Chapter 7, the first in the two-chapter sequence regarding time series, begins with the most basic time series models, namely, those univariate models employed when working with stationary time series
In our study, time series is stationary time series
implying no change over time in variance, and autocorrelation structure.
After an introduction to stationarity and an analysis of stationary time series
from both the time and frequency domains, the text covers topics such as linear filters, various stationary and non-stationary time series
models, and wavelets.
The Box--Jenkins Methodology is valid for only stationary time series
That means that stationary time series
are produced by means of the first or second differencing.
A stationary time series
is significant to a regression analysis based on the time series, because useful information or characteristics are difficult to identify in a nonstationary time series.
Topics include pile-up probabilities for the Laplace likelihood estimator of a non-vertible first order moving average, prediction errors in regression models with non-stationary regressors, forecasting unstable processes, determining order in general vector autoregressions, conditional-sum-of-squares estimation of models for stationary time series
with long memory, modeling macroeconomic time series via heavy tailed distributions, estimation errors in the Sharpe ratio for long-memory stochastic volatility, and multivariate volatility models.