Conference Agenda

This paper introduces an ANN approach to estimate the autoregressive process AR(1) when the autocorrelation parameter is near one. Traditional OLS estimators suffer from biases in small samples, necessitating various correction methods proposed in the literature. The ANN, trained on simulated data, outperforms these methods due to its nonlinear structure. Unlike competitors requiring simulations for bias corrections based on specific sample sizes, the ANN directly incorporates sample size as input, eliminating the need for repeated simulations. Stability tests involve exploring different ANN architectures and activation functions and robustness to varying distributions of the process innovations. Empirical applications on financial and industrial data highlight significant differences among methods, with ANN estimates suggesting lower persistence than other approaches.

We propose a new interactive locally differentially private mechanism for estimating Sobolev smooth spectral density functions of stationary Gaussian processes. Anonymization is achieved through two-stage truncation and subsequent Laplace perturbation. In particular, we show that our method achieves a pointwise L2-rate with a dependency of only $\alpha^2$ on the privacy parameter $\alpha$. This rate stands in contrast to the results of (Kroll, 2024), who proposed a non-interactive mechanism for spectral density estimation and showed a dependency of $\alpha^4$ on the privacy parameter for the uniform L2-rate.