The matter of time series based on computer prediction usually consists of stationary time series
and non-stationary time series
From the stationary test we found that, the first order difference of the logarithm of the GDP and carbon emissions are stationary time series
Stationary time series
have constant means and variances.
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.
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.
1949), Extrapolation, Interpolation and Smoothing of Stationary Time Series
, Chichester, Wiley.
However, when a shock occurs to a stationary time series
there is a tendency for the series to return to the long-run mean of the series.
Conclusion: In time series modeling of annual groundnut production amounts from the period of 1950-2015, the non-stationary time series
were converted into stationary time series
after taking the first difference of the data.