arXiv subjects

G. Kitagawa

Publications and source records attributed to G. Kitagawa.

5 recordsLinked to original sources

arXiv2024

A Triginometric Seasonal Component Model and its Application to Time Series with Two Types of Seasonality

A finite trigonometric series model for seasonal time series is considered in this paper. This component model is shown to be useful, in particular, for the modeling of time series with two types of seasonality, a long-period and a short period. This component model is also shown to be effective in the case of ordinary seasonal time series with only one seasonal component, if the seasonal pattern is simple and can be well represented by a small number of trigonometric components. As examples, electricity demand data, bi-hourly temperature data, CO2 data, and two economic time series are considered. The last section summarizes the findings from the emperical studies.

stat.ME↗

arXiv2024

Emperical Study on the Effect of Multi-Sampling in the Prediction Step of the Particle Filter

Particle filters are applicable to a wide range of nonlinear, non-Gaussian state-space models and have already been applied to a variety of problems. However, there is a problem in the calculation of smoothed distributions, where particles gradually degenerate and accuracy is reduced. The purpose of this paper is to consider the possibility of generating multiple particles in the prediction step of the particle filter and to empirically verify the effect using real data.

stat.CO↗

arXiv2023

Revisiting the Two-Filter Formula for Smoothing for State-Space Models

Smoothing algorithms for state-space models, i.e., fixed-interval smoothing, fixed-lag smoothing, and two-filter formula for smoothing, are examined using real examples. For linear and Gaussian state-space models, it is observed that similar posterior distributions can be obtained by properly defining the inverse filter. In the case of linear non-Gaussian state-space models, it is shown that Gaussian-sum smoothing is possible even for relatively high dimensional state-space model with Gaussian-mixture noise inputs by properly setting the inverse filter. The two-filter formula is also applicable for particle filter, but better results are obtained with fixed lag smoothing or with the average of forward and backward fixed lag smoothers.

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arXiv2023

A Note on the Relation Between Balenzela's Algorithm for Two-Filter Formula for Smoothing and Information Filter

Recent paper by Balenzuela et al. presented an exact algorithm for computing the posterior distribution of current and future observations given the current state, $p(x_n|y_n,\ldots ,y_N)$, which is required when computing fixed-interval smoother of the state by a two-filter formula. In this note, it will be shown that their algorithm is equivalent to the backward filter obtained by applying an information filter to the reverse state-space model. Although their algorithm is proposed for complex Gaussian mixture distribution models, in this note, we consider the case of simple state-space models with respect to filter computation.

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arXiv2020

Computation of the Gradient and the Hessian of the Log-likelihood of the State-space Model by the Kalman Filter

The maximum likelihood estimates of an ARMA model can be obtained by the Kalman filter based on the state-space representation of the model. This paper presents an algorithm for computing gradient of the log-likelihood by an extending the Kalman filter without resorting to the numerical difference. Three examples of seasonal adjustment model and ARMA model are presented to exemplified the specification of structural matrices and initial matrices. An extension of the algorithm to compute the Hessian matrix is also shown.

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