# Analysis, detection and correction of misspecified discrete time state space models

## TL;DR

This paper introduces a method to detect and correct parameter misspecifications in discrete-time state space models, improving the accuracy of hidden state inference by leveraging innovation correlation properties.

## Contribution

It proposes a novel optimization-based approach that uses innovation correlation to identify and correct parameter errors in weakly nonlinear Gaussian state space models.

## Key findings

- The method effectively detects misspecifications across various models.
- It can consistently estimate parameter bias.
- Demonstrated success on models of increasing complexity.

## Abstract

Misspecifications (i.e. errors on the parameters) of state space models lead to incorrect inference of the hidden states. This paper studies weakly nonlin-ear state space models with additive Gaussian noises and proposes a method for detecting and correcting misspecifications. The latter induce a biased estimator of the hidden state but also happen to induce correlation on innovations and other residues. This property is used to find a well-defined objective function for which an optimisation routine is applied to recover the true parameters of the model. It is argued that this method can consistently estimate the bias on the parameter. We demonstrate the algorithm on various models of increasing complexity.