• Corpus ID: 252531469

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

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