Time-Series Analysis

Question 1

Covariance stationary

Answer 1

A time series is covariance stationary if its mean, variance, and covariances with lagged and leading values do not change over time. Covariance stationarity is a requirement for using AR models. To determine if a time series is covariance stationary, we can run an AR model or perform the Dickey Fuller test.

Question 2

Root mean squared error (RMSE) criterion

Answer 2

Used to compare the accuracy of AR models in forecasting out-of-sample values. The model with the lower square root of the mean squared error (RMSE) for the out-of-sample data will have lower forecast error and will be expected to have better predictive power in the future

Question 3

Random walk time series

Answer 3

The value in one period is equal to the value in another period, plus a random error. A random walk process does not have a mean reverting level and is not stationary.

Question 4

Unit root

Answer 4

A time series has a unit root if the coefficient on the lagged depended variable is 1. A series with a unit root is not covariance stationary. Economic and finance time series frequently have unit roots. Data with a unit root must be first differenced before being used in a time series model.