Kalman filter

Machine learning for forecasting some stock market index

In this paper, we evaluate the QMLKF algorithm, designed in the previous paper [Benmoumen M. Numerical optimization of the likelihood function based on Kalman Filter in the GARCH models. Mathematical Modeling and Computing.  9 (3), 599–606 (2022)] for parameter estimation of GARCH models, by transposing it to real data and then present our machine learning for forecasting the returns of some stock indices.

Адаптивна фільтрація параметрів руху об‘єкта у горизонтальній площині

Реалізована процедура використання алгоритму класичного фільтра Калмана для оцінки параметрів руху об’єкта, що маневрує. Застосування фільтра Калмана мотивовано необхідністю мінімізувати дисперсію оцінки вектора випадкового процесу. Результати оцінки параметрів руху обробляють згладжуючим алгоритмом Рауч–Тюнга– Штрібеля також з метою мінімізації дисперсії. Алгоритми Калмана та Рауча–Тюнга– Штрібеля можна застосовувати для використання в оцінці параметрів руху автомобіля, повітряного судна, бойового снаряду.


Assessment of the dynamic systems state is widely used in various areas of technical activity. In practice, the most well-known and common methods of estimation are the methods of the Kalman filter and Luenberger observers. Most of the results known in the scientific literature for constructing estimates of the dynamic systems state in the presence of acting uncontrolled disturbances and noise are associated with stationary systems.

Numerical optimization of the likelihood function based on Kalman filter in the GARCH models

In this work, we propose a new estimate algorithm for the parameters of a $\mathrm{GARCH}(p,q)$ model.  This algorithm turns out to be very reliable in estimating the true parameter’s values of a given model.  It combines maximum likelihood method, Kalman filter algorithm and the simulated annealing (SA) method, without any assumptions about initial values.  Simulation results demonstrate that the algorithm is liable and promising.

Quasi-maximum likelihood estimation of the Component-GARCH model using the stochastic approximation algorithm with application to the S&P 500

The component GARCH (CGARCH) is suitable to better capture the short and long term of the volatility dynamic.  Nevertheless, the parameter space constituted by the constraints of the non-negativity of the conditional variance, stationary and existence of moments, is only ex-post defined via the GARCH representation of the CGARCH.  This is due to the lack of a general method to determine a priori the relaxed constraints of non-negativity of the CGARCH($N$) conditional variance for any $N\geq 1$.