Deck 14: Introduction to Time Series Regression and Forecasting

Question 1

Departures from stationarity

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

Answer 1

A

Question 2

The Times Series Regression with Multiple Predictors

Answer 2

A

Question 3

Negative autocorrelation in the change of a variable implies that

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

Answer 3

C

Question 4

The random walk model is an example of a

A)deterministic trend model.
B)binomial model.
C)stochastic trend model.
D)stationary model.

Question 5

The Granger Causality Test

Question 6

The forecast is

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 7

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

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 8

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

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 9

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

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

Question 10

Autoregressive distributed lag models include

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.

Question 11

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

A) the error in estimating the coefficients $\beta _ { 0 } \text { and } \beta _ { 1 } \text {. }$
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 12

Problems caused by stochastic trends include all of the following with the exception of

A)the estimator of an AR(1)is biased towards zero if its true value is one.
B)the model can no longer be estimated by OLS.
C)t-statistics on regression coefficients can have a nonnormal distribution, even in large samples.
D)the presence of spurious regression..

Question 13

The first difference of the logarithm of $Y _ { t }$ equals

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 14

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

Question 15

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

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

Question 16

Stationarity means that the

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 17

An autoregression is a regression

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.

Question 18

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

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 19

Time series variables fail to be stationary when

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 20

The AR(p) model

A) is defined as $Y _ { t } = \beta _ { 0 } + \beta _ { p } Y _ { t - p } + u _ { t }$
B) represents $Y _ { t }$ as a linear function of p of its lagged values.
C) can be represented as follows: $Y _ { t } = \beta _ { 0 } + \beta _ { 1 } X _ { t } + \beta _ { p } Y _ { t - p } + u _ { t }$
D) can be written as $Y _ { t } = \beta _ { 0 } + \beta _ { 1 } Y _ { t - 1 } + u _ { t - p }$

Question 21

(a)

Question 22

The Augmented Dickey Fuller (ADF)t-statistic

A)has a normal distribution in large samples.
B)has the identical distribution whether or not a trend is included or not.
C)is a two-sided test.
D)is an extension of the Dickey-Fuller test when the underlying model is AR(p) rather than AR(1).

Question 23

(Requires Appendix material): Show that the AR(1) process
be converted to a process.

Question 24

The following two graphs give you a plot of the United States aggregate unemployment
rate for the sample period 1962:I to 1999:IV, and the (log)level of real United States
GDP for the sample period 1962:I to 1995:IV.You want test for stationarity in both
cases.Indicate whether or not you should include a time trend in your Augmented
Dickey-Fuller test and why.

Question 25

You want to determine whether or not the unemployment rate for the United States has a
stochastic trend using the Augmented Dickey Fuller Test (ADF).The BIC suggests using
3 lags, while the AIC suggests 4 lags.
(a)Which of the two will you use for your choice of the optimal lag length?

Question 26

(a)

Question 27

If a "break" occurs in the population regression function, then

A)inference and forecasting are compromised when neglecting it.
B)an Augmented Dickey Fuller test, rather than the Dickey Fuller test, should be used to test for stationarity.
C)this suggests the presence of a deterministic trend in addition to a stochastic trend.
D)forecasting, but not inference, is unaffected, if the break occurs during the first half of the sample period.

Question 28

(a)Using quarterly data, when analyzing inflation and unemployment in the United States,
the textbook converted log levels of variables into growth rates by differencing the log
levels, and then multiplying these by 400.Given that you have monthly data, how would
you proceed here?

Question 29

Assume that the inflation rate is constant in the long-run and calculate the resulting
unemployment rate.What does the solution represent? Is it reasonable to assume that this
long-run solution is constant over the estimation period 1962-1999? If not, how could
you detect the instability?

Question 30

You have decided to use the Dickey Fuller (DF)test on the United States aggregate
unemployment rate (sample period 1962:I - 1995:IV).As a result, you estimate the
following AR(1)model You recall that your textbook mentioned that this form of the AR(1)is convenient
because it allows for you to test for the presence of a unit root by using the t- statistic of
the slope.Being adventurous, you decide to estimate the original form of the AR(1)
instead, which results in the following output

Question 31

Consider the following model t
where the superscript "e" indicates expected values.This may represent an example
where consumption depended on expected, or "permanent," income.Furthermore, let
expected income be formed as follows: 1
This particular type of expectation formation is called the "adaptive expectations
hypothesis."
(a)

Question 32

Having learned in macroeconomics that consumption depends on disposable income, you
want to determine whether or not disposable income helps predict future consumption.
You collect data for the sample period 1962:I to 1995:IV and plot the two variables.
(a)To determine whether or not past values of personal disposable income growth rates help
to predict consumption growth rates, you estimate the following relationship. The Granger causality test for the exclusion on all four lags of the GDP growth rate is
0.98.Find the critical value for the 1%, the 5%, and the 10% level from the relevant table
and make a decision on whether or not these additional variables Granger cause the
change in the growth rate of consumption.

Question 33

You set out to forecast the unemployment rate in the United States (UrateUS), using
quarterly data from 1960, first quarter, to 1999, fourth quarter.
(a)The following table presents the first four autocorrelations for the United States
aggregate unemployment rate and its change for the time period 1960 (first quarter)to
1999 (fourth quarter).Explain briefly what these two autocorrelations measure.

Question 34

(a)

Question 35

The textbook displayed the accompanying four economic time series with "markedly
different patterns." For each indicate what you think the sample autocorrelations of the
level (Y)and change ( ΔY )will be and explain your reasoning.
(a)

Question 36

You should use the QLR test for breaks in the regression coefficients, when

A)the Chow F-test has a p value of between 0.05 and 0.10.
B)the suspected break data is not known.
C)there are breaks in only some, but not all, of the regression coefficients.
D)the suspected break data is known.