Conditional and Marginal Mutual Information in Gaussian and Hyperbolic Decay Time Series
研究了高斯随机过程中未来状态的可预测性，推导了边际互信息和条件互信息的无穷级数表达式，并应用于长记忆模型，刻画了从持续性到反持续性、平稳长记忆到非平稳等转变的信息论特征。
We consider the amount of available information about an arbitrary future state of a Gaussian stochastic process. We derive an infinite series for the marginal mutual information in terms of the autocorrelation function. We derive an infinite series for the newly available information for prediction, the conditional mutual information, in terms of the moving average parameters, and directly characterize predictability in terms of sensitivity to random shocks. We apply our results to long memory, or more generally, hyperbolic decay models, and give information‐theoretic characterizations of the transition from persistence to anti‐persistence, stationary long memory to nonstationarity, and a stationary regime where the mutual information is not summable.