基于周期指数多项式逼近的有限记忆预测器
Limited memory predictors based on polynomial approximation of periodic exponents
摘要：
本文给出了连续时间过程有限记忆时不变线性积分预测器的传递函数，使得相应的预测核具有有界支持。结果表明，指数衰减傅立叶变换的过程是可预测的，这些预测在某种弱意义上，这意味着卷积积分在未来的时间可以近似因果卷积在过去的时间。对于给定的预测范围，预测器是基于加权$L_2$空间中的周期指数（复正弦曲线）的多项式近似。
英文摘要：
The paper presents transfer functions for limited memory time-invariant linear integral predictors for continuous time processes such that the corresponding predicting kernels have bounded support. It is shown that processes with exponentially decaying Fourier transforms are predictable with these predictors in some weak sense, meaning that convolution integrals over the future times can be approximated by causal convolutions over past times. For a given predicting horizon, the predictors are based on polynomial approximation of a periodic exponent (complex sinusoid) in a weighted $L_2$-space.
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