Abstract: Smoothed nonparametric density estimates can be useful in analysing nonlinear time series. Their asymptotic properties in weakly dependent series, including limiting distributions and mean squared error, are known to be similar to those in independent series. Robinson (1987) found evidence that these properties may not hold in strongly dependent, or ``long-memory'' Gaussian time series. The present paper derives normal and non-normal limiting distributions in case of long-memory nonlinear series, provides a numerical comparison of integrated mean squared error, and reports estimates based on simulated series.
Key words and phrases: Density estimation, long memory time series, nonlinear time series, normal and non-normal limiting distributions, integrated mean squared error.