Deck 16: Time Series Forecasting

Question 1

A positive autocorrelation implies that negative error terms will be followed by negative error terms.

Answer 1

True

Question 2

Removing the seasonal affect by dividing the actual time series observation by the estimated seasonal factor associated with the time series observation is called deseasonalization.

Answer 2

True

Question 3

Dummy variable regression would be an appropriate method to use to forecast a time series that exhibits a linear trend with no seasonal or cyclical patterns.

Answer 3

False

Question 4

The Laspeyres index assumes that the base period quantities are used in all successing time periods.

Question 5

A univariate time series model is used to predict future values of a time series based only upon past values of a time series.

Question 6

The multiplicative decomposition method should not be used to forecast for a time series with increasing seasonal variation.

Question 7

Dummy variables are used to model increasing seasonal variation.

Question 8

The simple exponential forecasting method would not be used to forecast seasonal data.

Question 9

When using moving averages to estimate the seasonal factors,we need to compute the centered moving average if there are an odd number of seasons.

Question 10

While a simple index is calculated by using the values of one time series,an aggregate index is computed based on the accumulated values of more than one time series.

Question 11

Simple exponential smoothing is an appropriate method for prediction purposes when there is a significant trend present in a time series data.

Question 12

When deseasonalizing a time series observation,the actual time series observation is divided by its seasonal factor.

Question 13

Exponential smoothing is a forecasting method that applies equal weights to the time series observations.

Question 14

Holt-Winters' double exponential smoothing would be an appropriate method to use to forecast a time series that exhibits a linear trend with no seasonal or cyclical patterns.

Question 15

In simple exponential smoothing,the smoothing constant is a number that determines how much weight it is attached to each observation.

Question 16

The forecaster who uses MSD (mean squared deviations)to measure the effectiveness of forecasting methods would prefer method 1 that results in several smaller forecast errors to method 2 that results in one large forecast error equal to the sum of the absolute values of several small forecast errors given by method 1.

Question 17

Cyclical variation exists when the magnitude of the seasonal swing does not depend on the level of a time series.

Question 18

Trend refers to a long-run upward or downward movement of a time series over a period of time.

Question 19

If a time series has constant seasonal variation,then the forecaster should use the multiplicative decomposition method to forecast future values of the time series.

Question 20

The purpose of computing moving averages and centred moving averages is to eliminate seasonal variations and irregular component from time series data.

Question 21

A major drawback of the aggregate price index is that:

A)It does not take into account the fact that some items in the market basket are purchased more frequently than others.
B)It is difficult to compute.
C)It is computed by using the values from a single time series or based on a single product.
D)Percentage comparisons cannot be made to the base year.

Question 22

When computing moving averages for quarterly sales data,a ______ period moving average is used.

A)2
B)3
C)4
D)5
E)8

Question 23

Which of the following is not a component of time series?

A)Trend
B)Seasonal
C)Cyclical
D)Irregular
E)Smoothing constant

Question 24

Suppose that the unadjusted seasonal factor for the month of April is 1.10.The sum of the 12 months' unadjusted seasonal factor values is 12.18.The normalized (adjusted)seasonal factor value for April is:

A)1.1165
B)1.0837
C)1.10
D)1.3398
E)Cannot be determined with the information provided.

Question 25

In the following table, we present prices for three commonly used products—bread, fruits, and beverages—for the years 2008 through 2012.
$\begin{array}{|l|l|l|l|}\hline &\text { Bread } & \text { Fruits } & \text { Beverages } \\\hline \text { Year } & (\$ \text { per loaf) } & (\$ \text { per } \mathrm{kg}) & (\$ \text { per } \mathrm{L}) \\\hline 2008 & \$ 1.21 & \$ 2.18 & \$ 0.75 \\\hline 2009 & \$ 1.23 & \$ 2.35 & \$ 0.75 \\\hline 2010 & \$ 1.29 & \$ 2.41 & \$ 0.77 \\\hline 2011 & \$ 1.35 & \$ 2.54 & \$ 0.77 \\\hline 2012 & \$ 1.42 & \$ 2.87 & \$ 0.78 \\\hline\end{array}$
Consider a family with the following yearly consumption for these products for the years 2008 through 2012.
$$\begin{array} { | l | l | l | l | } \hline &\text { Bread } & \text { Fruits } & \text { Beverages } \\\hline \text { Year } &\text { (loaves) } & (\mathrm{kg}) & (\mathrm{L}) \\\hline \mathbf { 2 0 0 8 } & 2,200 & 250 & 2,400 \\\hline \mathbf { 2 0 0 9 } & 2,200 & 235 & 2,450 \\\hline \mathbf { 2 0 1 0 } & 2,200 & 210 & 2,580 \\\hline \mathbf { 2 0 1 1 } & 2,200 & 180 & 2,690 \\\hline \mathbf { 2 0 1 2 } & 2,200 & 140 & 2,810 \\\hline\end{array}$$
Answer the following questions using 2008 as the base year.

-Compute the aggregate price index for 2011.

A)110.67
B)116.67
C)111.11
D)112.56
E)114.86

Question 26

A time series obtained from quarterly data exhibits an increasing linear trend and constant seasonal variation.The most appropriate way to model this time series would be to use

A)simple exponential smoothing.
B)multiplicative decomposition.
C)a multiple regression model with four predictor variables;one for time and three dummy variables.
D)Holt-Winters' double exponential smoothing model.
E)the Durbin-Watson statistic.

Question 27

The ________ component of a time series measures the fluctuations in a time series due to economic conditions of prosperity and recession with a duration of approximately 2 years or longer.

A)trend
B)seasonal variation
C)cycle
D)irregular component
E)random

Question 28

In the following table, we present prices for three commonly used products—bread, fruits, and beverages—for the years 2008 through 2012.
$\begin{array}{|l|l|l|l|}\hline &\text { Bread } & \text { Fruits } & \text { Beverages } \\\hline \text { Year } & (\$ \text { per loaf) } & (\$ \text { per } \mathrm{kg}) & (\$ \text { per } \mathrm{L}) \\\hline 2008 & \$ 1.21 & \$ 2.18 & \$ 0.75 \\\hline 2009 & \$ 1.23 & \$ 2.35 & \$ 0.75 \\\hline 2010 & \$ 1.29 & \$ 2.41 & \$ 0.77 \\\hline 2011 & \$ 1.35 & \$ 2.54 & \$ 0.77 \\\hline 2012 & \$ 1.42 & \$ 2.87 & \$ 0.78 \\\hline\end{array}$
Consider a family with the following yearly consumption for these products for the years 2008 through 2012.
$$\begin{array} { | l | l | l | l | } \hline &\text { Bread } & \text { Fruits } & \text { Beverages } \\\hline \text { Year } &\text { (loaves) } & (\mathrm{kg}) & (\mathrm{L}) \\\hline \mathbf { 2 0 0 8 } & 2,200 & 250 & 2,400 \\\hline \mathbf { 2 0 0 9 } & 2,200 & 235 & 2,450 \\\hline \mathbf { 2 0 1 0 } & 2,200 & 210 & 2,580 \\\hline \mathbf { 2 0 1 1 } & 2,200 & 180 & 2,690 \\\hline \mathbf { 2 0 1 2 } & 2,200 & 140 & 2,810 \\\hline\end{array}$$
Answer the following questions using 2008 as the base year.


-Compute the Paasche index for 2011.

A)101.68
B)112.67
C)105.46
D)108.41
E)100

Question 29

In general,the number of dummy variables used to model constant seasonal variation is equal to the number of _______.

A)seasons
B)seasons minus 1
C)seasons plus 1
D)seasons minus 2
E)seasons divided by two

Question 30

If the errors produced by a forecasting method for 3 observations are +3,+3 and -3,then what is the mean absolute deviation (MAD)?

A)9
B)0
C)3
D)-3
E)15

Question 31

Periodic patterns in a time series that complete themselves within a calendar year or less and then are repeated on a regular basis represent the __________ component of a time series.

A)trend
B)seasonal variations
C)cycle
D)irregular component
E)random

Question 32

The _______ component of time series reflects the long-run decline or growth in a time series.

A)trend
B)seasonal variation
C)cycle
D)irregular component
E)random

Question 33

If the errors produced by a forecasting method for 3 observations are +3,+3 and -3,then what is the mean squared deviation (MSD)?

A)9
B)0
C)3
D)-3
E)2

Question 34

The ________ component of time series refers to the erratic time-series movement that follows no recognizable or regular pattern.

A)trend
B)seasonal variation
C)cycle
D)irregular component
E)predicted

Question 35

A restaurant has been experiencing higher sales during the weekends compared to the weekdays.Daily restaurant sales patterns for this restaurant over a week are an example of _________ component of time series.

A)trend
B)seasonal variation
C)cycle
D)irregular component
E)random

Question 36

The no trend time series model is given by:

A) $y _ { t } = \beta _ { 0 } + \beta _ { 1 } t + \varepsilon _ { t }$
B) $y _ { t } = \beta _ { 0 } + \varepsilon _ { t }$
C) $y _ { t } = \beta _ { 0 } + \beta _ { 1 } t + \beta _ { 2 } t ^ { 2 } + \varepsilon _ { t }$
D) $y _ { t } = \beta _ { 0 } + \beta _ { 1 } \ln t + \varepsilon _ { t }$

Question 37

In the following table, we present prices for three commonly used products—bread, fruits, and beverages—for the years 2008 through 2012.
$\begin{array}{|l|l|l|l|}\hline &\text { Bread } & \text { Fruits } & \text { Beverages } \\\hline \text { Year } & (\$ \text { per loaf) } & (\$ \text { per } \mathrm{kg}) & (\$ \text { per } \mathrm{L}) \\\hline 2008 & \$ 1.21 & \$ 2.18 & \$ 0.75 \\\hline 2009 & \$ 1.23 & \$ 2.35 & \$ 0.75 \\\hline 2010 & \$ 1.29 & \$ 2.41 & \$ 0.77 \\\hline 2011 & \$ 1.35 & \$ 2.54 & \$ 0.77 \\\hline 2012 & \$ 1.42 & \$ 2.87 & \$ 0.78 \\\hline\end{array}$
Consider a family with the following yearly consumption for these products for the years 2008 through 2012.
$$\begin{array} { | l | l | l | l | } \hline &\text { Bread } & \text { Fruits } & \text { Beverages } \\\hline \text { Year } &\text { (loaves) } & (\mathrm{kg}) & (\mathrm{L}) \\\hline \mathbf { 2 0 0 8 } & 2,200 & 250 & 2,400 \\\hline \mathbf { 2 0 0 9 } & 2,200 & 235 & 2,450 \\\hline \mathbf { 2 0 1 0 } & 2,200 & 210 & 2,580 \\\hline \mathbf { 2 0 1 1 } & 2,200 & 180 & 2,690 \\\hline \mathbf { 2 0 1 2 } & 2,200 & 140 & 2,810 \\\hline\end{array}$$
Answer the following questions using 2008 as the base year.

-Compute the Laspeyres index for 2011.

A)100
B)101.73
C)108.91
D)105.62
E)114.11

Question 38

In the Durbin-Watson test,if the calculated d-statistic is greater than the upper value of the d-statistic,then:

A)We do not reject H₀which says the error terms are not autocorrelated.
B)We do reject H₀which says the error terms are not autocorrelated.
C)The test is inconclusive.
D)We do reject H₀,which says the error terms are positively or negatively autocorrelated.

Question 39

In the following table, we present prices for three commonly used products—bread, fruits, and beverages—for the years 2008 through 2012.
$\begin{array}{|l|l|l|l|}\hline &\text { Bread } & \text { Fruits } & \text { Beverages } \\\hline \text { Year } & (\$ \text { per loaf) } & (\$ \text { per } \mathrm{kg}) & (\$ \text { per } \mathrm{L}) \\\hline 2008 & \$ 1.21 & \$ 2.18 & \$ 0.75 \\\hline 2009 & \$ 1.23 & \$ 2.35 & \$ 0.75 \\\hline 2010 & \$ 1.29 & \$ 2.41 & \$ 0.77 \\\hline 2011 & \$ 1.35 & \$ 2.54 & \$ 0.77 \\\hline 2012 & \$ 1.42 & \$ 2.87 & \$ 0.78 \\\hline\end{array}$
Consider a family with the following yearly consumption for these products for the years 2008 through 2012.
$$\begin{array} { | l | l | l | l | } \hline &\text { Bread } & \text { Fruits } & \text { Beverages } \\\hline \text { Year } &\text { (loaves) } & (\mathrm{kg}) & (\mathrm{L}) \\\hline \mathbf { 2 0 0 8 } & 2,200 & 250 & 2,400 \\\hline \mathbf { 2 0 0 9 } & 2,200 & 235 & 2,450 \\\hline \mathbf { 2 0 1 0 } & 2,200 & 210 & 2,580 \\\hline \mathbf { 2 0 1 1 } & 2,200 & 180 & 2,690 \\\hline \mathbf { 2 0 1 2 } & 2,200 & 140 & 2,810 \\\hline\end{array}$$
Answer the following questions using 2008 as the base year.

-Compute the simple index for the price of fruits,per kilogram,in 2012.

A)75.96
B)131.65
C)118.22
D)124.37
E)152.77

Question 40

If the errors produced by a forecasting method for 3 observations are -1,-2 and -6,then what is the mean squared deviation (MSD)?

A)9
B)-9
C)3
D)13.67
E)15.99

Question 41

Seasonal variations are periodic patterns that complete themselves within one ______ or less and then are repeated on a regular basis.

A)day
B)decade
C)week
D)month
E)year

Question 42

A time series obtained from quarterly data exhibits an increasing linear trend and increasing seasonal variation.Which one of the following would be the most appropriate way to model this time series?

A)Simple exponential smoothing.
B)Multiplicative decomposition.
C)Box-Jenkins methodology.
D)Holt-Winters' double exponential smoothing model.
E)Durbin-Watson statistic.

Question 43

$\text { XYZ Company - Annual data }$
$\begin{array} { c c } \text { Actual Demand } & \text { Forecasted Demand } \\15 & 14 \\15 & 16 \\17 & 18 \\18 & 20 \\20 & 22 \\21 & 24\end{array}$

-Based on the information given in the table above,what is the MAD?

A)1.3333
B)1.6667
C)2.5
D)3.3333
E)4.5

Question 44

Consider the following time series with forecast values and errors.
$$\begin{array} { | l | l | } \hline \begin{array} { l } \text { Actual } \\\text { Demand }\end{array} & \begin{array} { l } \text { Forecast } \\\text { Demand }\end{array} \\\hline 10 & 9 \\\hline 13 & 15 \\\hline 15 & 16 \\\hline 11 & 13 \\\hline 12 & 10 \\\hline\end{array}$$

-Calculate the mean square deviation (MSD).

A)2.8
B)13.4
C)7.5
D)1.6
E)2.4

Question 45

A time series exhibits no trend,no seasonal variation,and no cycle.However,the average measurement appears to remain relatively constant over time.The most appropriate way to model this time series would be to use

A)simple exponential smoothing.
B)multiplicative decomposition.
C)a multiple regression model with four predictor variables;one for time and three dummy variables.
D)Holt-Winters' double exponential smoothing model.
E)a no-trend regression model.

Question 46

In a given week,the TSE (Toronto Stock Exchange)is generally open from Monday through Friday.If we wanted to use multiple regression method with dummy variables to study the impact of the day of the week on stock market performance,we would need ____ dummy variables.

A)5
B)52
C)4
D)3
E)365

Question 47

Assume that the current date is February 1, 2013. The linear regression model was applied to a monthly time series data based on the last 24 months' sales. (from January 2011 through December 2012). The following partial computer output summarizes the results.
$$\begin{array} { l c c } \text { Coeffficient } & \text { Estimate } & t \\\text { Intercept } & 4.3 & 2.07 \\\text { Slope } & 1.6 & 2.98\end{array}$$

-Determine the predicted sales for February 2013.

A)45.9
B)42.7
C)44.3
D)109.1
E)113.4

Question 48

$\text { XYZ Company - Annual data }$
$\begin{array} { c c } \text { Actual Demand } & \text { Forecasted Demand } \\15 & 14 \\15 & 16 \\17 & 18 \\18 & 20 \\20 & 22 \\21 & 24\end{array}$

-Based on the information given in the table above,what is the PE?

A)41.28
B)9.10
C)-41.28
D)-9.10
E)1.33

Question 49

Because the ____________ index employs the base period quantities in all succeeding periods,it allows for ready comparisons for identical quantities of goods purchased between the base period and all succeeding periods.

A)simple
B)aggregate
C)Laspeyres
D)Paasche
E)quantity

Question 50

$\text { XYZ Company - Annual data }$
$\begin{array} { c c } \text { Actual Demand } & \text { Forecasted Demand } \\15 & 14 \\15 & 16 \\17 & 18 \\18 & 20 \\20 & 22 \\21 & 24\end{array}$

-Based on the information given in the table above,what is the MSD?

A)1.3333
B)1.6667
C)2.5
D)3.3333
E)4.5

Question 51

In the multiplicative decomposition method,the centered moving averages provide an estimate of:

A)TR_t × SN_t
B)TR_t × CL_t
C)SN_t × CL_t
D)TR_t × IR_t
E)SN_t × IR_t

Question 52

When the magnitude of the seasonal swing does not depend on the level of a time series,we call this _________ seasonal variation.

A)increasing
B)cyclical
C)constant
D)decreasing
E)zero

Question 53

When there is _______________ seasonal variation,the magnitude of the seasonal swing does not depend on the level of the time series.

Question 54

Assume that the current date is February 1, 2013. The linear regression model was applied to a monthly time series data based on the last 24 months' sales. (from January 2011 through December 2012). The following partial computer output summarizes the results.
$$\begin{array} { l c c } \text { Coeffficient } & \text { Estimate } & t \\\text { Intercept } & 4.3 & 2.07 \\\text { Slope } & 1.6 & 2.98\end{array}$$

-The actual sales for February 2013 were 43.7.What is the forecast error for February 2013?

A)1.05
B)2.2
C)-2.2
D)0.95
E)4.84

Question 55

Consider the following time series with forecast values and errors.
$$\begin{array} { | l | l | } \hline \begin{array} { l } \text { Actual } \\\text { Demand }\end{array} & \begin{array} { l } \text { Forecast } \\\text { Demand }\end{array} \\\hline 10 & 9 \\\hline 13 & 15 \\\hline 15 & 16 \\\hline 11 & 13 \\\hline 12 & 10 \\\hline\end{array}$$

-Calculate the mean absolute deviation (MAD).

A)2.8
B)13.4
C)7.5
D)1.6
E)2.4

Question 56

A time series exhibits no trend,no seasonal variation,and no cycle.However,the average measurement is changing slowly over time.The most appropriate way to model this time series would be to use

A)simple exponential smoothing.
B)multiplicative decomposition.
C)a multiple regression model with four predictor variables;one for time and three dummy variables.
D)Holt-Winters' double exponential smoothing model.
E)a no-trend regression model.

Question 57

When using simple exponential smoothing,the value of the smoothing constant must be between ____ and ____.

A)0,×
B)0,100
C)-1,1
D)-1,0
E)0,1

Question 58

Consider the following time series with forecast values and errors.
$$\begin{array} { | l | l | } \hline \begin{array} { l } \text { Actual } \\\text { Demand }\end{array} & \begin{array} { l } \text { Forecast } \\\text { Demand }\end{array} \\\hline 10 & 9 \\\hline 13 & 15 \\\hline 15 & 16 \\\hline 11 & 13 \\\hline 12 & 10 \\\hline\end{array}$$

-Calculate the mean absolute deviation (MAPE).

A)2.8
B)13.4
C)7.5
D)1.6
E)2.4

Question 59

$\text { XYZ Company - Annual data }$
$\begin{array} { c c } \text { Actual Demand } & \text { Forecasted Demand } \\15 & 14 \\15 & 16 \\17 & 18 \\18 & 20 \\20 & 22 \\21 & 24\end{array}$

-Based on the information given in the table above,what is the MAPE?

A)41.28
B)9.10
C)-41.28
D)-9.10
E)1.33

Question 60

The demand for a product for the last six years has been 15,15,17,18,20,and 19.The manager wants to predict the demand for this time series using the following simple linear trend equation: tr_t= 12 + 2t.What are the forecast errors for the 5^th and 6^th years?

A)0,-3
B)0,+3
C)+2,+5
D)-2,-5
E)-1,-4

Question 61

A simple index is obtained by dividing the current value of a time series by the value of a time series in the _____ time period and by multiplying this ratio by 100.

Question 62

In the multiplicative decomposition method,the _________ moving average provides an estimate of TR_t × CL_t

Question 63

The basic difference between MAD and MSD is that MSD,unlike MAD,penalizes a forecasting technique much more for _____ errors.

Question 64

Periodic patterns in time series that repeat themselves within a calendar year or less are referred to as _____.

Question 65

When deseasonalizing time series observations,we divide the actual time series observation by its ___________.

Question 66

Weighting in exponential smoothing is accomplished by the use of a _____.

Question 67

The Durbin-Watson statistic is used to detect _____.

Question 68

Although the ________ index allows us to compare each period to the base period,it is difficult to compare the index at other points in time.

Question 69

The Laspeyres index and the Paasche index are both examples of _________ aggregate price indexes.

Question 70

The recurring up-and-down movement of a time series around trend levels that last more than one calendar year is called _____.

Question 71

The _______________ index is most useful if the base quantities provide a reasonable representation of consumption patterns in succeeding time periods.

Question 72

The _____ test is a test for first-order positive autocorrelation.

Question 73

When preparing a price index based on multiple products,if the price of each product is weighted by the quantity of the product purchased in a given period of time,the resulting index is called a ___________ price index.

Question 74

If a time series exhibits increasing seasonal variation,one approach is to first use a ______________ transformation that produces a transformed time series that exhibits constant seasonal variation.

Question 75

The upward or downward movement that characterizes a time series over a period of time is referred to as _____.

Question 76

A simple index is computed by using the values of one time series,while the _______ index is based on a "representative shopping basket" consisting of more than one time series.

Question 77

When using simple exponential smoothing,the more recent the time series observation,the _________ its corresponding weight.

Question 78

The purpose behind moving averages and centered moving averages is to eliminate season variations and _________.

Question 79

A positive autocorrelation implies that negative error terms will be followed by _________ error terms.

Question 80

A forecasting method that weights recent observations more heavily is called _____.