Question 1

If the actual value of a time series at time t and the forecast value for time t is denoted by At and Ft respectively, then the formula for the mean absolute deviation over a range of forecasted values is ________.

Accepted Answer

A)  MAD =  ∑t=1n∣At−Ft∣n\frac{\sum_{t=1}^{n}\left|A_{t}-F_{t}\right|}{n}n∑t=1n​∣At​−Ft​∣​ 
B)  MAD =  ∑t=1n(∣At−Ft∣) 2n\frac { \sum _ { t = 1 } ^ { n } \left( \left| A _ { t } - F _ { t } \right| \right)  ^ { 2 } } { n }n∑t=1n​(∣At​−Ft​∣) 2​ 
C)  MAD =  ∑t=1n∣At−F∣n\frac { \sum _ { t = 1 } ^ { n } \sqrt { \left| A _ { t } - F \right| } } { n }n∑t=1n​∣At​−F∣c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z"/>​​ 
D)  MAD =  ∑t=1n∣At−Ft2∣n\frac { \sum _ { t = 1 } ^ { n } \left| \frac { A _ { t } - F _ { t } } { 2 } \right| } { n }n∑t=1n​∣2At​−Ft​​∣​ A

Question 2

Use the data given below to answer the following question(s).
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 value of k is set at 3.(Hint: Optimize α value.)
 $\begin{array}{|c|c|}
\hline \text { Week } & \text { Units sold } \
\hline 1 & 88 \
\hline 2 & 44 \
\hline 3 & 54 \
\hline 4 & 65 \
\hline 5 & 72 \
\hline 6 & 85 \
\hline
\end{array}$
-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?

Accepted Answer

A)  bt = β(bt - 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 = β(at - at₋₁) + (1 -β) bt₋₁  D

Question 3

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

Accepted Answer

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

Question 4

Use the data shown below to answer the following question(s).
The table below is the data set of the Shiller Real Home Price Index for the years 1946-1956.
 $\begin{array}{c|c}
\text { Year } & \begin{array}{c}
\text { Real Home Price } \
\text { Index }
\end{array} \
\hline 1946 & 106.5058955 \
\hline 1947 & 109.3296707 \
\hline 1948 & 101.2225795 \
\hline 1949 & 100.0466076 \
\hline 1950 & 105.8948393 \
\hline 1951 & 103.8986687 \
\hline 1952 & 103.9743275 \
\hline 1953 & 114.7133093 \
\hline 1954 & 114.199126 \
\hline 1955 & 115.4621261 \
\hline 1956 & 115.3166155
\end{array}$
-Setting k = 3, determine the value of root mean square of errors.

Accepted Answer

The answer of Use the data shown below to answer...

Question 5

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

Accepted Answer

The answer of Explain the different types of Holt-Winters models...

Question 6

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 ________.

Accepted Answer

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

Question 7

Use the data given below to answer the following question(s).
The table below provides the sales data for JD Inc.for the year 1998.Given: α = 0.2, β = 0.15, and γ = 0.05 (Hint: Classify the data into quarters for the following question(s).)
 $\begin{array}{l}
\text { Umbrella Sales of JD Inc. }\
\begin{array}{|c|c|c|}
\hline \text { Year } & \text { Month } & \text { Units } \
\hline 1 & \text { Jan } & 3980 \
\hline 1 & \text { Feb } & 4000 \
\hline 1 & \text { Mar } & 4740 \
\hline 1 & \text { April } & 4720 \
\hline 1 & \text { May } & 4920 \
\hline 1 & \text { Jun } & 5140 \
\hline 1 & \text { July } & 4640 \
\hline 1 & \text { Aug } & 4520 \
\hline 1 & \text { Sep } & 4480 \
\hline 1 & \text { Oct } & 4690 \
\hline 1 & \text { Nov } & 4210 \
\hline 1 & \text { Dec } & 4418 \
\hline
\end{array}
\end{array}$
-What will be the predicted sales for umbrellas for the month of February of the next quarter?

Accepted Answer

A)  4530.19
B)  4645.06
C)  4883.76
D)  4818.07

Question 8

The actual value of the time series at time t and the forecast value for time t is denoted by At and Ft respectively.What is the formula used for calculating the mean absolute percentage error over a range of forecasted values?

Accepted Answer

A)  MAPE =  ∑t=1n∣At+Ft2∣n\frac { \sum _ { t = 1 } ^ { n } \left| \frac { A _ { t } + F _ { t } } { 2 } \right| } { n }n∑t=1n​∣2At​+Ft​​∣​ 
B)  MAPE =  ∑t=1n∣At+Ft2∣n\sqrt { \frac { \sum _ { t = 1 } ^ { n } \left| \frac { A _ { t } + F _ { t } } { 2 } \right| } { n } }n∑t=1n​∣2At​+Ft​​∣​l0 -0c4,-6.7,10,-10,18,-10 H400000v40H1013.1s-83.4,268,-264.1,840c-180.7,572,-277,876.3,-289,913c-4.7,4.7,-12.7,7,-24,7s-12,0,-12,0c-1.3,-3.3,-3.7,-11.7,-7,-25c-35.3,-125.3,-106.7,-373.3,-214,-744c-10,12,-21,25,-33,39s-32,39,-32,39c-6,-5.3,-15,-14,-27,-26s25,-30,25,-30c26.7,-32.7,52,-63,76,-91s52,-60,52,-60s208,722,208,722c56,-175.3,126.3,-397.3,211,-666c84.7,-268.7,153.8,-488.2,207.5,-658.5c53.7,-170.3,84.5,-266.8,92.5,-289.5zM1001 80h400000v40h-400000z"/>​ 
C)  MAPE =  ∑t=1n∣At−Ft∣n\frac { \sum _ { t = 1 } ^ { n } \left| A _ { t } - F _ { t } \right| } { n }n∑t=1n​∣At​−Ft​∣​ 
D)  MAPE =  ∑t=1n∣At+FtAt∣n\frac { \sum _ { t = 1 } ^ { n } \left| \frac { A _ { t } + F _ { t } } { A _ { t } } \right| } { n }n∑t=1n​∣At​At​+Ft​​∣​  × 100

Question 9

Use the data given below to answer the following question(s).
The worldwide sales of cars from 1981-1990 are shown in the table below.Given: α = 0.2 and β = 0.15 (Hint: Use XLMiner)
 $\begin{array}{|c|c|}
\hline \text { Year } & \begin{array}{c}
\text { Units sold in } \
\text { thousands }
\end{array} \
\hline 1981 & 888 \
\hline 1982 & 900 \
\hline 1983 & 1000 \
\hline 1984 & 1200 \
\hline 1985 & 1100 \
\hline 1986 & 1300 \
\hline 1987 & 1250 \
\hline 1988 & 1150 \
\hline 1989 & 1100 \
\hline 1990 & 1200 \
\hline
\end{array}$
-Using the double exponential smoothing, calculate the value of the mean absolute deviation for the given data.

Accepted Answer

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

Question 10

Use the data given below to answer the following question(s).
The table below provides the sales data for JD Inc.for the year 1998.Given: α = 0.2, β = 0.15, and γ = 0.05 (Hint: Classify the data into quarters for the following question(s).)
 $\begin{array}{l}
\text { Umbrella Sales of JD Inc. }\
\begin{array}{|c|c|c|}
\hline \text { Year } & \text { Month } & \text { Units } \
\hline 1 & \text { Jan } & 3980 \
\hline 1 & \text { Feb } & 4000 \
\hline 1 & \text { Mar } & 4740 \
\hline 1 & \text { April } & 4720 \
\hline 1 & \text { May } & 4920 \
\hline 1 & \text { Jun } & 5140 \
\hline 1 & \text { July } & 4640 \
\hline 1 & \text { Aug } & 4520 \
\hline 1 & \text { Sep } & 4480 \
\hline 1 & \text { Oct } & 4690 \
\hline 1 & \text { Nov } & 4210 \
\hline 1 & \text { Dec } & 4418 \
\hline
\end{array}
\end{array}$
-Using an appropriate Holt-Winters trend model, calculate the value of the mean absolute percentage error for the given data.

Accepted Answer

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

Question 11

Use the data given below to answer the following question(s).
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 value of k is set at 3.(Hint: Optimize α value.)
 $\begin{array}{|c|c|}
\hline \text { Week } & \text { Units sold } \
\hline 1 & 88 \
\hline 2 & 44 \
\hline 3 & 54 \
\hline 4 & 65 \
\hline 5 & 72 \
\hline 6 & 85 \
\hline
\end{array}$
-What is the difference between the forecasted and the actual value for the 3ʳᵈ week?

Accepted Answer

A)  5 phones
B)  6 phones
C)  4 phones
D)  3 phones

Question 12

Use the data given below to answer the following question(s).
The table below provides the sales data for JD Inc.for the year 1998.Given: α = 0.2, β = 0.15, and γ = 0.05 (Hint: Classify the data into quarters for the following question(s).)
 $\begin{array}{l}
\text { Umbrella Sales of JD Inc. }\
\begin{array}{|c|c|c|}
\hline \text { Year } & \text { Month } & \text { Units } \
\hline 1 & \text { Jan } & 3980 \
\hline 1 & \text { Feb } & 4000 \
\hline 1 & \text { Mar } & 4740 \
\hline 1 & \text { April } & 4720 \
\hline 1 & \text { May } & 4920 \
\hline 1 & \text { Jun } & 5140 \
\hline 1 & \text { July } & 4640 \
\hline 1 & \text { Aug } & 4520 \
\hline 1 & \text { Sep } & 4480 \
\hline 1 & \text { Oct } & 4690 \
\hline 1 & \text { Nov } & 4210 \
\hline 1 & \text { Dec } & 4418 \
\hline
\end{array}
\end{array}$
-Calculate the value of the mean square error using an appropriate Holt-Winters trend model for the given data.

Accepted Answer

A)  8.10
B)  346.26
C)  148092.89
D)  7.62

Question 13

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

Accepted Answer

A) True 
 B)False

Question 14

Use the data given below to answer the following question(s).
The worldwide sales of cars from 1981-1990 are shown in the table below.Given: α = 0.2 and γ = 0.05.(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 seasonality, the most appropriate forecasting model to determine the forecast of the time series is the ________ model.

Accepted Answer

A)  multiple regression
B)  Holt-Winters no trend smoothing
C)  double exponential smoothing
D)  Holt-Winters multiplicative

Question 15

Use the data given below to answer the following question(s).
The worldwide sales of cars from 1981-1990 are shown in the table below.Given: α = 0.2 and γ = 0.05.(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.

Accepted Answer

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

Question 16

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

Accepted Answer

A) True 
 B)False

Question 17

What is a stream of historical data known as?

Accepted Answer

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

Question 18

Use the data given below to answer the following question(s).
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 value of k is set at 3.(Hint: Optimize α value.)
 $\begin{array}{|c|c|}
\hline \text { Week } & \text { Units sold } \
\hline 1 & 88 \
\hline 2 & 44 \
\hline 3 & 54 \
\hline 4 & 65 \
\hline 5 & 72 \
\hline 6 & 85 \
\hline
\end{array}$
-Which of the following is the value of the root mean square error for the given data?

Accepted Answer

A)  11.56
B)  21.72
C)  13.87
D)  20.13

Question 19

Use the data given below to answer the following question(s).
The worldwide sales of cars from 1981-1990 are shown in the table below.Given: α = 0.2 and γ = 0.05.(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.

Accepted Answer

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

Question 20

Explain econometric models used in forecasting with examples.

Accepted Answer

The answer of Explain econometric models used in forecasting with...

Exam 10: Forecasting Techniques