Nonparametric Density Estimation, Prediction, and Regression for Markov Sequences
研究了在马尔可夫序列假设下，用非参数方法估计转移密度和条件期望，发现其收敛速度与独立同分布情形相同，且可放宽假设，为ARMA模型提供了替代方案。
Abstract Let {Xi } be a stationary Markov sequence having a transition probability density function f(y | x) giving the pdf of X i +1 | (Xi = x). In this study, nonparametric density and regression techniques are employed to infer f(y | x) and m(x) = E[X i + 1 | Xi = x]. It is seen that under certain regularity and Markovian assumptions, the asymptotic convergence rate of the nonparametric estimator mn (x) to the predictor m(x) is the same as it would have been had the Xi 's been independently and identically distributed, and this rate is optimal in a certain sense. Consistency can be maintained after differentiability and even the Markovian assumptions are abandoned. Computational and modeling ramifications are explored. I claim that my methodology offers an interesting alternative to the popular ARMA approach.