Because the regression approach can be used only for stationary time series
, stationarity of the time series is tested (Hill et al.
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.
Stationary time series
have constant means and variances.
The use of this method is restricted when we want to analyse stationary time series
(the ones which are not changeable in an analysed time).
It is in this sense that econometricians call models based on non stationary time series
"spurious regression" (see among others, Engle and Granger 1987; loannidis et al.
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.
Similar in format to the stationary time series
example, the plot above is a composite of four subplots that show the results of production levelling with a lead time, N, of 10 time periods for the nonstationary series that was previously plotted.
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.
(1995), 'Effects of the Hodrick-Prescott filter on trend and difference stationary time series
: implications for business cycle research', Journal of Economic Dynamics and Control, 19, 1-2, pp.