Deck 16: Time Series Forecasting and Index Numbers

Question 1

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

Answer 1

True

Question 2

When a forecaster uses a multiplicative decomposition model or time series regression model,she or he assumes that the time series components are changing over time.

Answer 2

False

Question 3

A time series decomposition method would not be used to forecast seasonal data.

Answer 3

False

Question 4

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 5

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

Question 6

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

Question 7

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

Question 8

The smoothing constant is a number that determines how much weight is attached to each observation.

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

The simple moving average method is primarily useful in determining the impact of trend on a 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

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.

Question 13

Dummy variables are used to model increasing seasonal variation.

Question 14

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

Question 15

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

Question 16

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

Question 17

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 18

A Paasche index more accurately provides a year-to-year comparison of the annual cost of selected products in the market-basket than a Laspeyres index.

Question 19

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

Question 20

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 21

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 H₀,which says the error terms are not autocorrelated.
B)We do reject H₀,which 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 22

Box-Jenkins methodology begins by determining if the time series under consideration is stationary.

Question 23

All of the following are forecasting methods except:

A)Holt-Winters double exponential smoothing.
B)Box-Jenkins.
C)Time series regression.
D)MAD autocorrelation.

Question 24

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

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

Question 25

Box-Jenkins models describe the future time series value by using past time series values,which are called autoregressive terms.

Question 26

Box-Jenkins methodology transforms nonstationary time series values into stationary time series values.

Question 27

Box-Jenkins models describe the future time series value by using a seasonal moving-average term when the SPAC dies down fairly quickly (at lags 12 and 24)and the SPC has a spike at lag 12 and cuts off after lag 12.

Question 28

Increasing seasonal variation implies that the time series is nonstationary with respect to its variance.

Question 29

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

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

Question 30

When a forecaster uses the ______________ method,she or he assumes that the time series components are changing slowly over time.

A)Time series regression
B)Exponential smoothing
C)Box-Jenkins
D)Multiplicative decomposition

Question 31

When a forecaster uses the _________________ method,she or he assumes that the time series components are changing quickly over time.

A)Time series regression
B)Simple exponential smoothing
C)Box-Jenkins
D)Multiplicative decomposition

Question 32

Box-Jenkins models describe the future time series value by using past error terms,which are called moving-average terms.

Question 33

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

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

Question 34

To carry out combined regular and seasonal differencing,you take the seasonal differences of the regular differences.

Question 35

Box-Jenkins models describe the future time series value by using a nonseasonal autoregressive term when the SAC dies down fairly quickly (at lags 12 and 24)and the SPAC has a spike at lag 12 and cuts off after lag 12.

Question 36

Cyclical differencing is one of the types of differencing used by the Box-Jenkins methodology.

Question 37

For monthly seasonal data,we define the nonseasonal level of the Sample Autocorrelation Function (SAC)to be lags 12 and 24.

Question 38

The no-trend time series model is given by:

A)TR_t = B₀ + B_1t.
B)TR_t = B₀.
C)TR_t = B₀ + B_1t + B_2t².
D)TR_t = B₀ + B_ln(t).

Question 39

A time series is considered stationary if the statistical properties follow a trend of cyclical variation.

Question 40

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

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

Question 41

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 42

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

A)Increasing seasonal
B)Cyclical seasonal
C)Constant seasonal
D)Decreasing seasonal
E)No seasonal

Question 43

Since a(n)____________ 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 44

A sustained long-term change in the level of the variable that is being forecasted per unit of time is:

A)A trend.
B)A time series.
C)Seasonality.
D)A change due to business cycles.

Question 45

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

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

Question 46

Assume that the current date is February 1,2003.The linear regression model was applied to a monthly time series based on the last 24 months' sales (from January 2000 through December 2002).The following partial computer output summarizes the results. $$\begin{array} { l c c } \text { Coefficient } & \text { Estimate } & \mathrm { t } \\\text { Intercept } & 4.3 & 2.07 \\\text { Slope } & 1.6 & 2.98\end{array}$$
Determine the predicted sales for this month.

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

Question 47

Which of the following time series forecasting methods would not be used to forecast seasonal data?

A)Dummy variable regression
B)Simple exponential smoothing
C)Time series decomposition
D)Multiplicative Winters method

Question 48

When the moving average method is used to estimate the seasonal factors with quarterly sales data,a ______ period moving average is used.

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

Question 49

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 a(n)_________ component of a time series.

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

Question 50

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

A)Trend × seasonal
B)Trend × cycle
C)Seasonal × cycle
D)Trend × irregular
E)Seasonal × irregular

Question 51

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 52

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:

A)Is larger than 1.1.
B)Is smaller than 1.1.
C)Is equal to 1.1.
D)Cannot be determined with the information provideD.

Question 53

The ___________ component of a time series refers to the erratic time series movements that follow no recognizable or regular pattern.

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

Question 54

Seasonal variations are periodic patterns in a time series that are repeated over time.For which one of the following time series variables is it not possible to recognize seasonal variations?

A)Quarters of the year
B)Months of the year
C)Days of the week
D)Hours of the day
E)Years

Question 55

A sequence of values of some variable or composite of variables taken at successive,uninterrupted time periods,is called a:

A)Least squares (linear)trend line.
B)Moving average.
C)Cyclical component.
D)Time series.
E)Seasonal factor.

Question 56

Assume that the current date is February 1,2003.The linear regression model was applied to a monthly time series based on the last 24 months' sales (from January 2000 through December 2002).The following partial computer output summarizes the results. $$\begin{array} { l c c } \text { Coefficient } & \text { Estimate } & \mathrm { t } \\\text { Intercept } & 4.3 & 2.07 \\\text { Slope } & 1.6 & 2.98\end{array}$$
At a significance level of .05,what is the value of the rejection point in testing the slope for significance?

A)1.717
B)1.96
C)2.074
D)1.645
E)2.064

Question 57

Which of the following time series forecasting methods would not be used to forecast a time series that exhibits a linear trend with no seasonal or cyclical patterns?

A)Dummy variable regression
B)Linear trend regression
C)Holt-Winters double exponential smoothing
D)Multiplicative Winters method
E)Both Dummy variable regression and Multiplicative Winters method

Question 58

The ___________ component of a time series consists of erratic and unsystematic fluctuations in the time series data.

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

Question 59

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
C)Cyclical
D)Irregular

Question 60

Those fluctuations that are associated with climate,holidays,and related activities are referred to as __________ variations.

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

Question 61

When there is first-order autocorrelation,the error term in period t is related to the error term in period ______.

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

Question 62

The basic difference between MAD and MSE is that MSE,unlike MAD,penalizes a forecasting technique much more for _________ errors than for _________ errors.

A)Large,small
B)Small,large
C)Small,zero
D)Zero,large

Question 63

The purpose behind moving averages and centered moving averages is to eliminate __________________.

A)Constant variation
B)Cyclical variation
C)Seasonal variation
D)Regular variation

Question 64

The Durbin-Watson statistic is used to detect _____________.

A)First-order autocorrelation
B)Exponential smoothing
C)Multiplicative decomposing
D)Irregular variation

Question 65

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

A)Constant variations
B)Cyclical variations
C)Seasonal variations
D)Regular variations

Question 66

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

A)Seasonal variation
B)Cyclical variation
C)A trend
D)Irregular variation

Question 67

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.Use this equation to forecast the demand for this product,and then calculate the MAD.

A)MAD = 1.333
B)MAD = 1.6
C)MAD = 2.0
D)MAD = 2.333
E)MAD = 2.5

Question 68

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

A)Durbin-Watson
B)MSD
C)MAD
D)Multiplicative Winters

Question 69

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.Use this equation to forecast the demand for this product,and then calculate the MSD.

A)MSD = 6
B)MSD = 3.3333
C)MSD = 7.0
D)MSD = 2
E)MSD = 2.4

Question 70

Weighting in exponential smoothing is accomplished by using _____________.

A)First-order autocorrelation
B)Smoothing constants
C)The Durbin-Watson method
D)Multiplicative decomposing

Question 71

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

A)Larger
B)Smaller
C)More irregular
D)More cyclical

Question 72

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

A)Constant variation
B)Cyclical variation
C)Seasonal variation
D)Irregular variation

Question 73

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

A)Irregular factor
B)Cyclical factor
C)Seasonal factor
D)Weighted aggregate factor

Question 74

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

A)Time series analysis
B)First-order autocorrelation
C)Multiplicative decomposition
D)Exponential smoothing

Question 75

As you probably know,in a given week,the NYSE (New York Stock Exchange)is generally open from Monday through Friday.If we wanted to use the 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 76

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.Then,_________ variables can be used to model the time series with constant seasonal variation.

A)Autocorrelation,dummy
B)Fractional power,dummy
C)Fractional power,constant
D)Autocorrelation,constant

Question 77

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

A)cyclical
B)constant
C)irregular
D)increasing

Question 78

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 79

The Holt-Winters double exponential smoothing method is used to forecast time series data with ___________.

A)Autocorrelation
B)A linear trend
C)Cyclical patterns
D)Moving averages

Question 80

When using simple exponential smoothing,the value of the smoothing constant α cannot be:

A)Negative.
B)Greater than zero.
C)Greater than 1.
D).99.
E)Both Negative and Greater than 1.