# An implimentation of the Differential Filter for Computing Gradient and Hessian of the Log-likelihood of Nonstationary Time Series Models

@inproceedings{Kitagawa2022AnIO, title={An implimentation of the Differential Filter for Computing Gradient and Hessian of the Log-likelihood of Nonstationary Time Series Models}, author={Genshiro Kitagawa}, year={2022} }

The state-space model and the Kalman ﬁlter provide us with uniﬁed and computationaly eﬃcient procedure for computing the log-likelihood of the diverse type of time series models. This paper presents an algorithm for computing the gradient and the Hessian matrix of the log-likelihood by extending the Kalman ﬁlter without resorting to the numerical diﬀerence. Diﬀerent from the previous paper [11], it is assumed that the observation noise variance R = 1. It is known that for univariate time series…

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