{"id":2892,"date":"2023-10-09T14:59:24","date_gmt":"2023-10-09T09:59:24","guid":{"rendered":"http:\/\/vestnik.polytech.tj\/?p=2892"},"modified":"2023-10-09T15:04:29","modified_gmt":"2023-10-09T10:04:29","slug":"nonlinear-models-for-time-series-forecasting-based-on-polynomial-functions","status":"publish","type":"post","link":"https:\/\/vestnik.polytech.tj\/?p=2892&lang=en","title":{"rendered":"NONLINEAR MODELS FOR TIME SERIES FORECASTING BASED ON POLYNOMIAL FUNCTIONS"},"content":{"rendered":"

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Authors<\/span><\/strong><\/p>\n

          <\/strong>Nizamitdinov A.I. \u2013 <\/strong>Doctor of philosophy(PhD), Senior Lecturer of Department of Digital <\/em>Economy, Polytechnic Institute of Tajik Technical University, Khujand, Republic of Tajikistan<\/em>, <\/em>ahlidin@gmail.com.<\/a><\/em><\/p>\n

Annotation<\/strong><\/span><\/p>\n

        The article discusses the basic algorithms for forecasting time series as a sequential set of data measured in time, i.e. defined in chronological order. The theoretical basis for constructing the used regression models is given. Time series forecasting models have been built. The results of model evaluation are analyzed using metrics for minimizing model errors. A comparative analysis of the obtained results of the models is given using the metric of the forecasting criterion, the mean absolute percentage error (Mean absolute percentage error or MAPE). The most commonly used regression methods for forecasting time series are used, such as linear regression model, polynomial model and cubic regression model. An empirical analysis of the time series was applied, the daily exchange rate of the Euro \/ US dollar for one year. The data includes 267 observations. The results obtained using the models used are compared with each other. It is concluded that a non-parametric model based on a cubic regression model shows a better result. It is noted that with the development of new technologies in the processing of large databases, new machine learning algorithms are being developed for forecasting time series in the context of the development of the digital economy.<\/em><\/p>\n

Key words<\/em><\/strong><\/span><\/p>\n

forecasting, time series, least squares method, polynomial models, cubic regression models.<\/em><\/p>\n<\/div>\n<\/div>\n

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Language<\/p>\n

english<\/span><\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n

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technical<\/span><\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n

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Year<\/p>\n

2022<\/span><\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n

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References<\/strong><\/span><\/p>\n

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      1. Abraham, B. (1981). Missing Observations in Time Series. Communications in statistics Theory A, 10, 1643-1653.<\/em><\/li>\n
      2. D. Marx and P.H.C. Eilers (1998). Direct generalized additive modeling with penalized likelihood, Computational Statistics and Data Analysis, 28, 193-209.<\/em><\/li>\n
      3. Beveridge, S. (1992). Least Squares Estimation of Missing Values in Time Series. Communications in statistics Theory A, 21(12), 3479-3496.<\/em><\/li>\n
      4. Brockwell, P. J., & Davis, R. A. (1991). Time Series: Theory and Methods. New York, USA: Springer-Verlag.<\/em><\/li>\n
      5. De Boor (1978). A Practical Guide to Splines, Springer, New York.<\/em><\/li>\n
      6. Hamilton, J. D. (1994). Time Series Analysis. New Jersey, USA: Princeton University Press.<\/em><\/li>\n
      7. Dierckx, Curve and surface fitting with splines, Clarendon Press, Oxford, 1993.<\/em><\/li>\n
      8. H.C. Eilers and B.D. Marx (1996). Flexible smoothing using B-splines and penalized likelihood (with comments and rejoinders). Statistical Science, 11(2), 89-121.<\/em><\/li>\n
      9. J. Green and B.W. Silverman, Nonparametric regression and generalized linear models. Chapman and Hall, London, 1994. <\/em><\/li>\n
      10. Robert H. Shumway, David S. Stoffer. Time Series Analysis and Its Applications. Springer, New York, 2006<\/em>.<\/em><\/li>\n
      11.  <\/li>\n<\/ol>\n<\/li>\n<\/ol>\n<\/li>\n<\/ol>\n<\/div>\n<\/div>\n

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        Publication date<\/span><\/strong><\/h2>\n

        09\/22\/2023<\/p>\n<\/div>\n<\/div>\n

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        <\/p>\n","protected":false},"excerpt":{"rendered":"

        Authors           Nizamitdinov A.I. \u2013 Doctor of philosophy(PhD), Senior Lecturer of Department of Digital Economy, Polytechnic Institute of Tajik Technical University, Khujand, Republic of Tajikistan, ahlidin@gmail.com. Annotation         The article discusses the basic algorithms for forecasting time series as a sequential set of data measured in time, i.e. defined in chronological order. The theoretical basis for constructing the used regression models is given. Time series forecasting models have been built. The results of model evaluation are analyzed using metrics for minimizing model errors.…<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[161],"tags":[382],"class_list":["post-2892","post","type-post","status-publish","format-standard","hentry","category-bulletin-of-pittu-2022","tag-bulletin-of-pittu-2022-2"],"acf":[],"featured_image_src":null,"author_info":{"display_name":"ilhomjonqodirov02","author_link":"https:\/\/vestnik.polytech.tj\/?author=1"},"_links":{"self":[{"href":"https:\/\/vestnik.polytech.tj\/index.php?rest_route=\/wp\/v2\/posts\/2892","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/vestnik.polytech.tj\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/vestnik.polytech.tj\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/vestnik.polytech.tj\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/vestnik.polytech.tj\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=2892"}],"version-history":[{"count":3,"href":"https:\/\/vestnik.polytech.tj\/index.php?rest_route=\/wp\/v2\/posts\/2892\/revisions"}],"predecessor-version":[{"id":2896,"href":"https:\/\/vestnik.polytech.tj\/index.php?rest_route=\/wp\/v2\/posts\/2892\/revisions\/2896"}],"wp:attachment":[{"href":"https:\/\/vestnik.polytech.tj\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=2892"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/vestnik.polytech.tj\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=2892"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/vestnik.polytech.tj\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=2892"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}