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Why is testing for non-stationarity important in regression analysis?
Why is testing for non-stationarity important in regression analysis?
Which model characterizes non-stationarity as a random walk with drift?
Which model characterizes non-stationarity as a random walk with drift?
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?
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?
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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?
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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?
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What is the characteristic of an I(2) series?
What is the characteristic of an I(2) series?
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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?
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What does an I(0) series indicate?
What does an I(0) series indicate?
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What does an I(1) series indicate?
What does an I(1) series indicate?
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What does an I(2) series indicate?
What does an I(2) series indicate?
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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?
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How do we generalize the concept of a non-stationary series?
How do we generalize the concept of a non-stationary series?
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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.
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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.
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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.
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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.
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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.
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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.
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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 $\phi > 1$.
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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 $I(d)$.
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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 $d$.
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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 $y_t = \phi y_{t-1} + u_t$.
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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.
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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.
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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.
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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.
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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.
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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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