An augmented Dickey–Fuller test can be applied to time series to determine whether they are covariance stationary The estimated partial autocorrelation of a covariance stationary time series can be used to identify the design sequence length in a plain recurrent neural network.  Plain recurrent neural networks are guaranteed to be stable, namely lagged unit impulses decay over time.  The Ljung–Box test is used to test whether the fitted model residual error is autocorrelated.  The half-life of a lag-1 unit impulse is the number of lags before the impulse has half its effect on the model output.