Time Series Econometrics Exam 1 Stationary: Practice Questions And Answers 100% Pass.

stationary - correct answer if its statistical properties do not change over time strictly stationary - correct answer if the joint distribution of the variable associated to any subsequence of times is the same as the joint distribution of the sequence of all times weakly stationary (covariance stationary) - correct answer if it has time invariant first and second moments strict stationarity requires that all the moments of the distribution are time invariant (weaker form of stationarity does not) - correct answer strict stationarity requires that all the moments of the distribution are time invariant (weaker form of stationarity does not) white noise process (textbook) - correct answer a sequence of random variables {Zt} with mean equal to 0, constant variance equal to sigma squared, and zero autocovariances (and autocorrelations) except at lag 0. If {Zt} is normally distributed, we shall speak of a Gaussian WN time series - correct answer any object that is observed over time, usually at regularly spaced intervals frequency - correct answer how many observations in a given time period high frequency - correct answer lots of observations per year low frequency - correct answer less observations per year microstructure noise - correct answer frequency of 6 minutes or less Assumtion 1 of a time series - correct answer a time series has been around forever and will continue to be around forever. - no initial or end conditions to worry about stochastic process - correct answer a collection of random variables indexed by time strongly (strictly) stationary - correct answer if a process is nth order stationary for all n = 1 to infinity - we will use a weaker definition of stationarity strict stationarity implies weak stationarity - correct answer strict stationarity implies weak stationarity white noise process (notes) - correct answer a process such that: - E(et) = E(es) = 0 for all s not equal to t - gamma_k = gamma_0 for k = 0 - gamma_k = 0 for k not equal to 0 gaussian (normal) white noise (notes) - correct answer - et normally distributed (with mean 0) - gamma_k = 0 for k not equal to 0 autocorrelation function of a process - correct answer can be used to describe the dependence structure of that process for any process the ACF is unique - correct answer for any process the ACF is unique partial autocorrelation function (PACF) - correct answer measures the linear dependence between Yt and Yt-k conditional on Yt-1,...,Yt-k+1 the PACF is unique - correct answer the PACF is unique "ergodic" in the mean - correct answer if a process is second order weakly stationary and p_k goes to 0 as k goes to infinity wold representation - correct answer any stationary time series can be uniquely represented as an infinite sum of a white noise process the wold representation is referred to as the MA(infinity) representation. (impulse response = MA(infinity)) - correct answer the wold representation is referred to as the MA(infinity) representation. (impulse response = MA(infinity)) Box-Jenkins - correct answer - pick the "best" model while minimizing p + q - pick the most parsimonious model! the likelihood function - correct answer L(Y^T; model) = joint probability of observing Y^T conditional on our model