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Social and Behavioral Sciences Commons™
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Full-Text Articles in Social and Behavioral Sciences
Nonlinear Regressions With Integrated Time Series, Joon Y. Park, Peter C.B. Phillips
Nonlinear Regressions With Integrated Time Series, Joon Y. Park, Peter C.B. Phillips
Cowles Foundation Discussion Papers
An asymptotic theory is developed for nonlinear regression with integrated processes. The models allow for nonlinear effects from unit root time series and therefore deal with the case of parametric nonlinear cointegration. The theory covers integrable, asymptotically homogeneous and explosive functions. Sufficient conditions for weak consistency are given and a limit distribution theory is provided. In general, the limit theory is mixed normal with mixing variates that depend on the sojourn time of the limiting Brownian motion of the integrated process. The rates of convergence depend on the properties of the nonlinear regression function, and are shown to be as …
Asymptotics For Nonlinear Transformations Of Integrated Time Series, Joon Y. Park, Peter C.B. Phillips
Asymptotics For Nonlinear Transformations Of Integrated Time Series, Joon Y. Park, Peter C.B. Phillips
Cowles Foundation Discussion Papers
An asymptotic theory for stochastic processes generated from nonlinear transformations of nonstationary integrated time series is developed. Various nonlinear functions of integrated series such as ARIMA time series are studied, and the asymptotic distributions of sample moments of such functions are obtained and analyzed. The transformations considered in the paper include a variety of functions that are used in practical nonlinear statistical analysis. It is shown that their asymptotic theory is quite different from that of integrated processes and stationary time series. When the transformation function is exponentially explosive, for instance, the convergence rate of sample functions is path-dependent. In …
Nonstationary Density Estimation And Kernel Autoregression, Peter C.B. Phillips, Joon Y. Park
Nonstationary Density Estimation And Kernel Autoregression, Peter C.B. Phillips, Joon Y. Park
Cowles Foundation Discussion Papers
An asymptotic theory is developed for the kernel density estimate of a random walk and the kernel regression estimator of a nonstationary first order autoregression. The kernel density estimator provides a consistent estimate of the local time spent by the randon walk in the spatial vicinity of a point that is determined in part by the argument of the density and in part by initial conditions. The kernel regression estimator is shown to be consistent and to have a mixed normal limit theory. The limit distribution has a mixing variate that is given by the reciprocal of the local time …