exhibits random behavior.
B) describes ups and downs over a time frame such as several years.
C) is one that repeats at fixed intervals of time, typically a year, month, week, or day.
D) is based on analysis of historical time-series data and are predicated on the assumption that the future is an extrapolation of the past.

Question 20

Use the data given below to answer the following questions).
The table provided below gives the sales details of the number of android smart phones at an electronic retail store for the past 6 weeks. The time series appears to be relatively stable, without trend, seasonal, or cyclical effects. The simple moving average value of k is set at 2. $$\begin{array} { | c | c | } \hline \text { Week } & \text { Units sold } \\\hline 1 & 88 \\\hline 2 & 44 \\\hline 3 & 54 \\\hline 4 & 65 \\\hline 5 & 72 \\\hline 6 & 85 \\\hline\end{array}$$

-For the given data, the simple moving average mean absolute deviation is .

A) 0.21
B) 20.12
C) 14.25
D) 207.13

Question 21

Use the data given below to answer the following questions).
The worldwide sales of cars from 1981-1990 are shown in the table below. Given: ? = 0.2, ? = 0.05, and season length = 1. Hint: Use XLMiner). $$\begin{array} { | c | c | } \hline \text { Year } & \begin{array} { c } \text { Units sold in } \\\text { thousands }\end{array} \\\hline 1 & 750 \\\hline 2 & 823 \\\hline 3 & 1034 \\\hline 4 & 1945 \\\hline 5 & 1556 \\\hline 6 & 1300 \\\hline 7 & 1346 \\\hline 8 & 1150 \\\hline 9 & 967 \\\hline 10 & 1200 \\\hline\end{array}$$

-Which of the following is the forecast value for the 6^th year?

A) 1256.06
B) 1328.04
C) 1321.31
D) 1327.24

Question 22

Use the data given below to answer the following questions).
The worldwide sales of cars from 1981-1990 are shown in the table below. Given: ? = 0.2, ? = 0.05, and season length = 1. Hint: Use XLMiner). $$\begin{array} { | c | c | } \hline \text { Year } & \begin{array} { c } \text { Units sold in } \\\text { thousands }\end{array} \\\hline 1 & 750 \\\hline 2 & 823 \\\hline 3 & 1034 \\\hline 4 & 1945 \\\hline 5 & 1556 \\\hline 6 & 1300 \\\hline 7 & 1346 \\\hline 8 & 1150 \\\hline 9 & 967 \\\hline 10 & 1200 \\\hline\end{array}$$

-If the given time series has a trend and no seasonality, the most appropriate forecasting model to determine the forecast of the time series is the model.

A) single exponential smoothing
B) Holt-Winters no trend smoothing
C) double exponential smoothing
D) Holt-Winters additive

Question 23

Use the data given below to answer the following questions).
The worldwide sales of cars from 1981-1990 are shown in the table below. Given: ? = 0.2 and
? = 0.15 Hint: Use XLMiner) $$\begin{array} { | c | c| } \hline \text { Year } & \begin{array} { c } \text { Units sold in } \\\text { thousands }\end{array} \\\hline 1981 & 888 \\\hline 1982 & 900 \\\hline 1983 & 1000 \\\hline 1984 & 1200 \\\hline 1985 & 1100 \\\hline 1986 & 1300 \\\hline 1987 & 1250 \\\hline 1988 & 1150 \\\hline 1989 & 1100 \\\hline 1990 & 1200 \\\hline\end{array}$$

-Identify the value of the mean square error using double exponential smoothing for the given set of data.

A) 8.10
B) 1.80
C) 91.27
D) 11976.17

Question 24

Use the data given below to answer the following questions).
The worldwide sales of cars from 1981-1990 are shown in the table below. Given: ? = 0.2, ? = 0.05, and season length = 1. Hint: Use XLMiner). $$\begin{array} { | c | c | } \hline \text { Year } & \begin{array} { c } \text { Units sold in } \\\text { thousands }\end{array} \\\hline 1 & 750 \\\hline 2 & 823 \\\hline 3 & 1034 \\\hline 4 & 1945 \\\hline 5 & 1556 \\\hline 6 & 1300 \\\hline 7 & 1346 \\\hline 8 & 1150 \\\hline 9 & 967 \\\hline 10 & 1200 \\\hline\end{array}$$

-If the given time series has no trend and no seasonality, the most appropriate forecasting model to determine the forecast of the time series is the model.

A) single moving average
B) Holt-Winters no-trend smoothing
C) double exponential smoothing
D) Holt-Winters additive

Question 25

A cyclical effect is one that repeats at fixed intervals of time, typically a year, month, week, or day.

Question 26

Use the data given below to answer the following questions).
The table below provides the sales data for JD Inc. for the year 1998. Given: ? = 0.2, ? = 0.15, and ? = 0.05 Hint: Use an additive Holt-Winters model.) $$\begin{array}{l}\text { Umbrella Sales of JD Inc. }\\\begin{array} { | c | c | c| } \hline \text { Year } & \text { Month } & \text { Units } \\\hline 1 & \text { Jan } & 3980 \\\hline 1 & \text { Feb } & 4000 \\\hline 1 & \text { Mar } & 4740 \\\hline 1 & \text { April } & 4720 \\\hline 1 & \text { May } & 4920 \\\hline 1 & \text { Jul } & 5140 \\\hline 1 & \text { July } & 4640 \\\hline 1 & \text { Aug } & 4520 \\\hline 1 & \text { Sep } & 4480 \\\hline 1 & \text { Oct } & 4690 \\\hline 1 & \text { Nov } & 4210 \\\hline 1 & \text { Dec } & 4418 \\\hline 2 & \text { Jan } & 4380 \\\hline 2 & \text { Feb } & 4400 \\\hline 2 & \text { Mar } & 5140 \\\hline 2 & \text { April } & 5120 \\\hline 2 & \text { May } & 5320 \\\hline 2 & \text { JuI } & 5540 \\\hline 2 & \text { July } & 5040 \\\hline 2 & \text { Aug } & 4920 \\\hline 2 & \text { sep } & 4880 \\\hline 2 & \text { Oct } & 5090 \\\hline 2 & \text { Nov } & 4610 \\\hline 2 & \text { Dec } & 4818 \\\hline\end{array}\end{array}$$

-Using an appropriate Holt-Winters trend model, calculate the value of the mean absolute percentage error for the given data.

A) 8.10
B) 330.01
C) 384.83
D) 7.21

Question 27

The indexes in the forecasting indicators provide a complete forecast.

Question 28

Indicators are measures that are believed to influence the behavior of a variable an individual wishes to forecast.

Question 29

Using double exponential smoothing, find the value of the root mean square error for the given data.

A) 8.10
B) 91.27
C) 11976.17
D) 109.44

Question 30

Use the data given below to answer the following questions).
The table below provides the sales data for JD Inc. for the year 1998. Given: ? = 0.2, ? = 0.15, and ? = 0.05 Hint: Use an additive Holt-Winters model.) $$\begin{array}{l}\text { Umbrella Sales of JD Inc. }\\\begin{array} { | c | c | c| } \hline \text { Year } & \text { Month } & \text { Units } \\\hline 1 & \text { Jan } & 3980 \\\hline 1 & \text { Feb } & 4000 \\\hline 1 & \text { Mar } & 4740 \\\hline 1 & \text { April } & 4720 \\\hline 1 & \text { May } & 4920 \\\hline 1 & \text { Jul } & 5140 \\\hline 1 & \text { July } & 4640 \\\hline 1 & \text { Aug } & 4520 \\\hline 1 & \text { Sep } & 4480 \\\hline 1 & \text { Oct } & 4690 \\\hline 1 & \text { Nov } & 4210 \\\hline 1 & \text { Dec } & 4418 \\\hline 2 & \text { Jan } & 4380 \\\hline 2 & \text { Feb } & 4400 \\\hline 2 & \text { Mar } & 5140 \\\hline 2 & \text { April } & 5120 \\\hline 2 & \text { May } & 5320 \\\hline 2 & \text { JuI } & 5540 \\\hline 2 & \text { July } & 5040 \\\hline 2 & \text { Aug } & 4920 \\\hline 2 & \text { sep } & 4880 \\\hline 2 & \text { Oct } & 5090 \\\hline 2 & \text { Nov } & 4610 \\\hline 2 & \text { Dec } & 4818 \\\hline\end{array}\end{array}$$

-What will be the predicted sales for umbrellas for the month of February of year 2?

A) 4530.19
B) 4648.21
C) 4883.76
D) 4818.07

Question 31

Use the data given below to answer the following questions).
The worldwide sales of cars from 1981-1990 are shown in the table below. Given: ? = 0.2, ? = 0.05, and season length = 1. Hint: Use XLMiner). $$\begin{array} { | c | c | } \hline \text { Year } & \begin{array} { c } \text { Units sold in } \\\text { thousands }\end{array} \\\hline 1 & 750 \\\hline 2 & 823 \\\hline 3 & 1034 \\\hline 4 & 1945 \\\hline 5 & 1556 \\\hline 6 & 1300 \\\hline 7 & 1346 \\\hline 8 & 1150 \\\hline 9 & 967 \\\hline 10 & 1200 \\\hline\end{array}$$

-Determine the value of the mean absolute deviation using the Holt-Winters no-trend model for the given data.

A) 367.35
B) 18.39
C) 21.70
D) 252.55

Question 32

For the given data, what is the sales forecast for the year 1992 in thousands)?

A) 1256.87
B) 1317.91
C) 1285.74
D) 1350.08

Question 33

Use the data shown below to answer the following questions).
The table below is the data set of the Shiller Real Home Price Index for the years 1946-1956.
Setting k = 3, determine the simple moving average forecast for the year 1950.

Question 34

Use the data given below to answer the following questions).
The worldwide sales of cars from 1981-1990 are shown in the table below. Given: ? = 0.2, ? = 0.05, and season length = 1. Hint: Use XLMiner). $$\begin{array} { | c | c | } \hline \text { Year } & \begin{array} { c } \text { Units sold in } \\\text { thousands }\end{array} \\\hline 1 & 750 \\\hline 2 & 823 \\\hline 3 & 1034 \\\hline 4 & 1945 \\\hline 5 & 1556 \\\hline 6 & 1300 \\\hline 7 & 1346 \\\hline 8 & 1150 \\\hline 9 & 967 \\\hline 10 & 1200 \\\hline\end{array}$$

-Which of the following is the value of the root mean square error for the given data?

A) 252.55
B) 367.35
C) 21.70
D) 109.76

Question 35

Use the data given below to answer the following questions).
The worldwide sales of cars from 1981-1990 are shown in the table below. Given: ? = 0.2, ? = 0.05, and season length = 1. Hint: Use XLMiner). $$\begin{array} { | c | c | } \hline \text { Year } & \begin{array} { c } \text { Units sold in } \\\text { thousands }\end{array} \\\hline 1 & 750 \\\hline 2 & 823 \\\hline 3 & 1034 \\\hline 4 & 1945 \\\hline 5 & 1556 \\\hline 6 & 1300 \\\hline 7 & 1346 \\\hline 8 & 1150 \\\hline 9 & 967 \\\hline 10 & 1200 \\\hline\end{array}$$

-Calculate the value of the mean absolute percentage error using the Holt-Winters no-trend model for the given data.

A) 8.10
B) 18.39
C) 21.70
D) 10.97

Question 36

Use the data given below to answer the following questions).
The table below provides the sales data for JD Inc. for the year 1998. Given: ? = 0.2, ? = 0.15, and ? = 0.05 Hint: Use an additive Holt-Winters model.) $$\begin{array}{l}\text { Umbrella Sales of JD Inc. }\\\begin{array} { | c | c | c| } \hline \text { Year } & \text { Month } & \text { Units } \\\hline 1 & \text { Jan } & 3980 \\\hline 1 & \text { Feb } & 4000 \\\hline 1 & \text { Mar } & 4740 \\\hline 1 & \text { April } & 4720 \\\hline 1 & \text { May } & 4920 \\\hline 1 & \text { Jul } & 5140 \\\hline 1 & \text { July } & 4640 \\\hline 1 & \text { Aug } & 4520 \\\hline 1 & \text { Sep } & 4480 \\\hline 1 & \text { Oct } & 4690 \\\hline 1 & \text { Nov } & 4210 \\\hline 1 & \text { Dec } & 4418 \\\hline 2 & \text { Jan } & 4380 \\\hline 2 & \text { Feb } & 4400 \\\hline 2 & \text { Mar } & 5140 \\\hline 2 & \text { April } & 5120 \\\hline 2 & \text { May } & 5320 \\\hline 2 & \text { JuI } & 5540 \\\hline 2 & \text { July } & 5040 \\\hline 2 & \text { Aug } & 4920 \\\hline 2 & \text { sep } & 4880 \\\hline 2 & \text { Oct } & 5090 \\\hline 2 & \text { Nov } & 4610 \\\hline 2 & \text { Dec } & 4818 \\\hline\end{array}\end{array}$$

-Calculate the value of the mean square error using an appropriate Holt-Winters trend model for the given data.

A) 8.10
B) 346.26
C) 140942.78
D) 7.62

Question 37

Which of the following equations is the trend line equation for the given data? Note: the fitted model assumes that the years are numbered 1 through 10, not the actual dates.)

A) 60.123x + 481.56
B) 48.16x + 481.86
C) 32.17x + 931.87
D) 57.15x + 503.81

Question 38

Use the data given below to answer the following questions).
The table below provides the sales data for JD Inc. for the year 1998. Given: ? = 0.2, ? = 0.15, and ? = 0.05 Hint: Use an additive Holt-Winters model.) $$\begin{array}{l}\text { Umbrella Sales of JD Inc. }\\\begin{array} { | c | c | c| } \hline \text { Year } & \text { Month } & \text { Units } \\\hline 1 & \text { Jan } & 3980 \\\hline 1 & \text { Feb } & 4000 \\\hline 1 & \text { Mar } & 4740 \\\hline 1 & \text { April } & 4720 \\\hline 1 & \text { May } & 4920 \\\hline 1 & \text { Jul } & 5140 \\\hline 1 & \text { July } & 4640 \\\hline 1 & \text { Aug } & 4520 \\\hline 1 & \text { Sep } & 4480 \\\hline 1 & \text { Oct } & 4690 \\\hline 1 & \text { Nov } & 4210 \\\hline 1 & \text { Dec } & 4418 \\\hline 2 & \text { Jan } & 4380 \\\hline 2 & \text { Feb } & 4400 \\\hline 2 & \text { Mar } & 5140 \\\hline 2 & \text { April } & 5120 \\\hline 2 & \text { May } & 5320 \\\hline 2 & \text { JuI } & 5540 \\\hline 2 & \text { July } & 5040 \\\hline 2 & \text { Aug } & 4920 \\\hline 2 & \text { sep } & 4880 \\\hline 2 & \text { Oct } & 5090 \\\hline 2 & \text { Nov } & 4610 \\\hline 2 & \text { Dec } & 4818 \\\hline\end{array}\end{array}$$

-What is the value of the mean absolute deviation for the given data?

A) 8.10
B) 340.73
C) 14.82
D) 7.62

Question 39

Use the data shown below to answer the following questions).
The table below is the data set of the Shiller Real Home Price Index for the years 1946-1956.
Setting k = 5, calculate the simple moving average forecast for the year 1951.

Question 40

Using double exponential smoothing, calculate the value of the mean absolute deviation for the given data.

A) 8.10
B) 1.80
C) 91.27
D) 11976.17

Question 41

If a time series has seasonality but no trend, the most appropriate model used for forecasting is the Holt-Winters multiplicative model.

Question 42

Explain the different types of Holt-Winters models used in forecasting.

Question 43

Explain econometric models used in forecasting with examples.

Question 44

Write a short note on indicators and indexes used in forecasting.

Question 45

Explain the significance of using double moving average and double exponential smoothing models.

Question 46

The Holt-Winters additive model applies to time series whose amplitude increases or decreases over time.

Question 47

What is simple exponential smoothing?