{"id":3514,"date":"2025-06-12T07:29:01","date_gmt":"2025-06-12T07:29:01","guid":{"rendered":"https:\/\/jita-au.com\/?p=3514"},"modified":"2025-09-24T12:31:49","modified_gmt":"2025-09-24T12:31:49","slug":"a-hybrid-model-based-on-chaos-theory-and-artificial-immune-systems-for-the-analysis-and-classification-of-stock-market-anomalies","status":"publish","type":"post","link":"https:\/\/jita-au.com\/index.php\/2025\/06\/12\/a-hybrid-model-based-on-chaos-theory-and-artificial-immune-systems-for-the-analysis-and-classification-of-stock-market-anomalies\/","title":{"rendered":"A HYBRID MODEL BASED ON CHAOS THEORY AND AR\u0422IFICIAL IMMUNE SYS\u0422EMS FOR \u0422HE ANALYSIS AND CLASSIFICA\u0422ION OF S\u0422OCK MARKE\u0422 ANOMALIES"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-post\" data-elementor-id=\"3514\" class=\"elementor elementor-3514\" data-elementor-settings=\"{&quot;ha_cmc_init_switcher&quot;:&quot;no&quot;}\">\n\t\t\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-e232701 elementor-section-height-min-height elementor-section-full_width elementor-hidden-tablet elementor-hidden-mobile elementor-section-height-default elementor-section-items-middle wpr-particle-no wpr-jarallax-no wpr-parallax-no wpr-sticky-section-no\" data-id=\"e232701\" data-element_type=\"section\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;,&quot;_ha_eqh_enable&quot;:false}\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-cb97594\" data-id=\"cb97594\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-a18c791 elementor-widget__width-inherit ha-has-bg-overlay elementor-widget elementor-widget-heading\" data-id=\"a18c791\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Vol. 15 No. 1 (2025): JITA - APEIRON<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-b2fff26 elementor-widget elementor-widget-heading\" data-id=\"b2fff26\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\"><b>MARKO M. \u017dIVANOVI\u0106, EMILIJA KISI\u0106<b><\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-52044bb elementor-widget-divider--view-line elementor-widget elementor-widget-divider\" data-id=\"52044bb\" data-element_type=\"widget\" data-widget_type=\"divider.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-divider\">\n\t\t\t<span class=\"elementor-divider-separator\">\n\t\t\t\t\t\t<\/span>\n\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-1c82606 elementor-widget elementor-widget-heading\" data-id=\"1c82606\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">A HYBRID MODEL BASED ON CHAOS THEORY AND AR\u0422IFICIAL IMMUNE SYS\u0422EMS FOR \u0422HE ANALYSIS AND CLASSIFICA\u0422ION OF S\u0422OCK MARKE\u0422 ANOMALIES<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-c297c9e elementor-widget-divider--view-line elementor-widget elementor-widget-divider\" data-id=\"c297c9e\" data-element_type=\"widget\" data-widget_type=\"divider.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-divider\">\n\t\t\t<span class=\"elementor-divider-separator\">\n\t\t\t\t\t\t<\/span>\n\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-455c8d6 e-grid e-con-full wpr-particle-no wpr-jarallax-no wpr-parallax-no wpr-sticky-section-no e-con e-parent\" data-id=\"455c8d6\" data-element_type=\"container\" data-settings=\"{&quot;_ha_eqh_enable&quot;:false}\">\n\t\t\t\t<div class=\"elementor-element elementor-element-dcea8af elementor-widget__width-initial elementor-widget elementor-widget-heading\" data-id=\"dcea8af\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Review paper<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-0579899 elementor-widget__width-initial elementor-widget elementor-widget-heading\" data-id=\"0579899\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">DOI: https:\/\/doi.org\/10.7251\/JIT2501015Z<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-2f3b63f elementor-align-center elementor-widget elementor-widget-button\" data-id=\"2f3b63f\" data-element_type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t\t\t<a class=\"elementor-button elementor-button-link elementor-size-sm\" href=\"https:\/\/jita-au.com\/wp-content\/uploads\/2025\/06\/Pages-from-JITA_Vol-15_Issue-1-2.pdf\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t\t\t\t<span class=\"elementor-button-text\">Download Article PDF<\/span>\n\t\t\t\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-cb7c4cb elementor-widget__width-inherit elementor-widget elementor-widget-heading\" data-id=\"cb7c4cb\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Abstract<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-61aebe3 elementor-widget__width-inherit elementor-widget elementor-widget-text-editor\" data-id=\"61aebe3\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>In this paper, a system for analyzing chaotic patterns in financial markets has been developed by combining classical chaos metrics with artificial immune systems for anomaly detection. Implemented indicators include the Lyapunov exponent, correlation dimension, approximate entropy, Hurst exponent, and the distance from a reference Lorenz trajectory. These metrics enable the detection of changes in market stability and predictability over time. An adaptive algorithm inspired by artificial immune systems was developed for identifying anomalous behaviors, adjusting detectors based on detected deviations. The results are presented through a series of interactive visualizations, including 3D plots, time series, and anomaly density maps. In addition to standard analysis, the system supports false alarm detection through controlled parameter variations. This approach provides deeper insights into the complex dynamics of financial markets and can serve as a tool for forecasting periods of instability.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-5c5f19e elementor-widget elementor-widget-heading\" data-id=\"5c5f19e\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Keywords: anomaly detection, artificial immune systems, chaos metrics, financial markets, lorenz attractor, lyapunov exponent<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-f6f6b9b elementor-widget elementor-widget-heading\" data-id=\"f6f6b9b\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\"><b>Paper received:<\/b> 4.5.2025.<br><b>Paper accepted:<\/b> 25.5.2025.<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-6dd494a wpr-logo-position-center elementor-widget elementor-widget-wpr-logo\" data-id=\"6dd494a\" data-element_type=\"widget\" data-widget_type=\"wpr-logo.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\n\t\t\t<div class=\"wpr-logo elementor-clearfix\">\n\n\t\t\t\t\t\t\t\t<picture class=\"wpr-logo-image\">\n\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t<img decoding=\"async\" src=\"https:\/\/jita-au.com\/wp-content\/uploads\/2024\/03\/cc-by-1.png\" alt=\"\">\n\n\t\t\t\t\t\t\t\t\t\t\t<a class=\"wpr-logo-url\" rel=\"home\" aria-label=\"\" href=\"https:\/\/jita-au.com\/\"><\/a>\n\t\t\t\t\t\t\t\t\t<\/picture>\n\t\t\t\t\n\t\t\t\t\n\t\t\t\t\t\t\t\t\t<a class=\"wpr-logo-url\" rel=\"home\" aria-label=\"\" href=\"https:\/\/jita-au.com\/\"><\/a>\n\t\t\t\t\n\t\t\t<\/div>\n\t\t\t\t\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-cb049d1 elementor-widget elementor-widget-shortcode\" data-id=\"cb049d1\" data-element_type=\"widget\" data-widget_type=\"shortcode.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-shortcode\"><div class=\"post-views content-post post-3514 entry-meta load-static\">\r\n\t\t\t\t<span class=\"post-views-icon dashicons dashicons-chart-bar\"><\/span> <span class=\"post-views-label\">Post Views:<\/span> <span class=\"post-views-count\">1,158<\/span>\r\n\t\t\t<\/div><\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-8502ce8 elementor-widget elementor-widget-shortcode\" data-id=\"8502ce8\" data-element_type=\"widget\" data-widget_type=\"shortcode.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-shortcode\">Downloaded Article PDF: <span class=\"snr-download-count-num\" data-post-id=\"0\">0<\/span> times\n<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-511d0df elementor-section-height-min-height elementor-section-full_width elementor-hidden-mobile elementor-hidden-desktop elementor-hidden-laptop elementor-section-height-default elementor-section-items-middle wpr-particle-no wpr-jarallax-no wpr-parallax-no wpr-sticky-section-no\" data-id=\"511d0df\" data-element_type=\"section\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;,&quot;_ha_eqh_enable&quot;:false}\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-0acee9c\" data-id=\"0acee9c\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-c0e98b3 elementor-widget__width-inherit ha-has-bg-overlay elementor-widget elementor-widget-heading\" data-id=\"c0e98b3\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Vol. 15 No. 1 (2025): JITA - APEIRON<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-e6b43c5 elementor-widget elementor-widget-heading\" data-id=\"e6b43c5\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\"><b>MARKO M. \u017dIVANOVI\u0106, EMILIJA KISI\u0106<b><\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-68f1849 elementor-widget-divider--view-line elementor-widget elementor-widget-divider\" data-id=\"68f1849\" data-element_type=\"widget\" data-widget_type=\"divider.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-divider\">\n\t\t\t<span class=\"elementor-divider-separator\">\n\t\t\t\t\t\t<\/span>\n\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-186a6b2 elementor-widget elementor-widget-heading\" data-id=\"186a6b2\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">A HYBRID MODEL BASED ON CHAOS THEORY AND AR\u0422IFICIAL IMMUNE SYS\u0422EMS FOR \u0422HE ANALYSIS AND CLASSIFICA\u0422ION OF S\u0422OCK MARKE\u0422 ANOMALIES<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-7b2f501 elementor-widget-divider--view-line elementor-widget elementor-widget-divider\" data-id=\"7b2f501\" data-element_type=\"widget\" data-widget_type=\"divider.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-divider\">\n\t\t\t<span class=\"elementor-divider-separator\">\n\t\t\t\t\t\t<\/span>\n\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-5027126 elementor-widget__width-initial elementor-widget elementor-widget-heading\" data-id=\"5027126\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Review paper<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-4a5312c elementor-widget__width-initial elementor-widget elementor-widget-heading\" data-id=\"4a5312c\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">DOI: https:\/\/doi.org\/10.7251\/JIT2501015Z<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-8d7a912 elementor-align-center elementor-widget elementor-widget-button\" data-id=\"8d7a912\" data-element_type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t\t\t<a class=\"elementor-button elementor-button-link elementor-size-sm\" href=\"https:\/\/jita-au.com\/wp-content\/uploads\/2025\/06\/Pages-from-JITA_Vol-15_Issue-1-2.pdf\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t\t\t\t<span class=\"elementor-button-text\">Download Article PDF<\/span>\n\t\t\t\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-580ffd3 elementor-widget__width-inherit elementor-widget elementor-widget-heading\" data-id=\"580ffd3\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Abstract<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-211717e elementor-widget__width-inherit elementor-widget elementor-widget-text-editor\" data-id=\"211717e\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>In this paper, a system for analyzing chaotic patterns in financial markets has been developed by combining classical chaos metrics with artificial immune systems for anomaly detection. Implemented indicators include the Lyapunov exponent, correlation dimension, approximate entropy, Hurst exponent, and the distance from a reference Lorenz trajectory. These metrics enable the detection of changes in market stability and predictability over time. An adaptive algorithm inspired by artificial immune systems was developed for identifying anomalous behaviors, adjusting detectors based on detected deviations. The results are presented through a series of interactive visualizations, including 3D plots, time series, and anomaly density maps. In addition to standard analysis, the system supports false alarm detection through controlled parameter variations. This approach provides deeper insights into the complex dynamics of financial markets and can serve as a tool for forecasting periods of instability.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-62b72c3 elementor-widget elementor-widget-heading\" data-id=\"62b72c3\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Keywords: anomaly detection, artificial immune systems, chaos metrics, financial markets, lorenz attractor, lyapunov exponent<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-8018c62 elementor-widget elementor-widget-heading\" data-id=\"8018c62\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\"><b>Paper received:<\/b> 4.5.2025.<br><b>Paper accepted:<\/b> 25.5.2025.<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-f4dcd16 wpr-logo-position-center elementor-widget elementor-widget-wpr-logo\" data-id=\"f4dcd16\" data-element_type=\"widget\" data-widget_type=\"wpr-logo.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\n\t\t\t<div class=\"wpr-logo elementor-clearfix\">\n\n\t\t\t\t\t\t\t\t<picture class=\"wpr-logo-image\">\n\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t<img decoding=\"async\" src=\"https:\/\/jita-au.com\/wp-content\/uploads\/2024\/03\/cc-by-1.png\" alt=\"\">\n\n\t\t\t\t\t\t\t\t\t\t\t<a class=\"wpr-logo-url\" rel=\"home\" aria-label=\"\" href=\"https:\/\/jita-au.com\/\"><\/a>\n\t\t\t\t\t\t\t\t\t<\/picture>\n\t\t\t\t\n\t\t\t\t\n\t\t\t\t\t\t\t\t\t<a class=\"wpr-logo-url\" rel=\"home\" aria-label=\"\" href=\"https:\/\/jita-au.com\/\"><\/a>\n\t\t\t\t\n\t\t\t<\/div>\n\t\t\t\t\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-0f73093 elementor-widget elementor-widget-shortcode\" data-id=\"0f73093\" data-element_type=\"widget\" data-widget_type=\"shortcode.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-shortcode\"><div class=\"post-views content-post post-3514 entry-meta load-static\">\r\n\t\t\t\t<span class=\"post-views-icon dashicons dashicons-chart-bar\"><\/span> <span class=\"post-views-label\">Post Views:<\/span> <span class=\"post-views-count\">1,158<\/span>\r\n\t\t\t<\/div><\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-0923aec elementor-widget elementor-widget-shortcode\" data-id=\"0923aec\" data-element_type=\"widget\" data-widget_type=\"shortcode.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-shortcode\">Downloaded Article PDF: <span class=\"snr-download-count-num\" data-post-id=\"0\">0<\/span> times\n<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-2d980b8 elementor-section-height-min-height elementor-section-full_width elementor-hidden-tablet elementor-hidden-desktop elementor-hidden-laptop elementor-section-height-default elementor-section-items-middle wpr-particle-no wpr-jarallax-no wpr-parallax-no wpr-sticky-section-no\" data-id=\"2d980b8\" data-element_type=\"section\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;,&quot;_ha_eqh_enable&quot;:false}\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-d772afa\" data-id=\"d772afa\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-5597455 elementor-widget__width-inherit elementor-widget-mobile__width-inherit ha-has-bg-overlay elementor-widget elementor-widget-heading\" data-id=\"5597455\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Vol. 15 No. 1 (2025): JITA - APEIRON<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-f3e70ee elementor-widget elementor-widget-heading\" data-id=\"f3e70ee\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\"><b>MARKO M. \u017dIVANOVI\u0106, EMILIJA KISI\u0106<b><\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-b0a72e2 elementor-widget-divider--view-line elementor-widget elementor-widget-divider\" data-id=\"b0a72e2\" data-element_type=\"widget\" data-widget_type=\"divider.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-divider\">\n\t\t\t<span class=\"elementor-divider-separator\">\n\t\t\t\t\t\t<\/span>\n\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-87a3678 elementor-widget elementor-widget-heading\" data-id=\"87a3678\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">A HYBRID MODEL BASED ON CHAOS THEORY AND AR\u0422IFICIAL IMMUNE SYS\u0422EMS FOR \u0422HE ANALYSIS AND CLASSIFICA\u0422ION OF S\u0422OCK MARKE\u0422 ANOMALIES<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-96936f4 elementor-widget-divider--view-line elementor-widget elementor-widget-divider\" data-id=\"96936f4\" data-element_type=\"widget\" data-widget_type=\"divider.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-divider\">\n\t\t\t<span class=\"elementor-divider-separator\">\n\t\t\t\t\t\t<\/span>\n\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-f04febc elementor-widget__width-initial elementor-widget-mobile__width-inherit elementor-widget elementor-widget-heading\" data-id=\"f04febc\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Review paper<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-389228b elementor-widget__width-initial elementor-widget-mobile__width-inherit elementor-widget elementor-widget-heading\" data-id=\"389228b\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">DOI: https:\/\/doi.org\/10.7251\/JIT2501015Z<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-73b8917 elementor-align-center elementor-widget elementor-widget-button\" data-id=\"73b8917\" data-element_type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t\t\t<a class=\"elementor-button elementor-button-link elementor-size-sm\" href=\"https:\/\/jita-au.com\/wp-content\/uploads\/2025\/06\/Pages-from-JITA_Vol-15_Issue-1-2.pdf\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t\t\t\t<span class=\"elementor-button-text\">Download Article PDF<\/span>\n\t\t\t\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-80faf79 elementor-widget__width-inherit elementor-widget elementor-widget-heading\" data-id=\"80faf79\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Abstract<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-8cefffd elementor-widget__width-inherit elementor-widget elementor-widget-text-editor\" data-id=\"8cefffd\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>In this paper, a system for analyzing chaotic patterns in financial markets has been developed by combining classical chaos metrics with artificial immune systems for anomaly detection. Implemented indicators include the Lyapunov exponent, correlation dimension, approximate entropy, Hurst exponent, and the distance from a reference Lorenz trajectory. These metrics enable the detection of changes in market stability and predictability over time. An adaptive algorithm inspired by artificial immune systems was developed for identifying anomalous behaviors, adjusting detectors based on detected deviations. The results are presented through a series of interactive visualizations, including 3D plots, time series, and anomaly density maps. In addition to standard analysis, the system supports false alarm detection through controlled parameter variations. This approach provides deeper insights into the complex dynamics of financial markets and can serve as a tool for forecasting periods of instability.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-0c5e44b elementor-widget elementor-widget-heading\" data-id=\"0c5e44b\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Keywords: anomaly detection, artificial immune systems, chaos metrics, financial markets, lorenz attractor, lyapunov exponent<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-c779524 elementor-widget elementor-widget-heading\" data-id=\"c779524\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\"><b>Paper received:<\/b> 4.5.2025.<br><b>Paper accepted:<\/b> 25.5.2025.<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-dee52ab wpr-logo-position-center elementor-widget elementor-widget-wpr-logo\" data-id=\"dee52ab\" data-element_type=\"widget\" data-widget_type=\"wpr-logo.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\n\t\t\t<div class=\"wpr-logo elementor-clearfix\">\n\n\t\t\t\t\t\t\t\t<picture class=\"wpr-logo-image\">\n\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t<img decoding=\"async\" src=\"https:\/\/jita-au.com\/wp-content\/uploads\/2024\/03\/cc-by-1.png\" alt=\"\">\n\n\t\t\t\t\t\t\t\t\t\t\t<a class=\"wpr-logo-url\" rel=\"home\" aria-label=\"\" href=\"https:\/\/jita-au.com\/\"><\/a>\n\t\t\t\t\t\t\t\t\t<\/picture>\n\t\t\t\t\n\t\t\t\t\n\t\t\t\t\t\t\t\t\t<a class=\"wpr-logo-url\" rel=\"home\" aria-label=\"\" href=\"https:\/\/jita-au.com\/\"><\/a>\n\t\t\t\t\n\t\t\t<\/div>\n\t\t\t\t\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-5cb9871 elementor-widget elementor-widget-shortcode\" data-id=\"5cb9871\" data-element_type=\"widget\" data-widget_type=\"shortcode.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-shortcode\"><div class=\"post-views content-post post-3514 entry-meta load-static\">\r\n\t\t\t\t<span class=\"post-views-icon dashicons dashicons-chart-bar\"><\/span> <span class=\"post-views-label\">Post Views:<\/span> <span class=\"post-views-count\">1,158<\/span>\r\n\t\t\t<\/div><\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-6e60d4c elementor-widget elementor-widget-shortcode\" data-id=\"6e60d4c\" data-element_type=\"widget\" data-widget_type=\"shortcode.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-shortcode\">Downloaded Article PDF: <span class=\"snr-download-count-num\" data-post-id=\"0\">0<\/span> times\n<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"<p>Vol. 15 No. 1 (2025): JITA &#8211; APEIRON MARKO M. \u017dIVANOVI\u0106, EMILIJA KISI\u0106 A HYBRID MODEL BASED ON CHAOS THEORY AND AR\u0422IFICIAL IMMUNE SYS\u0422EMS FOR \u0422HE ANALYSIS AND CLASSIFICA\u0422ION OF S\u0422OCK MARKE\u0422 ANOMALIES Review paper DOI: https:\/\/doi.org\/10.7251\/JIT2501015Z Download Article PDF Abstract In this paper, a system for analyzing chaotic patterns in financial markets has been developed by combining classical chaos metrics with artificial immune systems for anomaly detection. Implemented indicators include the Lyapunov exponent, correlation dimension, approximate entropy, Hurst exponent, and the distance from a reference Lorenz trajectory. These metrics enable the detection of changes in market stability and predictability over time. An adaptive algorithm inspired by artificial immune systems was developed for identifying anomalous behaviors, adjusting detectors based on detected deviations. The results are presented through a series of interactive visualizations, including 3D plots, time series, and anomaly density maps. In addition to standard analysis, the system supports false alarm detection through controlled parameter variations. This approach provides deeper insights into the complex dynamics of financial markets and can serve as a tool for forecasting periods of instability. Keywords: anomaly detection, artificial immune systems, chaos metrics, financial markets, lorenz attractor, lyapunov exponent Paper received: 4.5.2025.Paper accepted: 25.5.2025. Vol. 15 No. 1 (2025): JITA &#8211; APEIRON MARKO M. \u017dIVANOVI\u0106, EMILIJA KISI\u0106 A HYBRID MODEL BASED ON CHAOS THEORY AND AR\u0422IFICIAL IMMUNE SYS\u0422EMS FOR \u0422HE ANALYSIS AND CLASSIFICA\u0422ION OF S\u0422OCK MARKE\u0422 ANOMALIES Review paper DOI: https:\/\/doi.org\/10.7251\/JIT2501015Z Download Article PDF Abstract In this paper, a system for analyzing chaotic patterns in financial markets has been developed by combining classical chaos metrics with artificial immune systems for anomaly detection. Implemented indicators include the Lyapunov exponent, correlation dimension, approximate entropy, Hurst exponent, and the distance from a reference Lorenz trajectory. These metrics enable the detection of changes in market stability and predictability over time. An adaptive algorithm inspired by artificial immune systems was developed for identifying anomalous behaviors, adjusting detectors based on detected deviations. The results are presented through a series of interactive visualizations, including 3D plots, time series, and anomaly density maps. In addition to standard analysis, the system supports false alarm detection through controlled parameter variations. This approach provides deeper insights into the complex dynamics of financial markets and can serve as a tool for forecasting periods of instability. Keywords: anomaly detection, artificial immune systems, chaos metrics, financial markets, lorenz attractor, lyapunov exponent Paper received: 4.5.2025.Paper accepted: 25.5.2025. Vol. 15 No. 1 (2025): JITA &#8211; APEIRON MARKO M. \u017dIVANOVI\u0106, EMILIJA KISI\u0106 A HYBRID MODEL BASED ON CHAOS THEORY AND AR\u0422IFICIAL IMMUNE SYS\u0422EMS FOR \u0422HE ANALYSIS AND CLASSIFICA\u0422ION OF S\u0422OCK MARKE\u0422 ANOMALIES Review paper DOI: https:\/\/doi.org\/10.7251\/JIT2501015Z Download Article PDF Abstract In this paper, a system for analyzing chaotic patterns in financial markets has been developed by combining classical chaos metrics with artificial immune systems for anomaly detection. Implemented indicators include the Lyapunov exponent, correlation dimension, approximate entropy, Hurst exponent, and the distance from a reference Lorenz trajectory. These metrics enable the detection of changes in market stability and predictability over time. An adaptive algorithm inspired by artificial immune systems was developed for identifying anomalous behaviors, adjusting detectors based on detected deviations. The results are presented through a series of interactive visualizations, including 3D plots, time series, and anomaly density maps. In addition to standard analysis, the system supports false alarm detection through controlled parameter variations. This approach provides deeper insights into the complex dynamics of financial markets and can serve as a tool for forecasting periods of instability. Keywords: anomaly detection, artificial immune systems, chaos metrics, financial markets, lorenz attractor, lyapunov exponent Paper received: 4.5.2025.Paper accepted: 25.5.2025.<\/p>\n","protected":false},"author":1,"featured_media":3508,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"elementor_header_footer","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-3514","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-uncategorized"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v26.8 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>A HYBRID MODEL BASED ON CHAOS THEORY AND AR\u0422IFICIAL IMMUNE SYS\u0422EMS FOR \u0422HE ANALYSIS AND CLASSIFICA\u0422ION OF S\u0422OCK MARKE\u0422 ANOMALIES - JITA -Journal of Information Technology and Application<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/jita-au.com\/index.php\/2025\/06\/12\/a-hybrid-model-based-on-chaos-theory-and-artificial-immune-systems-for-the-analysis-and-classification-of-stock-market-anomalies\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"A HYBRID MODEL BASED ON CHAOS THEORY AND AR\u0422IFICIAL IMMUNE SYS\u0422EMS FOR \u0422HE ANALYSIS AND CLASSIFICA\u0422ION OF S\u0422OCK MARKE\u0422 ANOMALIES - JITA -Journal of Information Technology and Application\" \/>\n<meta property=\"og:description\" content=\"Vol. 15 No. 1 (2025): JITA &#8211; APEIRON MARKO M. \u017dIVANOVI\u0106, EMILIJA KISI\u0106 A HYBRID MODEL BASED ON CHAOS THEORY AND AR\u0422IFICIAL IMMUNE SYS\u0422EMS FOR \u0422HE ANALYSIS AND CLASSIFICA\u0422ION OF S\u0422OCK MARKE\u0422 ANOMALIES Review paper DOI: https:\/\/doi.org\/10.7251\/JIT2501015Z Download Article PDF Abstract In this paper, a system for analyzing chaotic patterns in financial markets has been developed by combining classical chaos metrics with artificial immune systems for anomaly detection. Implemented indicators include the Lyapunov exponent, correlation dimension, approximate entropy, Hurst exponent, and the distance from a reference Lorenz trajectory. These metrics enable the detection of changes in market stability and predictability over time. An adaptive algorithm inspired by artificial immune systems was developed for identifying anomalous behaviors, adjusting detectors based on detected deviations. The results are presented through a series of interactive visualizations, including 3D plots, time series, and anomaly density maps. In addition to standard analysis, the system supports false alarm detection through controlled parameter variations. This approach provides deeper insights into the complex dynamics of financial markets and can serve as a tool for forecasting periods of instability. Keywords: anomaly detection, artificial immune systems, chaos metrics, financial markets, lorenz attractor, lyapunov exponent Paper received: 4.5.2025.Paper accepted: 25.5.2025. Vol. 15 No. 1 (2025): JITA &#8211; APEIRON MARKO M. \u017dIVANOVI\u0106, EMILIJA KISI\u0106 A HYBRID MODEL BASED ON CHAOS THEORY AND AR\u0422IFICIAL IMMUNE SYS\u0422EMS FOR \u0422HE ANALYSIS AND CLASSIFICA\u0422ION OF S\u0422OCK MARKE\u0422 ANOMALIES Review paper DOI: https:\/\/doi.org\/10.7251\/JIT2501015Z Download Article PDF Abstract In this paper, a system for analyzing chaotic patterns in financial markets has been developed by combining classical chaos metrics with artificial immune systems for anomaly detection. Implemented indicators include the Lyapunov exponent, correlation dimension, approximate entropy, Hurst exponent, and the distance from a reference Lorenz trajectory. These metrics enable the detection of changes in market stability and predictability over time. An adaptive algorithm inspired by artificial immune systems was developed for identifying anomalous behaviors, adjusting detectors based on detected deviations. The results are presented through a series of interactive visualizations, including 3D plots, time series, and anomaly density maps. In addition to standard analysis, the system supports false alarm detection through controlled parameter variations. This approach provides deeper insights into the complex dynamics of financial markets and can serve as a tool for forecasting periods of instability. Keywords: anomaly detection, artificial immune systems, chaos metrics, financial markets, lorenz attractor, lyapunov exponent Paper received: 4.5.2025.Paper accepted: 25.5.2025. Vol. 15 No. 1 (2025): JITA &#8211; APEIRON MARKO M. \u017dIVANOVI\u0106, EMILIJA KISI\u0106 A HYBRID MODEL BASED ON CHAOS THEORY AND AR\u0422IFICIAL IMMUNE SYS\u0422EMS FOR \u0422HE ANALYSIS AND CLASSIFICA\u0422ION OF S\u0422OCK MARKE\u0422 ANOMALIES Review paper DOI: https:\/\/doi.org\/10.7251\/JIT2501015Z Download Article PDF Abstract In this paper, a system for analyzing chaotic patterns in financial markets has been developed by combining classical chaos metrics with artificial immune systems for anomaly detection. Implemented indicators include the Lyapunov exponent, correlation dimension, approximate entropy, Hurst exponent, and the distance from a reference Lorenz trajectory. These metrics enable the detection of changes in market stability and predictability over time. An adaptive algorithm inspired by artificial immune systems was developed for identifying anomalous behaviors, adjusting detectors based on detected deviations. The results are presented through a series of interactive visualizations, including 3D plots, time series, and anomaly density maps. In addition to standard analysis, the system supports false alarm detection through controlled parameter variations. This approach provides deeper insights into the complex dynamics of financial markets and can serve as a tool for forecasting periods of instability. Keywords: anomaly detection, artificial immune systems, chaos metrics, financial markets, lorenz attractor, lyapunov exponent Paper received: 4.5.2025.Paper accepted: 25.5.2025.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/jita-au.com\/index.php\/2025\/06\/12\/a-hybrid-model-based-on-chaos-theory-and-artificial-immune-systems-for-the-analysis-and-classification-of-stock-market-anomalies\/\" \/>\n<meta property=\"og:site_name\" content=\"JITA -Journal of Information Technology and Application\" \/>\n<meta property=\"article:published_time\" content=\"2025-06-12T07:29:01+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2025-09-24T12:31:49+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/jita-au.com\/wp-content\/uploads\/2025\/06\/JITA_Vol-15_Issue-1-scaled.jpg\" \/>\n\t<meta property=\"og:image:width\" content=\"1920\" \/>\n\t<meta property=\"og:image:height\" content=\"2560\" \/>\n\t<meta property=\"og:image:type\" content=\"image\/jpeg\" \/>\n<meta name=\"author\" content=\"admin\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"admin\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"4 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\/\/jita-au.com\/index.php\/2025\/06\/12\/a-hybrid-model-based-on-chaos-theory-and-artificial-immune-systems-for-the-analysis-and-classification-of-stock-market-anomalies\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/jita-au.com\/index.php\/2025\/06\/12\/a-hybrid-model-based-on-chaos-theory-and-artificial-immune-systems-for-the-analysis-and-classification-of-stock-market-anomalies\/\"},\"author\":{\"name\":\"admin\",\"@id\":\"https:\/\/jita-au.com\/#\/schema\/person\/d4becda53cfcbc99c449927eabf3877f\"},\"headline\":\"A HYBRID MODEL BASED ON CHAOS THEORY AND AR\u0422IFICIAL IMMUNE SYS\u0422EMS FOR \u0422HE ANALYSIS AND CLASSIFICA\u0422ION OF S\u0422OCK MARKE\u0422 ANOMALIES\",\"datePublished\":\"2025-06-12T07:29:01+00:00\",\"dateModified\":\"2025-09-24T12:31:49+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/jita-au.com\/index.php\/2025\/06\/12\/a-hybrid-model-based-on-chaos-theory-and-artificial-immune-systems-for-the-analysis-and-classification-of-stock-market-anomalies\/\"},\"wordCount\":647,\"publisher\":{\"@id\":\"https:\/\/jita-au.com\/#organization\"},\"image\":{\"@id\":\"https:\/\/jita-au.com\/index.php\/2025\/06\/12\/a-hybrid-model-based-on-chaos-theory-and-artificial-immune-systems-for-the-analysis-and-classification-of-stock-market-anomalies\/#primaryimage\"},\"thumbnailUrl\":\"https:\/\/jita-au.com\/wp-content\/uploads\/2025\/06\/JITA_Vol-15_Issue-1-scaled.jpg\",\"inLanguage\":\"en-US\"},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/jita-au.com\/index.php\/2025\/06\/12\/a-hybrid-model-based-on-chaos-theory-and-artificial-immune-systems-for-the-analysis-and-classification-of-stock-market-anomalies\/\",\"url\":\"https:\/\/jita-au.com\/index.php\/2025\/06\/12\/a-hybrid-model-based-on-chaos-theory-and-artificial-immune-systems-for-the-analysis-and-classification-of-stock-market-anomalies\/\",\"name\":\"A HYBRID MODEL BASED ON CHAOS THEORY AND AR\u0422IFICIAL IMMUNE SYS\u0422EMS FOR \u0422HE ANALYSIS AND CLASSIFICA\u0422ION OF S\u0422OCK MARKE\u0422 ANOMALIES - 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JITA -Journal of Information Technology and Application","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/jita-au.com\/index.php\/2025\/06\/12\/a-hybrid-model-based-on-chaos-theory-and-artificial-immune-systems-for-the-analysis-and-classification-of-stock-market-anomalies\/","og_locale":"en_US","og_type":"article","og_title":"A HYBRID MODEL BASED ON CHAOS THEORY AND AR\u0422IFICIAL IMMUNE SYS\u0422EMS FOR \u0422HE ANALYSIS AND CLASSIFICA\u0422ION OF S\u0422OCK MARKE\u0422 ANOMALIES - JITA -Journal of Information Technology and Application","og_description":"Vol. 15 No. 1 (2025): JITA &#8211; APEIRON MARKO M. \u017dIVANOVI\u0106, EMILIJA KISI\u0106 A HYBRID MODEL BASED ON CHAOS THEORY AND AR\u0422IFICIAL IMMUNE SYS\u0422EMS FOR \u0422HE ANALYSIS AND CLASSIFICA\u0422ION OF S\u0422OCK MARKE\u0422 ANOMALIES Review paper DOI: https:\/\/doi.org\/10.7251\/JIT2501015Z Download Article PDF Abstract In this paper, a system for analyzing chaotic patterns in financial markets has been developed by combining classical chaos metrics with artificial immune systems for anomaly detection. Implemented indicators include the Lyapunov exponent, correlation dimension, approximate entropy, Hurst exponent, and the distance from a reference Lorenz trajectory. These metrics enable the detection of changes in market stability and predictability over time. An adaptive algorithm inspired by artificial immune systems was developed for identifying anomalous behaviors, adjusting detectors based on detected deviations. The results are presented through a series of interactive visualizations, including 3D plots, time series, and anomaly density maps. In addition to standard analysis, the system supports false alarm detection through controlled parameter variations. This approach provides deeper insights into the complex dynamics of financial markets and can serve as a tool for forecasting periods of instability. Keywords: anomaly detection, artificial immune systems, chaos metrics, financial markets, lorenz attractor, lyapunov exponent Paper received: 4.5.2025.Paper accepted: 25.5.2025. Vol. 15 No. 1 (2025): JITA &#8211; APEIRON MARKO M. \u017dIVANOVI\u0106, EMILIJA KISI\u0106 A HYBRID MODEL BASED ON CHAOS THEORY AND AR\u0422IFICIAL IMMUNE SYS\u0422EMS FOR \u0422HE ANALYSIS AND CLASSIFICA\u0422ION OF S\u0422OCK MARKE\u0422 ANOMALIES Review paper DOI: https:\/\/doi.org\/10.7251\/JIT2501015Z Download Article PDF Abstract In this paper, a system for analyzing chaotic patterns in financial markets has been developed by combining classical chaos metrics with artificial immune systems for anomaly detection. Implemented indicators include the Lyapunov exponent, correlation dimension, approximate entropy, Hurst exponent, and the distance from a reference Lorenz trajectory. These metrics enable the detection of changes in market stability and predictability over time. An adaptive algorithm inspired by artificial immune systems was developed for identifying anomalous behaviors, adjusting detectors based on detected deviations. The results are presented through a series of interactive visualizations, including 3D plots, time series, and anomaly density maps. In addition to standard analysis, the system supports false alarm detection through controlled parameter variations. This approach provides deeper insights into the complex dynamics of financial markets and can serve as a tool for forecasting periods of instability. Keywords: anomaly detection, artificial immune systems, chaos metrics, financial markets, lorenz attractor, lyapunov exponent Paper received: 4.5.2025.Paper accepted: 25.5.2025. Vol. 15 No. 1 (2025): JITA &#8211; APEIRON MARKO M. \u017dIVANOVI\u0106, EMILIJA KISI\u0106 A HYBRID MODEL BASED ON CHAOS THEORY AND AR\u0422IFICIAL IMMUNE SYS\u0422EMS FOR \u0422HE ANALYSIS AND CLASSIFICA\u0422ION OF S\u0422OCK MARKE\u0422 ANOMALIES Review paper DOI: https:\/\/doi.org\/10.7251\/JIT2501015Z Download Article PDF Abstract In this paper, a system for analyzing chaotic patterns in financial markets has been developed by combining classical chaos metrics with artificial immune systems for anomaly detection. Implemented indicators include the Lyapunov exponent, correlation dimension, approximate entropy, Hurst exponent, and the distance from a reference Lorenz trajectory. These metrics enable the detection of changes in market stability and predictability over time. An adaptive algorithm inspired by artificial immune systems was developed for identifying anomalous behaviors, adjusting detectors based on detected deviations. The results are presented through a series of interactive visualizations, including 3D plots, time series, and anomaly density maps. In addition to standard analysis, the system supports false alarm detection through controlled parameter variations. This approach provides deeper insights into the complex dynamics of financial markets and can serve as a tool for forecasting periods of instability. Keywords: anomaly detection, artificial immune systems, chaos metrics, financial markets, lorenz attractor, lyapunov exponent Paper received: 4.5.2025.Paper accepted: 25.5.2025.","og_url":"https:\/\/jita-au.com\/index.php\/2025\/06\/12\/a-hybrid-model-based-on-chaos-theory-and-artificial-immune-systems-for-the-analysis-and-classification-of-stock-market-anomalies\/","og_site_name":"JITA -Journal of Information Technology and Application","article_published_time":"2025-06-12T07:29:01+00:00","article_modified_time":"2025-09-24T12:31:49+00:00","og_image":[{"width":1920,"height":2560,"url":"https:\/\/jita-au.com\/wp-content\/uploads\/2025\/06\/JITA_Vol-15_Issue-1-scaled.jpg","type":"image\/jpeg"}],"author":"admin","twitter_card":"summary_large_image","twitter_misc":{"Written by":"admin","Est. reading time":"4 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