Question 1

A stochastic process is best described as
A)deterministic
B)theoretical
C)random
D)mean reverting

Accepted Answer

A stochastic process is a mathematical model used to describe random or probabilistic events. Therefore, it is best described as random.

Question 2

What is the null hypothesis of the Dickey-Fuller Test 2?
A)the series is non-stationary over time
B)the series is stationary
C)the series is first order integrated
D)the series are cointegrated

Accepted Answer

The null hypothesis of the Dickey-Fuller test 2 is that the series is non-stationary over time, meaning it has a unit root. The alternative hypothesis is that the series is stationary, meaning it does not have a unit root.

Question 3

An ARDL model with nonstationary variables is a(n)
A)error correction model
B)VEC
C)VAR
D)variance decomposition

Accepted Answer

An ARDL model with nonstationary variables is an error correction model, which is used to estimate equilibrium relationships between nonstationary variables. The error correction term represents the speed at which the system corrects deviations from the long-run equilibrium relationship. VEC (vector error correction) and VAR (vector autoregression) are also models for analyzing time series data, but they require stationary variables. Variance decomposition is a method for decomposing the forecast error variance of a time series into contributions from various sources.

Question 4

What is the difference between the Dickey-Fuller Tests 1,2,and 3?
A)they test for stationarity around zero,stationarity around a constant,and stationarity around a trend line,respectively
B)they test $\rho$<1,$\rho$>1,and $\rho$=1,respectively
C)they use t, $ \tau $,and F tests,respectively
D)they test for integration of orders 1,2 and 3 respectively.

Accepted Answer

The Dickey-Fuller tests 1, 2, and 3 test for stationarity around zero, stationarity around a constant, and stationarity around a trend line, respectively.

Question 5

Why should augmented Dickey-Fuller tests always be used when performing econometric analysis?
A)the augmented tests allow for more degrees of freedom
B)so we can test hypotheses using a t-distribution
C)since no assumptions about the sign of $\rho$ are needed to perform a one-tailed test
D)to confirm that error terms are not autocorrelated

Accepted Answer

Augmented Dickey-Fuller tests are used to test for stationarity in time series data. Stationarity is an important assumption for many econometric analyses, as it ensures that the error terms are not autocorrelated. Therefore, it is important to use augmented Dickey-Fuller tests to confirm stationarity and avoid biased and inaccurate results.

Question 6

Which of the following is a common way to convert a nonstationary series to a stationary series?
A)first differencing
B)cointegrating
C)running a spurious regression
D)estimating distributed lags

Accepted Answer

First differencing is a common way to remove the trend and convert a nonstationary series to a stationary series. Differencing can make the series stationary by eliminating the trend and reducing the effect of seasonality or other time-dependent patterns.

Question 7

What is the null hypothesis of the Dickey-Fuller Test 2?
A)the series is non-stationary over time
B)the series is stationary
C)the series is first order integrated
D)the series are cointegrated

Accepted Answer

The null hypothesis of the Dickey-Fuller Test 2 is that the series is non-stationary over time. The alternative hypothesis is that the series is stationary.

Question 8

What does it mean for a series to have a unit root?
A)it has a constant mean equal to 1
B)it has a constant variance equal to 1
C)it is stationary
D)it is integrated of order 1

Accepted Answer

The answer of What does it mean for a series...

Question 9

The minimum number of times a series must be differenced to generate a stationary series is the
A)unit root
B)order of integration
C)trend coefficient
D)spurious regression degree

Accepted Answer

The order of integration, also known as the degree of differencing, represents the minimum number of times a series must be differenced to make it stationary. A stationary series has a constant mean and variance over time, making it easier to model and analyze. If a series is not stationary and contains a unit root, it must be differenced to remove the non-stationary component.

Question 10

Which of the following is a common way to convert a nonstationary series to a stationary series?
A)detrending
B)autoregression
C)estimating distributed lags
D)cointegrating

Accepted Answer

Detrending involves removing any trend or drift in the data, which can make the series stationary. Autoregression, estimating distributed lags, and cointegrating may also be used in certain cases, but detrending is a common and straightforward method for achieving stationarity.

Question 11

Which of the following is not a necessary condition for a variable to be stationary? A)E(y_t)= $\mu$ B)var(y_t)= $\sigma$ ² C)cov(y_t,y_t+s)= cov(y_t,y_t-s)= $\gamma$_s D)E(y_t - y_t-1)= $\pi$

Accepted Answer

The correct answer is D because a necessary condition for a variable to be stationary is that its statistical properties (mean, variance, and autocovariance) do not depend on time. Conditions A, B, and C relate to the mean, variance, and autocovariance being constant over time, which are necessary for stationarity. However, D, which implies a constant change in the variable over time, is not a necessary condition for stationarity. Stationarity does not require the differences between consecutive observations to be constant.

Question 12

What is the null hypothesis of the Dickey-Fuller Test 1?
A)the series is non-stationary over time
B)the series is stationary
C)the series is first order integrated
D)the series are cointegrated

Accepted Answer

The null hypothesis of the Dickey-Fuller Test is that the series is non-stationary over time. If the test fails to reject the null hypothesis, it is concluded that the series is non-stationary and further analysis is required to determine if it can be transformed to a stationary series.

Question 13

If series y and z have similar stochastic trends,but are otherwise unrelated,they are said to be
A)cointegrated
B)cotrending
C)converging
D)jointly stationary

Accepted Answer

If two series have similar stochastic trends, they may still have a long-term relationship or equilibrium that keeps them from drifting too far apart. This is known as cointegration. The other options are not applicable in this case.

Question 14

Which non-stationary time series has a constant mean but non-constant variance?
A)random walk
B)AR(1)with linear trent
C)random walk with drift
D)deterministic trend

Accepted Answer

The answer of Which non-stationary time series has a constant...

Question 15

How do you find the first difference in y_t? A)y_t- y_t-1 B)dy/ dt C)y_t - D)(y_t - ²

Accepted Answer

To find the first difference in y_t, we need to subtract the previous value of y_t i.e. y_t-1. Hence, option A, y_t- y_t-1, is the correct answer.

Question 16

What is a spurious regression?
A)statistically significant but meaningless results generated by regression analysis of non-stationary data
B)the results generated by regression analysis of a station variable dependent on a non-stationary series
C)regression analysis where endogenous and exogenous variables are reversed
D)regression analysis that is impossible due to lack of identification

Accepted Answer

A spurious regression occurs in a situation where there appears to be a significant relationship between two variables in a regression model, but in reality, there is no causal relationship between the variables. This happens when both variables are non-stationary, meaning that they both have a trend or a random walk component. Since both variables are trending upward over time, for example, we might see a very high correlation between them even though they are not actually related. Thus a spurious regression is essentially statistically significant but meaningless results generated by regression analysis of non-stationary data.

Quiz 13: Regression With Time Series Data: Nonstationary Variables

A stochastic process is best described as

What is the null hypothesis of the Dickey-Fuller Test 2?

An ARDL model with nonstationary variables is a(n)

What is the difference between the Dickey-Fuller Tests 1,2,and 3?

Why should augmented Dickey-Fuller tests always be used when performing econometric analysis?

Which of the following is a common way to convert a nonstationary series to a stationary series?

What is the null hypothesis of the Dickey-Fuller Test 2?

What does it mean for a series to have a unit root?

The minimum number of times a series must be differenced to generate a stationary series is the

Which of the following is a common way to convert a nonstationary series to a stationary series?

Which of the following is not a necessary condition for a variable to be stationary?

What is the null hypothesis of the Dickey-Fuller Test 1?

If series y and z have similar stochastic trends,but are otherwise unrelated,they are said to be

Which non-stationary time series has a constant mean but non-constant variance?

How do you find the first difference in yt?

What is a spurious regression?

How do you find the first difference in y_t?