Time Series Analysis

Question 1

A time series

Answer 1

set of observations for a variable over time

Question 2

time series model

Answer 2

captures the time-series pattern and allows us to make predictions about the variable in the future.

Question 3

primary limitation of trend models

Answer 3

not useful if the residuals exhibit serial correlation.

Question 4

autoregressive model (AR)

Answer 4

dependent variable is regressed against one or more lagged values of itself

Question 5

dependent variable is regressed against one or more lagged values of itself

Answer 5

time series being modeled is covariance stationary

Question 6

A time series is covariance stationary if it satisfies the following three conditions:

Answer 6

 1- Constant and finite expected value.
 2- Constant and finite variance.
 3- Constant and finite covariance

Question 7

one-period-ahead forecast for an AR(1) model

Answer 7

xt+1=b0+b1xt

Question 8

two-step-ahead forecast for an AR(1) model

Answer 8

xt+2=b0+b1xt+1

Question 9

When an AR model is correctly specified, the residual terms

Answer 9

will not exhibit serial correlation

Question 10

Serial correlation (or autocorrelation) means the error terms

Answer 10

positively or negatively correlated.

Question 11

When the error terms are correlated

Answer 11

standard errors are unreliable and t-tests can incorrectly show statistical significance or insignificance.

Question 12

mean reversion

Answer 12

tendency to move toward its mean

Question 13

mean reversion formula

Answer 13

xt=b0(1−b1)

Question 14

root mean squared error(RMSE)

Answer 14

accuracy of autoregressive models in forecasting out-of-sample values

Question 15

lower RMSE for the out-of-sample data

Answer 15

lower forecast error and will be expected to have better predictive power in the future.

Question 16

The procedure to test whether an AR time-series model is correctly specified involves three steps:

Answer 16

1-Estimate the AR model being evaluated using linear regression.
2-Calculate the autocorrelations of the model’s residuals.
3-Test whether the autocorrelations are significant.

Question 17

Random Walk

Answer 17

the predicted value equals the value of the series in the previous period plus a random error term.

Question 18

random walk equation

Answer 18

xt = xt–1 + εt

Question 19

Random Walk with a Drift Equation

Answer 19

xt = b0 + b1xt–1 + εt

Question 20

Random Walk with a Drift

Answer 20

the intercept term is not equal to zero.

Question 21

Neither a random walk nor a random walk with a drift exhibits

Answer 21

covariance stationarity

Question 22

a random walk, with or without a drift, exhibits

Answer 22

unit root (b1 = 1).

Question 23

A time series has a unit root if

Answer 23

the coefficient on the lagged dependent variable is equal to one.

Question 24

To determine whether a time series is covariance stationary

Answer 24

(1) run an AR model and examine autocorrelations, or
(2) perform the Dickey Fuller test.

Question 25

first differencing

Answer 25

If we believe a time series is a random walk (i.e., has a unit root), we can transform the data to a covariance stationary using first differencing

Question 26

Seasonality in a time series is tested by

Answer 26

calculating the autocorrelations of error terms.

Question 27

autoregressive conditional heteroskedasticity (ARCH)

Answer 27

problem associated with the correlation of variances of the error terms

Question 28

autoregressive conditional heteroskedasticity (ARCH) exists if

Answer 28

the variance of the residuals in one period is dependent on the variance of the residuals in a previous period

Question 29

he ARCH(1) regression model is expressed as:

Answer 29

ε2t =a0+a1ˆε2t−1+μt If a1, is statistically different from zero, the time series is ARCH(1).

Question 30

ARCH model can be used to predict the variance of the residuals in future periods

Answer 30

σ2t+1=a0+a1ε2t

Question 31

Cointegration

Answer 31

means that two time series are economically linked or follow the same trend and that relationship is not expected to change

Question 32

To test whether two time series are cointegrated

Answer 32

(1) if neither time series has a unit root, then the regression can be used; (2) if only one series has a unit root, the regression results will be invalid; (3) if both time series have a unit root and are cointegrated, then the regression can be used; (4) if both time series have a unit root but are not cointegrated, the regression results will be invalid.

Question 33

to determine whether two times series are cointegrated.

Answer 33

Dickey Fuller test with critical t-values is used

Question 34

RMSE equals

Answer 34

the square root of the average squared error.