Asymptotic properties of empirical characteristic-function estimation

Establish the consistency and asymptotic normality of the empirical characteristic function estimator for the causal non-causal convolution autoregressive model by verifying the general conditions given by Knight and Yu.

Background

Because the observation kernel of the causal non-causal convolution autoregressive model does not have a density, the paper estimates its parameters using an empirical characteristic function estimator rather than maximum likelihood.

General consistency and asymptotic-normality results for empirical characteristic function estimators are available in Knight and Yu, but the paper does not verify that their assumptions hold for the causal non-causal convolution autoregressive model. The authors therefore defer the estimator's asymptotic analysis and study only its finite-sample behavior.

References

It is, however, not immediately clear whether the general conditions in hold for the causal non-causal convolution autoregressive model. We therefore leave the asymptotic properties of the empirical characteristic function estimator for the causal non-causal convolution autoregressive model for future research, but study its finite-sample properties in the next section.

— Causal Non-causal State Space Models and the Modelling of Financial Bubbles  (2608.28115 - Krabbe, 28 Aug 2026) in Section 3.2, Statistical Inference