Deck 15: Time-Series Forecasting and Index Numbers

Question 1

A stationary time-series data has only trend, but no cyclical or seasonal effects.

Answer 1

False

Question 2

If autocorrelation occurs in regression analysis, then the confidence intervals and tests using the t and F distributions are no longer strictly applicable.

Answer 2

True

Question 3

Although seasonal effects can confound a trend analysis, a regression model is robust to these effects and the researcher does not need to adjust for seasonality prior to using a regression model to analyze trends.

Answer 3

False

Question 4

Naïve forecasting models have no useful applications because they do not take into account data trend, cyclical effects or seasonality.

Question 5

One of the main techniques for isolating the effects of seasonality is decomposition.

Question 6

An exponential smoothing technique in which the smoothing constant alpha is equal to one is equivalent to a regression forecasting model.

Question 7

If the trend equation is linear in time, the slope indicates the increase, or decrease when negative, in the forecasted value of the response value Y for the next time period.

Question 8

One of the main techniques for isolating the effects of seasonality is reconstitution.

Question 9

For large datasets, the mean error (ME)and mean absolute deviation (MAD)always have the same numerical value.

Question 10

When the error terms of a regression forecasting model are correlated the problem of autocorrelation occurs.

Question 11

If the trend equation is quadratic in time t=1….T, the forecast value for the next time period, T+1, depends on time T.

Question 12

When a trucking firm uses the number of shipments for January of the previous year as the forecast for January next year, it is using a naïve forecasting model.

Question 13

The long-term general direction of data is referred to as series.

Question 14

Two popular general categories of smoothing techniques are averaging models and exponential models.

Question 15

Forecast error is the difference between the value of the response variable and those of the explanatory variables.

Question 16

Linear regression models cannot be used to analyze quadratic trends in time-series data.

Question 17

The first step of isolating seasonal effects is to remove the trend and cycles effects.

Question 18

Once the seasonal effects have been isolated, these effects can be removed from the original data through desensitizing.

Question 19

Time-series data are data gathered on a desired characteristic at a particular point in time.

Question 20

Two popular general categories of smoothing techniques are exponential models and logarithmic models.

Question 21

A simple index number is the ratio of the base period divided by the period of interest, multiplied by 100.

Question 22

Using a three-month moving average, the forecast value for October made at the end of September in the following time series would be ____________. $$\begin{array} { | r | r | } \hline \text { July } & 5 \\\hline \text { Amg } & 11 \\\hline \text { Sent } & 13 \\\hline \text { Oct } & 6 \\\hline\end{array}$$

A)11.60
B)10.00
C)9.07
D)8.06
E)9.67

Question 23

One of the ways to overcome the autocorrelation problem in a regression forecasting model is to increase the level of significance for the F test

Question 24

A time series with forecast values and error terms is presented in the following table.The mean absolute deviation (MAD)for this forecast is ___________. $\begin{array}{|r|r|r|r|}\hline \text { Monthh } & \text { Actual } & \text { Forecast} & \text { Error } \\\hline \text { July } & 5 & & \\\hline \text { Aug } & 11 & 5 & 6.00 \\\hline \text { Sept } & 13 & 6.8 & 6.20 \\\hline \text { Oct } & 6 & 8.66 & -2.66 \\\hline \text { Nov } & 5 & 7.862 & -2.86 \\\hline\end{array}$

A)3.54
B)7.41
C)4.43
D)17.72
E)4.34

Question 25

A time series analysis was performed to determine the number of new online customers that joined the 'Jelly of the Month Club'.The actual number of new customers, the forecast values and the error terms are presented in the following table.The mean absolute deviation (MAD)for this forecast is ___________. $\begin{array}{|r|r|r|r|}\hline \text { Monthh } & \text { Actual } & \text { Forecast} & \text { Error } \\\hline \text { July } &4 & & \\\hline \text { Aug } & 6 & 5 &-1 \\\hline \text { Sept } & 3 & 6 &3 \\\hline \text { Oct } & 9 & 8& -1 \\\hline \text { Nov } &8 &9& 1 \\\hline\end{array}$

A)-0.50
B)0.50
C)1.50
D)7.00
E)3.00

Question 26

Unweighted price indexes can only compare across the entire successive time period for which there is data.

Question 27

In statistics, the Winters' Three Parameter statistic is a test statistic used to detect the presence of autocorrelation in the residuals from a regression analysis.

Question 28

A small value of the Durbin-Watson statistic indicates that successive error terms are positively correlated.

Question 29

A time series with forecast values and error terms is presented in the following table.The mean squared error (MSE)for this forecast is ___________. $\begin{array}{|r|r|r|r|}\hline \text { Monthh } & \text { Actual } & \text { Forecast} & \text { Error } \\\hline \text { July } & 5 & & \\\hline \text { Aug } & 11 & 5 & 6.00 \\\hline \text { Sept } & 13 & 6.8 & 6.20 \\\hline \text { Oct } & 6 & 8.66 & -2.66 \\\hline \text { Nov } & 5 & 7.862 & -2.86 \\\hline\end{array}$

A)13.33
B)17.94
C)89.71
D)22.43
E)32.34

Question 30

When forecasting with exponential smoothing, data from previous periods is _________.

A)given equal importance
B)given exponentially increasing importance
C)ignored
D)given exponentially decreasing importance
E)linearly decreasing importance

Question 31

A time series with forecast values and error terms is presented in the following table.The mean error (ME)for this forecast is ___________. $\begin{array}{|r|r|r|r|}\hline \text { Monthh } & \text { Actual } & \text { Forecast} & \text { Error } \\\hline \text { July } & 5 & & \\\hline \text { Aug } & 11 & 5 & 6.00 \\\hline \text { Sept } & 13 & 6.8 & 6.20 \\\hline \text { Oct } & 6 & 8.66 & -2.66 \\\hline \text { Nov } & 5 & 7.862 & -2.86 \\\hline\end{array}$

A)1.67
B)1.34
C)6.68
D)3.67
E)2.87

Question 32

Use of a smoothing constant value less than 0.5 in an exponential smoothing model gives more weight to ___________.

A)the actual value for the current period
B)the actual value for the previous period
C)the forecast for the current period
D)the forecast for the previous period
E)the forecast for the next period

Question 33

In exponential smoothing models, the value of the smoothing constant may be any number between ___________.

A)-1 and 1
B)-5 and 5
C)0 and 1
D)0 and 10
E)0 and 100

Question 34

A time series analysis was performed to determine the number of new online customers that joined the 'Jelly of the Month Club'.The actual number of new customers, the forecast values and the error terms are presented in the following table.The mean error (ME)for this forecast is ___________. $\begin{array}{|r|r|r|r|}\hline \text { Monthh } & \text { Actual } & \text { Forecast} & \text { Error } \\\hline \text { July } &4 & & \\\hline \text { Aug } & 6 & 5 &-1 \\\hline \text { Sept } & 3 & 6 &3 \\\hline \text { Oct } & 9 & 8& -1 \\\hline \text { Nov } &8 &9& 1 \\\hline\end{array}$

A)-0.50
B)0.50
C)1.50
D)7.00
E)3.00

Question 35

One of the ways to overcome the autocorrelation problem in a regression forecasting model is to transform the variables by taking the first-differences.

Question 36

Index numbers are used to compare various time frame measures to a base time period measure.

Question 37

Autoregression is a multiple regression technique in which the independent variables are time-lagged versions of the dependent variable.

Question 38

A time series analysis was performed to determine the number of new online customers that joined the 'Jelly of the Month Club'.The actual number of new customers, the forecast values and the error terms are presented in the following table.The mean squared error (MSE)for this forecast is ___________. $\begin{array}{|r|r|r|r|}\hline \text { Monthh } & \text { Actual } & \text { Forecast} & \text { Error } \\\hline \text { July } &4 & & \\\hline \text { Aug } & 6 & 5 &-1 \\\hline \text { Sept } & 3 & 6 &3 \\\hline \text { Oct } & 9 & 8& -1 \\\hline \text { Nov } &8 &9& 1 \\\hline\end{array}$

A)-0.50
B)0.50
C)1.50
D)7.00
E)3.00

Question 39

Use of a smoothing constant value greater than 0.5 in an exponential smoothing model gives more weight to ___________.

A)the actual value for the current period
B)the actual value for the previous period
C)the forecast for the current period
D)the forecast for the previous period
E)the forecast for the next period

Question 40

Autocorrelation in a regression forecasting model can be detected by the F test.

Question 41

The following graph of a time-series data suggests a _______________ trend.

A)linear
B)quadratic
C)cosine
D)tangential
E)flat

Question 42

Fitting a linear trend to 36 monthly data points (January 2011 = 1, February 2011 =2, March 2011 = 3, etc.)produced the following tables. The projected trend value for January 2014 is ________.

A)231.39
B)555.71
C)339.50
D)447.76
E)355.71

Question 43

The following graph of time-series data suggests a _______________ trend.

A)linear
B)quadratic
C)cosine
D)tangential
E)flat

Question 44

The forecast value for August was 22 and the actual value turned out to be 19.Using exponential smoothing with $\alpha$ = 0.30, the forecast value for September would be ______.

A)21.1
B)19.9
C)18.1
D)22.9
E)21.0

Question 45

Using a three-month moving average (with weights of 6, 3, and 1 for the most current value, next most current value and oldest value, respectively), the forecast value for October made at the end of September in the following time series would be__________. $$\begin{array} { | r | r | } \hline \text { July } & 5 \\\hline \text { Amg } & 11 \\\hline \text { Sent } & 13 \\\hline \text { Oct } & 6 \\\hline\end{array}$$

A)11.60
B)10.00
C)9.67
D)8.60
E)6.11

Question 46

The following graph of a time-series data suggests a _______________ trend.

A)linear
B)tangential
C)cosine
D)quadratic
E)flat

Question 47

What is the forecast for the Period 7 using a 3-period moving average technique, given the following time-series data for six past periods? $$\begin{array} { | l | l | l | l | l | l | l | } \hline \text { Period } & 1 & 2 & 3 & 4 & 5 & 6 \\\hline \text { Value } & 136 & 126 & - 146 & - 148 & - 156 & 164 \\\hline\end{array}$$

A)164.67
B)156.00
C)148.00
D)126.57
E)158.67

Question 48

The city golf course is interested in starting a junior golf program.The golf pro has collected data on the number of youths under 13 that have played golf during the last 4 months.Using a three-month moving average, the forecast value for November in the following time series would be ____________. $$\begin{array} { | c | r | } \hline \text { Joly } & 28 \\\hline \text { Ang } & 27 \\\hline \text { Sept } & 17 \\\hline \text { Oct } & 19 \\\hline\end{array}$$

A)24
B)21
C)21.56
D)19.22
E)22

Question 49

The city golf course is interested in starting a junior golf program.The golf pro has collected data on the number of youths under 13 that have played golf during the last 4 months.Using a three-month moving average (with weights of 5, 3, and 1 for the most current value, next most current value and oldest value, respectively), the forecast value for October made at the end of September in the following time series would be __________. $$\begin{array} { | c | r | } \hline \text { Joly } & 28 \\\hline \text { Ang } & 27 \\\hline \text { Sept } & 17 \\\hline \text { Oct } & 19 \\\hline\end{array}$$

A)24
B)21
C)21.56
D)19.22
E)22

Question 50

The city golf course is interested in starting a junior golf program.The golf pro has collected data on the number of youths under 13 that have played golf during the last 4 months.Using a three-month moving average, the forecast value for October made at the end of September in the following time series would be ____________. $$\begin{array} { | c | r | } \hline \text { Joly } & 28 \\\hline \text { Ang } & 27 \\\hline \text { Sept } & 17 \\\hline \text { Oct } & 19 \\\hline\end{array}$$

A)24
B)21
C)21.56
D)19.22
E)22

Question 51

Fitting a linear trend to 36 monthly data points (January 2011 = 1, February 2011 =2, March 2011 = 3, etc.)produced the following tables. The projected trend value for January 2014 is ________.

A)544.29
B)868.61
C)652.39
D)760.50
E)876.90

Question 52

Using a three-month moving average (with weights of 6, 3, and 1 for the most current value, next most current value and oldest value, respectively), the forecast value for November in the following time series is ____________. $$\begin{array} { | r | r | } \hline \text { July } & 5 \\\hline \text { Amg } & 11 \\\hline \text { Sent } & 13 \\\hline \text { Oct } & 6 \\\hline\end{array}$$

A)11.60
B)10.00
C)9.67
D)8.06
E)8.60

Question 53

Using a three-month moving average, the forecast value for November in the following time series is ____________. $$\begin{array} { | r | r | } \hline \text { July } & 5 \\\hline \text { Amg } & 11 \\\hline \text { Sent } & 13 \\\hline \text { Oct } & 6 \\\hline\end{array}$$

A)11.60
B)10.00
C)9.67
D)8.60
E)6.00

Question 54

The city golf course is interested in starting a junior golf program.The golf pro has collected data on the number of youths under 13 that have played golf during the last 4 months.Using a three-month moving average (with weights of 5, 3, and 1 for the most current value, next most current value and oldest value, respectively), the forecast value for November in the following time series would be ____________. $$\begin{array} { | c | r | } \hline \text { Joly } & 28 \\\hline \text { Ang } & 27 \\\hline \text { Sept } & 17 \\\hline \text { Oct } & 19 \\\hline\end{array}$$

A)24
B)21
C)21.56
D)19.22
E)22

Question 55

The ratios of "actuals to moving averages" (seasonal indexes)for a time series are presented in the following table as percentages. $$\begin{array} { | r | r | r | r | r | r | } \hline & 2008 & 2009 & 2010 & 2011 & 2012 \\\hline Q _ { 1 } & & 112.22 & 110.78 & 111.22 & 111.87 \\\hline Q _ { 2 } & & 100.65 & 108.68 & 103.78 & 101.95 \\\hline Q _ { 3 } & 97.76 & 99.08 & 97.68 & 97.61 & \\\hline Q _ { 4 } & 86.61 & 95.00 & 94.64 & 92.92 & \\\hline\end{array}$$ The final (completely adjusted)estimate of the seasonal index for Q₄ is __________.

A)86.61
B)90.90
C)93.78
D)92.29
E)93.00

Question 56

Calculating the "ratios of actuals to moving average" is a common step in time series decomposition.The results (the quotients)of this step estimate the ________.

A)trend and cyclical components
B)seasonal and irregular components
C)cyclical and irregular components
D)trend and seasonal components
E)irregular components

Question 57

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

A)Trend
B)Seasonal fluctuations
C)Cyclical fluctuations
D)Normal fluctuations
E)Irregular fluctuations

Question 58

The high and low values of the "ratios of actuals to moving average" are ignored when finalizing the seasonal index for a period (month or quarter)in time series decomposition.The rationale for this is to ________.

A)reduce the sample size
B)eliminate autocorrelation
C)minimize serial correlation
D)eliminate the irregular component
E)eliminate the trend

Question 59

The forecast value for September was 21.1 and the actual value turned out to be 18.Using exponential smoothing with $\alpha$ = 0.30, the forecast value for October would be ______.

A)18.09
B)18.93
C)20.17
D)21.00
E)17.07

Question 60

The ratios of "actuals to moving averages" (seasonal indexes)for a time series are presented in the following table as percentages. $$\begin{array} { | r | r | r | r | r | r | } \hline & 2008 & 2009 & 2010 & 2011 & 2012 \\\hline Q _ { 1 } & & 112.22 & 110.78 & 111.22 & 111.87 \\\hline Q _ { 2 } & & 100.65 & 108.68 & 103.78 & 101.95 \\\hline Q _ { 3 } & 97.76 & 99.08 & 97.68 & 97.61 & \\\hline Q _ { 4 } & 86.61 & 95.00 & 94.64 & 92.92 & \\\hline\end{array}$$ The final (completely adjusted)estimate of the seasonal index for Q₁ is __________.

A)109.733
B)109.921
C)113.853
D)113.492
E)111.545

Question 61

The effect of a four-quarter moving average on can be described as ______________ the seasonal effects of the data.

A)emphasizing
B)dampening
C)removing
D)incorporating
E)normalizing

Question 62

When constructing a weighted aggregate price index, the weights usually are _____.

A)prices of substitute items
B)prices of complementary items
C)quantities of the respective items
D)squared quantities of the respective items
E)quality of individual items

Question 63

The motivation for using an index number is to ________________.

A)transform the data to a standard normal distribution
B)transform the data for a linear model
C)eliminate bias from the sample
D)reduce data to an easier-to-use, more convenient form
E)reduce the variance in the data

Question 64

If the seasonal index values for four consecutive quarters are 86.3, 105.6, 99.2, and 100, respectively, then which quarter has the most activity compared with the base quarter?

A)Q₁
B)Q₂
C)cannot be determined
D)Q₃
E)Q₄

Question 65

Jim Royo, Manager of Billings Building Supply (BBS), wants to develop a model to forecast BBS's monthly sales (in $1,000's).He selects the dollar value of residential building permits (in $10,000)as the predictor variable.An analysis of the data yielded the following tables. Jim's calculated value for the Durbin-Watson statistic is 1.14.Using $\alpha$ = 0.05, the appropriate decision is: _________.

A)do not reject H₀: $\rho$ = 0
B)reject H₀: $\rho$ = 0
C)do not reject H₀: $\rho$$\neq$ 0
D)the test is inconclusive
E)reject H₀: $\rho$ ≠ 0

Question 66

Index numbers facilitate comparison of ____________.

A)means
B)data over time
C)variances
D)samples
E)deviations

Question 67

Weighted aggregate price indexes are also known as _______.

A)unbalanced indexes
B)balanced indexes
C)value indexes
D)multiplicative indexes
E)overall indexes

Question 68

In an autoregressive forecasting model, the independent variable(s)is (are)______.

A)time-lagged values of the dependent variable
B)first-order differences of the dependent variable
C)second-order, or higher, differences of the dependent variable
D)first-order quotients of the dependent variable
E)time-lagged values of the independent variable

Question 69

Jim Royo, Manager of Billings Building Supply (BBS), wants to develop a model to forecast BBS's monthly sales (in $1,000's).He selects the dollar value of residential building permits (in $10,000)as the predictor variable.An analysis of the data yielded the following tables. Using $\alpha$ = 0.05 the critical value of the Durbin-Watson statistic, d_U, is _________.

A)1.54
B)1.42
C)1.43
D)1.44
E)1.85

Question 70

Jim Royo, Manager of Billings Building Supply (BBS), wants to develop a model to forecast BBS's monthly sales (in $1,000's).He selects the dollar value of residential building permits (in $10,000)as the predictor variable.An analysis of the data yielded the following tables. Jim's calculated value for the Durbin-Watson statistic is 1.93.Using $\alpha$ = 0.05, the appropriate decision is: _________.

A)do not reject H₀: $\rho$ = 0
B)reject H₀: $\rho$ ≠ 0
C)do not reject: $\rho$$\neq$ 0
D)the test is inconclusive
E)reject H₀: $\rho$ = 0

Question 71

Analysis of data for an autoregressive forecasting model produced the following tables. The forecasting model is __________.

A)ŷ_t = 3.745787 + 0.082849y_t-1 + 0.035709y_t-2
B)ŷ_t = 3.85094 + 0.70434y_t-1 - 0.62669y_t-2
C)ŷ_t = 0.84426 - 1.66023y_t-1 + 14.65023y_t-2
D)ŷ_t = 0.34299 + 0.13822y_t-1 + 9.69y_t-2
E)ŷ_t = 0.34299 + 0.13822y_t-1 - 6.69y_t-2

Question 72

Analysis of data for an autoregressive forecasting model produced the following tables. The actual values of this time series, y, were 228, 54, and 191 for May, June, and July, respectively.The forecast value predicted by the model for July is __________.

A)-101.00
B)104.54
C)218.71
D)21.56
E)-77.81

Question 73

Analysis of data for an autoregressive forecasting model produced the following tables. The results indicate that __________.

A)the first predictor, y_t-1, is significant at the 10% level
B)the second predictor, y_t-2, is significant at the 1% level
C)all predictor variables are significant at the 5% level
D)none of the predictor variables are significant at the 5% level
E)the overall regression model is not significant at 5% level

Question 74

Using 2010 as the base year, the 2012 value of a simple price index for the following price data is _____________. $$\begin{array} { | c | c | c | c | c | c | c | } \hline \text { Year} & 2008 & 2009 & 2010 & 2011 & 2012 & 2013 \\\hline \text { Price } & 29,88 & 32.69 & 42.04 & 46.18 & 47,98 & 48.32 \\\hline\end{array}$$

A)77.60
B)114.13
C)160.58
D)99.30
E)100.00

Question 75

Given several years of quarterly data and finding the four quarter moving average from Q₃ of the second year through Q₂ of the third year would be placed on the decomposition table between which two quarters?

A)second year Q₃ and Q₄
B)second year Q₄ and third year Q₂
C)third year Q₁ and Q₂
D)third year Q₂ and Q₃
E)second year Q₄ and third year Q₁

Question 76

A seasonal index for quarterly data is found as the ratio of ____________ to ___________ and is then multiplied by 100.

A)actuals; medians
B)moving average; 8
C)actuals; moving averages
D)actuals; 4
E)100; actuals

Question 77

Analysis of data for an autoregressive forecasting model produced the following tables. The actual values of this time series, y, were 228, 54, and 191 for May, June, and July, respectively.The predicted (forecast)value for August is __________.

A)-101.00
B)104.54
C)218.71
D)21.56
E)-77.81

Question 78

Often, index numbers are expressed as ____________.

A)percentages
B)frequencies
C)cycles
D)regression coefficients
E)correlation coefficients

Question 79

Typically, the denominator used to calculate an index number is a measurement for the ____________ period.

A)base
B)current
C)spanning
D)intermediate
E)peak

Question 80

Jim Royo, Manager of Billings Building Supply (BBS), wants to develop a model to forecast BBS's monthly sales (in $1,000's).He selects the dollar value of residential building permits (in $10,000)as the predictor variable.An analysis of the data yielded the following tables. Using $\alpha$ = 0.05 the critical value of the Durbin-Watson statistic, d_L, is _________.

A)1.24
B)1.22
C)1.13
D)1.15
E)1.85