Smoothing Estimation of Stochastic Processes. Part II. Two Filter Formulae.
Techanical summary rept.,
WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER
Pagination or Media Count:
In this article these two-filter results and some new ones are derived in a simple way in a very general setting for arbitrary nonstationary processes. It turns out however that only if a wide-sense i.e. second order Markovian assumption is added can one of the filters be viewed as a backwards filter. The remainder of the paper is organized as follows. Section 2 recalls some smoothing formulae that apply to both continuous and discrete observations. Section 3 discusses two types of two-filter-like formulae for general nonstationary processes. In Section 4 one of the filters is shown to be a backwards least squares estimate provided a wide sense Markovian assumption is satisfied. Section 5 contains a derivation of some backwards filters. In Section 6 some additional two-filter-like formulae are given. The final section is a conlusion.
- Statistics and Probability