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Why is testing for non-stationarity important in regression analysis?
Why is testing for non-stationarity important in regression analysis?
- Non-stationary variables have finite persistence of shocks, leading to accurate regression analysis.
- Non-stationary variables can lead to spurious regressions with high R2 values, even if the variables are unrelated. (correct)
- Stationary variables always lead to valid hypothesis tests about regression parameters.
- Trending variables do not affect the validity of asymptotic analysis assumptions.
Which model characterizes non-stationarity as a random walk with drift?
Which model characterizes non-stationarity as a random walk with drift?
- $y_t = \mu + y_{t-1} + u_t$ (correct)
- $y_t = \alpha + \beta t^2 + u_t$
- $y_t = \mu + \frac{1}{2}y_{t-1} + u_t$
- $y_t = \alpha + \beta t + u_t$
What happens to the standard assumptions for asymptotic analysis if the variables in a regression model are non-stationary?
What happens to the standard assumptions for asymptotic analysis if the variables in a regression model are non-stationary?
- The standard assumptions for asymptotic analysis will not be valid. (correct)
- The standard assumptions for asymptotic analysis become more accurate.
- The standard assumptions for asymptotic analysis will always hold true.
- The standard assumptions for asymptotic analysis will lead to higher t-ratios.
What is the general form of an explosive process in the given context?
What is the general form of an explosive process in the given context?
What does a value of $\phi > 1$ indicate in the context of non-stationarity?
What does a value of $\phi > 1$ indicate in the context of non-stationarity?
What is required to induce stationarity in the case of deterministic non-stationarity?
What is required to induce stationarity in the case of deterministic non-stationarity?
What is the characteristic of an I(2) series?
What is the characteristic of an I(2) series?
What is the basic objective of testing for a unit root in time series?
What is the basic objective of testing for a unit root in time series?
What does an I(0) series indicate?
What does an I(0) series indicate?
What does an I(1) series indicate?
What does an I(1) series indicate?
What does an I(2) series indicate?
What does an I(2) series indicate?
What are the characteristics of I(0), I(1), and I(2) series?
What are the characteristics of I(0), I(1), and I(2) series?
How do we generalize the concept of a non-stationary series?
How do we generalize the concept of a non-stationary series?
Non-stationary series can lead to spurious regressions, where a regression of one variable on another could have a high R2 even if the two are totally unrelated.
Non-stationary series can lead to spurious regressions, where a regression of one variable on another could have a high R2 even if the two are totally unrelated.
The random walk model with drift is given by the equation $y_t = \mu + y_{t-1} + u_t$ where $u_t$ is an iid process.
The random walk model with drift is given by the equation $y_t = \mu + y_{t-1} + u_t$ where $u_t$ is an iid process.
If the variables in a regression model are not stationary, the standard assumptions for asymptotic analysis will not be valid, and the usual t-ratios will not follow a t-distribution.
If the variables in a regression model are not stationary, the standard assumptions for asymptotic analysis will not be valid, and the usual t-ratios will not follow a t-distribution.
There are two models frequently used to characterize non-stationarity: the random walk model with drift and the deterministic trend process.
There are two models frequently used to characterize non-stationarity: the random walk model with drift and the deterministic trend process.
An I(2) series contains two unit roots and so would require differencing twice to induce stationarity.
An I(2) series contains two unit roots and so would require differencing twice to induce stationarity.
Detrending a stochastic non-stationary series involves differencing the series to induce stationarity.
Detrending a stochastic non-stationary series involves differencing the series to induce stationarity.
The model $y_t = \mu + \phi y_{t-1} + u_t$ characterizes the non-stationarity as an explosive process when $\phi > 1$.
The model $y_t = \mu + \phi y_{t-1} + u_t$ characterizes the non-stationarity as an explosive process when $\phi > 1$.
A series that is integrated of order $d$ is said to be $I(d)$.
A series that is integrated of order $d$ is said to be $I(d)$.
If a non-stationary series $y_t$ must be differenced $d$ times before it becomes stationary, then it is said to be integrated of order $d$.
If a non-stationary series $y_t$ must be differenced $d$ times before it becomes stationary, then it is said to be integrated of order $d$.
The basic objective of testing for a unit root in time series is to test the null hypothesis that $\phi = 1$ in the model $y_t = \phi y_{t-1} + u_t$.
The basic objective of testing for a unit root in time series is to test the null hypothesis that $\phi = 1$ in the model $y_t = \phi y_{t-1} + u_t$.
An I(0) series is a non-stationary series that contains no unit roots and is already stationary.
An I(0) series is a non-stationary series that contains no unit roots and is already stationary.
If $\phi > 1$, shocks to the system are not only persistent through time, they are also propagated, leading to an increasingly large influence.
If $\phi > 1$, shocks to the system are not only persistent through time, they are also propagated, leading to an increasingly large influence.
Consumer prices have been argued to have 2 unit roots, indicating a high degree of non-stationarity.
Consumer prices have been argued to have 2 unit roots, indicating a high degree of non-stationarity.
The majority of economic and financial series contain a single unit root, making them $I(1)$ series.
The majority of economic and financial series contain a single unit root, making them $I(1)$ series.
The second case, $yt = \mu + yt-1 + u_t$, is known as deterministic non-stationarity and requires detrending to induce stationarity.
The second case, $yt = \mu + yt-1 + u_t$, is known as deterministic non-stationarity and requires detrending to induce stationarity.
The first difference operator, $\Delta$, is used to induce stationarity in a non-stationary series.
The first difference operator, $\Delta$, is used to induce stationarity in a non-stationary series.
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