Strong consistency of the distribution estimator in the nonlinear autoregressive time series. (English) Zbl 1343.62056
Summary: This paper considers the uniform strong consistency of the error cumulative distribution function (CDF) estimator. Under appropriate assumptions, the classical Glivenko-Cantelli Theorem is obtained for the residual based empirical error CDF in the nonlinear autoregressive time series.
MSC:
| 62M10 | Time series, auto-correlation, regression, etc. in statistics (GARCH) |
| 62G07 | Density estimation |
| 62G20 | Asymptotic properties of nonparametric inference |
| 60G10 | Stationary stochastic processes |
| 60F15 | Strong limit theorems |
Keywords:
nonlinear autoregressive time series; distribution estimator; strong consistency; Glivenko-Cantelli theorem; residuals; stationary processReferences:
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