Time Series Econometrics Exam 2 Important Questions With Multiple Choices And Verified Answers.

*All stationary processes are I(0) but not all I(0) processes are stationary* - correct answer *All stationary processes are I(0) but not all I(0) processes are stationary* Unit root - correct answer A feature of some stochastic processes (such as random walks) that can cause problems in statistical inference involving time series models. A linear stochastic process has a unit root if 1 is a root of the process's characteristic equation. Such a process is non-stationary but does not always have a trend Random walk - correct answer A stochastic or random process, that describes a path that consists of a succession of random steps on some mathematical space such as the integers Spurious regression - correct answer A regression that provides misleading statistical evidence of a linear relationship between independent non-stationary variables. In fact, the non-stationarity may be due to the presence of a unit root in both variables Trend stationary - correct answer If an underlying trend (function solely of time) can be removed, leaving a stationary process Difference stationary (data has stochastic trend) - correct answer If the process requires differencing to be made stationary *If a process is difference stationary then it possesses one or more unit roots* - correct answer *If a process is difference stationary then it possesses one or more unit roots* *It is possible for a time series to be non-stationary, yet have no unit root and be trend-stationary (not common though)* - correct answer *It is possible for a time series to be non-stationary, yet have no unit root and be trend-stationary (not common though)* Dickey-Fuller test - correct answer Tests the null hypothesis that a unit root is present in an autoregressive model. The alternative hypothesis is different depending on which version of the test is used, but is usually stationarity or trend-stationarity Why perform a Dickey-Fuller test? - correct answer To test for stationarity How do you test for stationarity? - correct answer A Dickey-Fuller test What are we looking for in a Dickey-Fuller test? - correct answer A unit root What is a drift (for a random walk) - correct answer A slow steady change Deterministic trends - correct answer Trends that are constant, positive or negative, independent of time for the whole life of the series Examples of Non-Stationary Processes - correct answer random walk with or without a drift and deterministic trends Non-stationary data - correct answer Have means, variances and covariances that change over time. Non-stationary behaviors can be trends, cycles, random walks or combinations of the three *useful unit root tests will manage to tell deterministic time trends apart from stochastic ones to generate decompositions of a series {Yt} in the stochastic trend versus time trend stationary components* - correct answer *useful unit root tests will manage to tell deterministic time trends apart from stochastic ones to generate decompositions of a series {Yt} in the stochastic trend versus time trend stationary components* Stochastic trend equivalent to... - correct answer RW with drift process Deterministic trends (TEXTBOOK) - correct answer Functions of time Stochastic trends (TEXTBOOK) - correct answer Equivalent to saying RW with drift process - Which is: If the random walk model predicts that the value at time "t" will equal the last period's value plus a constant, or drift (α), and a white noise term (εt), then the process is random walk with a drift. It also does not revert to a long-run mean and has variance dependent on t