Estimating the Lag Structure of a Nonlinear Time Series Model
Melvin J. Hinich · Journal of the American Statistical Association · 1979
Suppose that the time series {Y(t)} is the output of a linear plus quadratic filter observed with additive noise. The relationship is a second-order approximation to a nonlinear distributed lag model. Assume that the input to the filter {X(t)} is a stationary Gaussian process. This article presents a relatively simple procedure for determining the values of the parameters of the quadratic filter by using the sample cross bispectrum between the two series. The asymptotic properties of the parameter estimates are derived when the spectrum of {X(t)} is known. Artificial data results are presented.