Recognition of time series based on the noise reduction by using the adaptive filters and the Hidden Markov model and its applications

摘要

For the recognition of time series with colored noise based on the Hidden Markov Model, some extension of ordinary HMM is discussed, but are bearing some problem, since in these methods the number of states increase exponentially, and sometime become untractable. Previpously, we proposed a noise reduction by using the adaptive filters, and then utilize conventional HMM procedure. In the report, we propose a hierarchical HMM for the recognition of economic time series based on the noise reduction. At first, the innovation is generated by using a prediction filter, and then we identify the noise assuming that the noise-less signal is mixed to noise using the adaptive filters. HMM which occurs in the inverse filtering. Catogirized symbols by the first stage of the HMM are delivered to the second stage of the HMM for the recognition of economic time series.