Testing for Non-Stationarity in Finance
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Questions and Answers

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?

  • $y_t = \mu + y_{t-1} + u_t$ (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?

  • 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?

    <p>$y_t = \mu + \phi y_{t-1} + u_t$ where $\phi &gt; 1$</p> Signup and view all the answers

    What does a value of $\phi > 1$ indicate in the context of non-stationarity?

    <p>Shocks to the system are not only persistent through time, but also propagated to have an increasingly large influence.</p> Signup and view all the answers

    What is required to induce stationarity in the case of deterministic non-stationarity?

    <p>Detrending</p> Signup and view all the answers

    What is the characteristic of an I(2) series?

    <p>It contains two unit roots and would require differencing twice to induce stationarity.</p> Signup and view all the answers

    What is the basic objective of testing for a unit root in time series?

    <p>$\phi = 1$</p> Signup and view all the answers

    What does an I(0) series indicate?

    <p>It is a stationary series.</p> Signup and view all the answers

    What does an I(1) series indicate?

    <p>It contains one unit root and would require differencing once to induce stationarity.</p> Signup and view all the answers

    What does an I(2) series indicate?

    <p>It contains two unit roots and would require differencing twice to induce stationarity.</p> Signup and view all the answers

    What are the characteristics of I(0), I(1), and I(2) series?

    <p>I(2) series contains two unit roots, I(1) series contains one unit root, and I(0) series is stationary.</p> Signup and view all the answers

    How do we generalize the concept of a non-stationary series?

    <p>By considering the case where the series contains more than one 'unit root', requiring more than one application of the first difference operator, $\Delta$, to induce stationarity.</p> Signup and view all the answers

    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.

    <p>True</p> Signup and view all the answers

    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.

    <p>True</p> Signup and view all the answers

    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.

    <p>True</p> Signup and view all the answers

    There are two models frequently used to characterize non-stationarity: the random walk model with drift and the deterministic trend process.

    <p>True</p> Signup and view all the answers

    An I(2) series contains two unit roots and so would require differencing twice to induce stationarity.

    <p>True</p> Signup and view all the answers

    Detrending a stochastic non-stationary series involves differencing the series to induce stationarity.

    <p>True</p> Signup and view all the answers

    The model $y_t = \mu + \phi y_{t-1} + u_t$ characterizes the non-stationarity as an explosive process when $\phi > 1$.

    <p>True</p> Signup and view all the answers

    A series that is integrated of order $d$ is said to be $I(d)$.

    <p>True</p> Signup and view all the answers

    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 $d$.

    <p>True</p> Signup and view all the answers

    The basic objective of testing for a unit root in time series is to test the null hypothesis that $\phi = 1$ in the model $y_t = \phi y_{t-1} + u_t$.

    <p>True</p> Signup and view all the answers

    An I(0) series is a non-stationary series that contains no unit roots and is already stationary.

    <p>False</p> Signup and view all the answers

    If $\phi > 1$, shocks to the system are not only persistent through time, they are also propagated, leading to an increasingly large influence.

    <p>True</p> Signup and view all the answers

    Consumer prices have been argued to have 2 unit roots, indicating a high degree of non-stationarity.

    <p>True</p> Signup and view all the answers

    The majority of economic and financial series contain a single unit root, making them $I(1)$ series.

    <p>False</p> Signup and view all the answers

    The second case, $yt = \mu + yt-1 + u_t$, is known as deterministic non-stationarity and requires detrending to induce stationarity.

    <p>False</p> Signup and view all the answers

    The first difference operator, $\Delta$, is used to induce stationarity in a non-stationary series.

    <p>True</p> Signup and view all the answers

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