Question 1

To choose the number of lags in either an autoregression or in a time series regression model with multiple predictors, you can use any of the following test statistics with the exception of the

Accepted Answer

A)  F-statistic.
B)  Akaike Information Criterion.
C)  Bayes Information Criterion.
D)  Augmented Dickey-Fuller test. D

Question 2

An autoregression is a regression

Accepted Answer

A)  of a dependent variable on lags of regressors.
B)  that allows for the errors to be correlated.
C)  model that relates a time series variable to its past values.
D)  to predict sales in a certain industry. C

Question 3

Autoregressive distributed lag models include

Accepted Answer

A)  current and lagged values of the error term.
B)  lags of the dependent variable, and lagged values of additional predictor variables.
C)  current and lagged values of the residuals.
D)  lags and leads of the dependent variable. B

Question 4

Pseudo out of sample forecasting can be used for the following reasons with the exception of

Accepted Answer

A)  giving the forecaster a sense of how well the model forecasts at the end of the sample.
B)  estimating the RMSFE.
C)  analyzing whether or not a time series contains a unit root.
D)  evaluating the relative forecasting performance of two or more forecasting models.

Question 5

Time series variables fail to be stationary when

Accepted Answer

A)  the economy experiences severe fluctuations.
B)  the population regression has breaks.
C)  there is strong seasonal variation in the data.
D)  there are no trends.

Question 6

The root mean squared forecast error (RMSFE)is defined as

Accepted Answer

A)    E[∣YT−Y^T∣T−1∣]\sqrt { E \left[ \left| Y _ { T } - \hat { Y } _ { T } \right| _ { T - 1 } \mid \right] }E[c10,0,16.667,-5,20,-15 v-585 v-600 v-585 c-2.667,-10,-9.667,-15,-21,-15c-10,0,-16.667,5,-20,15z M188 15 H145 v585 v600 v585 h43z"/>​YT​−Y^T​c10,0,16.667,-5,20,-15 v-585 v-600 v-585 c-2.667,-10,-9.667,-15,-21,-15c-10,0,-16.667,5,-20,15z M188 15 H145 v585 v600 v585 h43z"/>​T−1​∣]c339.3,-1799.3,509.3,-2700,510,-2702 l0 -0c3.3,-7.3,9.3,-11,18,-11 H400000v40H1017.7s-90.5,478,-276.2,1466c-185.7,988,-279.5,1483,-281.5,1485c-2,6,-10,9,-24,9c-8,0,-12,-0.7,-12,-2c0,-1.3,-5.3,-32,-16,-92c-50.7,-293.3,-119.7,-693.3,-207,-1200c0,-1.3,-5.3,8.7,-16,30c-10.7,21.3,-21.3,42.7,-32,64s-16,33,-16,33s-26,-26,-26,-26s76,-153,76,-153s77,-151,77,-151c0.7,0.7,35.7,202,105,604c67.3,400.7,102,602.7,104,606zM1001 80h400000v40H1017.7z"/>​ 
B)    E[(YT+1−Y^T+1∣T) 2]\sqrt { E \left[ \left( Y _ { T + 1 } - \left. \hat { Y } _ { T + 1 } \right| _ { T } \right)  ^ { 2 } \right] }E[(YT+1​−Y^T+1​c10,0,16.667,-5,20,-15 v-585 v-600 v-585 c-2.667,-10,-9.667,-15,-21,-15c-10,0,-16.667,5,-20,15z M188 15 H145 v585 v600 v585 h43z"/>​T​) 2]c339.3,-1799.3,509.3,-2700,510,-2702 l0 -0c3.3,-7.3,9.3,-11,18,-11 H400000v40H1017.7s-90.5,478,-276.2,1466c-185.7,988,-279.5,1483,-281.5,1485c-2,6,-10,9,-24,9c-8,0,-12,-0.7,-12,-2c0,-1.3,-5.3,-32,-16,-92c-50.7,-293.3,-119.7,-693.3,-207,-1200c0,-1.3,-5.3,8.7,-16,30c-10.7,21.3,-21.3,42.7,-32,64s-16,33,-16,33s-26,-26,-26,-26s76,-153,76,-153s77,-151,77,-151c0.7,0.7,35.7,202,105,604c67.3,400.7,102,602.7,104,606zM1001 80h400000v40H1017.7z"/>​ 
C)    (YT−Y^T∣T−1) 2\sqrt { \left( Y _ { T } - \left. \hat { Y } _ { T } \right| _ { T - 1 } \right)  ^ { 2 } }(YT​−Y^T​c10,0,16.667,-5,20,-15 v-585 v-600 v-585 c-2.667,-10,-9.667,-15,-21,-15c-10,0,-16.667,5,-20,15z M188 15 H145 v585 v600 v585 h43z"/>​T−1​) 2c339.3,-1799.3,509.3,-2700,510,-2702 l0 -0c3.3,-7.3,9.3,-11,18,-11 H400000v40H1017.7s-90.5,478,-276.2,1466c-185.7,988,-279.5,1483,-281.5,1485c-2,6,-10,9,-24,9c-8,0,-12,-0.7,-12,-2c0,-1.3,-5.3,-32,-16,-92c-50.7,-293.3,-119.7,-693.3,-207,-1200c0,-1.3,-5.3,8.7,-16,30c-10.7,21.3,-21.3,42.7,-32,64s-16,33,-16,33s-26,-26,-26,-26s76,-153,76,-153s77,-151,77,-151c0.7,0.7,35.7,202,105,604c67.3,400.7,102,602.7,104,606zM1001 80h400000v40H1017.7z"/>​ 
D)    E[(YT−Y^T∣T−1) ]\sqrt { E \left[ \left( Y _ { T } - \left. \hat { Y } _ { T } \right| _ { T - 1 } \right)  \right] }E[(YT​−Y^T​c10,0,16.667,-5,20,-15 v-585 v-600 v-585 c-2.667,-10,-9.667,-15,-21,-15c-10,0,-16.667,5,-20,15z M188 15 H145 v585 v600 v585 h43z"/>​T−1​) ]c339.3,-1799.3,509.3,-2700,510,-2702 l0 -0c3.3,-7.3,9.3,-11,18,-11 H400000v40H1017.7s-90.5,478,-276.2,1466c-185.7,988,-279.5,1483,-281.5,1485c-2,6,-10,9,-24,9c-8,0,-12,-0.7,-12,-2c0,-1.3,-5.3,-32,-16,-92c-50.7,-293.3,-119.7,-693.3,-207,-1200c0,-1.3,-5.3,8.7,-16,30c-10.7,21.3,-21.3,42.7,-32,64s-16,33,-16,33s-26,-26,-26,-26s76,-153,76,-153s77,-151,77,-151c0.7,0.7,35.7,202,105,604c67.3,400.7,102,602.7,104,606zM1001 80h400000v40H1017.7z"/>​

Question 7

Stationarity means that the

Accepted Answer

A)  error terms are not correlated.
B)  probability distribution of the time series variable does not change over time.
C)  time series has a unit root.
D)  forecasts remain within 1.96 standard deviation outside the sample period.

Question 8

The time interval between observations can be all of the following with the exception of data collected

Accepted Answer

A)  daily.
B)  by decade.
C)  bi-weekly.
D)  across firms.

Question 9

In order to make reliable forecasts with time series data, all of the following conditions are needed with the exception of

Accepted Answer

A)  coefficients having been estimated precisely.
B)  the regression having high explanatory power.
C)  the regression being stable.
D)  the presence of omitted variable bias.

Question 10

The first difference of the logarithm of Yt equals

Accepted Answer

A)  the first difference of Y.
B)  the difference between the lead and the lag of Y.
C)  approximately the growth rate of Y when the growth rate is small.
D)  the growth rate of Y exactly.

Question 11

The forecast is

Accepted Answer

A)  made for some date beyond the data set used to estimate the regression.
B)  another word for the OLS predicted value.
C)  equal to the residual plus the OLS predicted value.
D)  close to 1.96 times the standard deviation of Y during the sample.

Question 12

Negative autocorrelation in the change of a variable implies that

Accepted Answer

A)  the variable contains only negative values.
B)  the series is not stable.
C)  an increase in the variable in one period is, on average, associated with a decrease in the next.
D)  the data is negatively trended.

Question 13

The Granger Causality Test

Accepted Answer

A)  uses the F-statistic to test the hypothesis that certain regressors have no predictive content for the dependent variable beyond that contained in the other regressors.
B)  establishes the direction of causality (as used in common parlance) between X and Y in addition to correlation.
C)  is a rather complicated test for statistical independence.
D)  is a special case of the Augmented Dickey-Fuller test.

Question 14

The Times Series Regression with Multiple Predictors

Accepted Answer

A)  is the same as the ADL(p,q) with additional predictors and their lags present.
B)  gives you more than one prediction.
C)  cannot be estimated by OLS due to the presence of multiple lags.
D)  requires that the k regressors and the dependent variable have nonzero, finite eighth moments.

Question 15

One reason for computing the logarithms (ln), or changes in logarithms, of economic time series is that

Accepted Answer

A)  numbers often get very large.
B)  economic variables are hardly ever negative.
C)  they often exhibit growth that is approximately exponential.
D)  natural logarithms are easier to work with than base 10 logarithms.

Question 16

One of the sources of error in the RMSFE in the AR(1)model is

Accepted Answer

A)  the error in estimating the coefficients β0 and β1.
B)  due to measuring variables in logarithms.
C)  that the value of the explanatory variable is not known with certainty when making a forecast.
D)  the model only looks at the previous period's value of Y when the entire history should be taken into account.

Question 17

The jth autocorrelation coefficient is defined as

Accepted Answer

A)    cov⁡(Yt,Yt−1) var⁡(YJ) var⁡(Yt−1) \frac { \operatorname { cov } \left( Y _ { t } , Y _ { t } - 1 \right)  } { \sqrt { \operatorname { var } \left( Y _ { J } \right)  \operatorname { var } \left( Y _ { t } - 1 \right)  } }var(YJ​) var(Yt​−1) 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"/>​cov(Yt​,Yt​−1) ​ 
B)    cov⁡(Yt,Yt−j−1) var⁡(Yt) var⁡(Yt−j) \frac { \operatorname { cov } \left( Y _ { t } , Y _ { t } - j - 1 \right)  } { \sqrt { \operatorname { var } \left( Y _ { t } \right)  \operatorname { var } \left( Y _ { t - j } \right)  } }var(Yt​) var(Yt−j​) 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"/>​cov(Yt​,Yt​−j−1) ​ 
C)    cov⁡(Yt,ut) var⁡(Yt) var⁡(ut) \frac { \operatorname { cov } \left( Y _ { t } , u _ { t } \right)  } { \sqrt { \operatorname { var } \left( Y _ { t } \right)  \operatorname { var } \left( u _ { t } \right)  } }var(Yt​) var(ut​) 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"/>​cov(Yt​,ut​) ​ 
D)    cov⁡(Yt,Yt−j) var⁡(Yt) var⁡(Yt−j) \frac { \operatorname { cov } \left( Y _ { t } , Y _ { t } - j \right)  } { \sqrt { \operatorname { var } \left( Y _ { t } \right)  \operatorname { var } \left( Y _ { t - j } \right)  } }var(Yt​) var(Yt−j​) 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"/>​cov(Yt​,Yt​−j) ​

Question 18

The ADL(p,q)model is represented by the following equation

Accepted Answer

A)  Yt = β0 + βpYt-p + δqXt-q + ut.
B)  Yt = β0 + β1Yt-1 + β2Yt-2 + ... + βpYt-p + δqut-q.
C)  Yt = β0 + β1Yt-1 + β2Yt-2 + ... + βpYt-p + δ0 + δ1Xt-1 + ut-q.
D)  Yt = β0 + β1Yt-1 + β2Yt-2 + ... + βpYt-p + δ1Xt-1 + δ2Xt-2 + ... + δqXt-q + ut.

Question 19

The AR(p)model

Accepted Answer

A)  is defined as Yt = β0 + βpYt-p + ut.
B)  represents Yt as a linear function of p of its lagged values.
C)  can be represented as follows: Yt = β0 + β1Xt + βpYt-p + ut.
D)  can be written as Yt = β0 + β1Yt-1 + ut-p.

Question 20

Departures from stationarity

Accepted Answer

A)  jeopardize forecasts and inference based on time series regression.
B)  occur often in cross-sectional data.
C)  can be made to have less severe consequences by using log-log specifications.
D)  cannot be fixed.

Exam 14: Introduction to Time Series Regression and Forecasting

To choose the number of lags in either an autoregression or in a time series regression model with multiple predictors, you can use any of the following test statistics with the exception of the

An autoregression is a regression

Autoregressive distributed lag models include

Pseudo out of sample forecasting can be used for the following reasons with the exception of

Time series variables fail to be stationary when

The root mean squared forecast error (RMSFE) is defined as

Stationarity means that the

The time interval between observations can be all of the following with the exception of data collected

In order to make reliable forecasts with time series data, all of the following conditions are needed with the exception of

The first difference of the logarithm of Y_t equals

The forecast is

Negative autocorrelation in the change of a variable implies that

The Granger Causality Test

The Times Series Regression with Multiple Predictors

One reason for computing the logarithms (ln) , or changes in logarithms, of economic time series is that

One of the sources of error in the RMSFE in the AR(1) model is

The j^th autocorrelation coefficient is defined as

The ADL(p,q) model is represented by the following equation

The AR(p) model

Departures from stationarity