Nonparametric Estimation of a Class of Nonlinear Time Series Models
The problem of estimation of nonlinear time series models which are a composition of nonlinear elements and linear stochastic processes is considered. The compositions studied include the cascade and parallel connections. The problem of nonparametric estimation of underlying nonlinearities is examined. It is resolved by solving Fredholm’s integral equations of the second kind arising in the estimation problem. As a result, the nonparametric orthogonal series estimates of nonlinearities are derived and their asymptotic as well as some small sample properties are established.
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