Measuring Statistical Asymmetries of Stochastic Processes: Study of the Autoregressive Process

0545595 - ÚI 2022 CH eng J - Článek v odborném periodiku
Yamashita Rios de Sousa, Arthur Matsuo - Takayasu, H. - Takayasu, M.
Measuring Statistical Asymmetries of Stochastic Processes: Study of the Autoregressive Process.
Entropy. Roč. 20, č. 7 (2018), č. článku 511. E-ISSN 1099-4300
Klíčová slova: entropy * symmetries * divergence * sequences * series * model * statistical symmetry * Kullback-Leibler divergence * stochastic process * autoregressive model * time series analysis
Impakt faktor: 2.419, rok: 2018

We use the definition of statistical symmetry as the invariance of a probability distribution under a given transformation and apply the concept to the underlying probability distribution of stochastic processes. To measure the degree of statistical asymmetry, we take the Kullback-Leibler divergence of a given probability distribution with respect to the corresponding transformed one and study it for the Gaussian autoregressive process using transformations on the temporal correlations' structure. We then illustrate the employment of this notion as a time series analysis tool by measuring local statistical asymmetries of foreign exchange market price data for three transformations that capture distinct autocorrelation behaviors of the series-independence, non-negative correlations and Markovianity-obtaining a characterization of price movements in terms of each statistical symmetry.
Trvalý link: http://hdl.handle.net/11104/0322273