[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-117871-en":3,"doc-seo-117871-105":30,"detail-sidebar-cat-0-en-105":91},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":4,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":27,"seo_description":14,"update_tm":28,"read_time":29},117871,34359740700684,"Finn","https://ap-avatar.wpscdn.com/avatar/1f400023980c374ae676?_k=1777273430885731487",8,"Research & Report","Econometrics of Machine Learning Methods in Economic Forecasting","Economic forecasting is traditionally built on maximum likelihood estimation, yet its drawbacks become critical with modern, high-parameter settings. This chapter frames forecasting as decision theory with loss functions and emphasizes learning rules that target the minimization of expected loss. It highlights the bias–variance trade-off and how regularization and dimensionality reduction can control variance and reduce overfitting. The discussion connects prominent machine learning tools—deep learning, random forests, gradient boosting, penalized and ridge regression—to established statistical ideas while focusing on time-series lags, panel/tensor data, nowcasting, Granger causality, cross-validation, and classification.","arXiv :2308 . 10993v1 [ econ .EM] 21 Aug 2023  \nEconometrics of Machine Learning Methods in Economic Forecasting  \nAndrii Babii∗ Eric Ghysels† Jonas Striaukas‡  \nAugust 23, 2023  \n∗ University of North Carolina at Chapel Hill-Gardner Hall, CB 3305 Chapel Hill, NC 27599- 3305. Email: [babii.andrii@gmail.com](babii.andrii@gmail.com).  \n†Department of Economics and Kenan-Flagler Business School, University of North Carolina– Chapel Hill. Email: [eghysels@unc.edu](eghysels@unc.edu).  \n‡Department of Finance, Copenhagen Business School, Frederiksberg, Denmark. Email: [jonas.striaukas@gmail.com](jonas.striaukas@gmail.com).  \n1 Introduction  \nEconomic forecasting has traditionally relied on simple models estimated with the maximum likelihood (MLE) approach. The limitations of the MLE are well known as eloquently described in Bradley and Trevor (2021):  \n“Arguably the 20th century’s most influential piece of applied mathematics, maximum likelihood continues to be a prime method of choice in the statistician’s toolkit. Roughly speaking, maximum likelihood provides nearly unbiased estimates of nearly minimum variance, and does so in an automatic way. That being said, maximum likelihood estimation has shown itself to be an inadequate and dangerous tool in many 21st century applications. Again speaking roughly, unbiased can be an unavoidable luxury when there are hundreds or thousands of parameters to estimate atthe same time.”  \nJames and Stein (1961) made this point dramatically in a much simpler setting involving just a couple of parameters. The machine learning (ML) methods developed over roughly the past 60 years have revolutionized decision-making across various fields. At its core, ML involves formulating a loss or cost function for forecasting rules. In this context, a forecasting rule, denoted as f (xt ), predicts the value of a target variable, yt+h, at a future horizon, h, based on information available at time t. The loss function, ℓ (yt+h, f (xt )), quantifies the error incurred by the forecasted value compared to the actual outcome.  \nThe central goal is to approximate the optimal decision rule, f ∗ , which minimizes the expected loss, E [ℓ(yt+h, f (xt ))] . This approach has its roots in the decision theory, see Wald (1949), and is adopted in statistical learning, see Vapnik (1999), and economic forecasting, see Granger and Pesaran (2000) . For instance, when employing a quadratic loss function, ℓ (yt+h, f (xt )) = (yt+h − f(xt ))2 , the optimal decision rule corresponds to the (non-linear) regression, f ∗ (xt ) = E [yt+h|xt ] with respect tof (xt) .1  \nThe data-driven decision rules lead to the bias-variance trade-off in the forecasting performance. Flexible nonparametric techniques offer a solution by reducing bias at the cost of increasing variance, leading to potential overfitting issues. Atthe same time, regularization and dimensionality reduction introduce some bias to reduce the variance. Machine learning offers a wide array of nonparametric and high-dimensional tools, enabling flexible and accurate approximations of the optimal decision rules, adapting to the bias-variance trade-off, and optimizing the forecasting performance.  \nMany of the widely used ML tools relate to known and well-established statistical  \n1 Equivalently, we could consider the regression model, yt+h = f ∗ (xt )+εt+h with E[εt+h|xt] = 0 .  \nmethods. For example, deep learning can be understood as a regression model with nonlinearities generated by a multi-layer neural network; see Hornik, Stinchcombe, and White (1990) and Chen (2007) .2 Random forests and gradient boosting which can be understood as a new generation of regression and classification trees; see Breiman, Friedman, Stone, and Olshen (1984) . The penalized regression can be traced back to the idea of shrinkage, see James and Stein (1961), regularization of ill-posed inverse problems, see Tikhonov (1963), and the ridge regression, see Hoerland Kennard (1970a,b) .3  \nWhile the developm","cbCaieyslEA279aL","https://ap.wps.com/l/cbCaieyslEA279aL","pdf",551608,1,25,"English","en",105,"# Introduction\n## High-Dimensional Projections\n## Time Series","[{\"question\":\"How does the chapter define the forecasting objective in economic forecasting?\",\"answer\":\"It formulates forecasting rules that predict yt+h using information xt, and evaluates them through a loss function. The goal is to approximate the optimal rule that minimizes expected loss.\"},{\"question\":\"Why is maximum likelihood estimation considered limited in many 21st-century applications?\",\"answer\":\"Maximum likelihood can become inadequate and even dangerous when problems involve hundreds or thousands of parameters, where estimation at scale makes its favorable properties hard to sustain.\"},{\"question\":\"Which machine learning topics does the chapter focus on for time series and forecasting practice?\",\"answer\":\"It emphasizes treatment of time-series lags, panel and tensor data, nowcasting, high-dimensional Granger causality tests, time-series cross-validations, and classification.\"}]","Econometrics of Machine Learning Methods in Economic Forecasting | PDF",1785680088,63,{"code":4,"msg":31,"data":32},"ok",{"site_id":24,"language":23,"slug":33,"title":13,"keywords":34,"description":14,"schema_data":35,"social_meta":86,"head_meta":88,"extra_data":90,"updated_unix":28},"econometrics-of-machine-learning-methods-in-economic-forecasting","",{"@graph":36,"@context":85},[37,54,68],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,48,51],{"item":41,"name":42,"@type":43,"position":20},"https://docshare.wps.com","Home","ListItem",{"item":45,"name":46,"@type":43,"position":47},"https://docshare.wps.com/document/","Document",2,{"item":49,"name":12,"@type":43,"position":50},"https://docshare.wps.com/document/research-report/",3,{"item":52,"name":13,"@type":43,"position":53},"https://docshare.wps.com/document/econometrics-of-machine-learning-methods-in-economic-forecasting/117871/",4,{"url":52,"name":13,"@type":55,"author":56,"headline":13,"publisher":58,"fileFormat":61,"inLanguage":23,"description":14,"dateModified":62,"datePublished":62,"encodingFormat":61,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":57},"Person",{"url":41,"name":59,"@type":60},"DocShare","Organization","application/pdf","2026-08-02",true,{"@type":65,"interactionType":66,"userInteractionCount":4},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71,77,81],{"name":72,"@type":73,"acceptedAnswer":74},"How does the chapter define the forecasting objective in economic forecasting?","Question",{"text":75,"@type":76},"It formulates forecasting rules that predict yt+h using information xt, and evaluates them through a loss function. The goal is to approximate the optimal rule that minimizes expected loss.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"Why is maximum likelihood estimation considered limited in many 21st-century applications?",{"text":80,"@type":76},"Maximum likelihood can become inadequate and even dangerous when problems involve hundreds or thousands of parameters, where estimation at scale makes its favorable properties hard to sustain.",{"name":82,"@type":73,"acceptedAnswer":83},"Which machine learning topics does the chapter focus on for time series and forecasting practice?",{"text":84,"@type":76},"It emphasizes treatment of time-series lags, panel and tensor data, nowcasting, high-dimensional Granger causality tests, time-series cross-validations, and classification.","https://schema.org",{"og:url":52,"og:type":87,"og:title":13,"og:site_name":59,"og:description":14},"article",{"robots":89,"canonical":52},"index,follow",{"doc_id":7,"site_id":24},{"code":4,"msg":5,"data":92},[93,97,101,105,110,115,120,123,128,131,135],{"id":20,"doc_module":4,"doc_module_name":46,"category_name":94,"show_sort_weight":95,"slug":96},"Story & Novel",90,"story-novel",{"id":47,"doc_module":4,"doc_module_name":46,"category_name":98,"show_sort_weight":99,"slug":100},"Literature",80,"literature",{"id":53,"doc_module":4,"doc_module_name":46,"category_name":102,"show_sort_weight":103,"slug":104},"Exam",70,"exam",{"id":106,"doc_module":4,"doc_module_name":46,"category_name":107,"show_sort_weight":108,"slug":109},5,"Comic",60,"comic",{"id":111,"doc_module":4,"doc_module_name":46,"category_name":112,"show_sort_weight":113,"slug":114},6,"Technology",50,"technology",{"id":116,"doc_module":4,"doc_module_name":46,"category_name":117,"show_sort_weight":118,"slug":119},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":46,"category_name":12,"show_sort_weight":121,"slug":122},30,"research-report",{"id":124,"doc_module":4,"doc_module_name":46,"category_name":125,"show_sort_weight":126,"slug":127},9,"Religion & Spirituality",20,"religion-spirituality",{"id":126,"doc_module":4,"doc_module_name":46,"category_name":129,"show_sort_weight":126,"slug":130},"World Cup","world-cup",{"id":132,"doc_module":4,"doc_module_name":46,"category_name":133,"show_sort_weight":132,"slug":134},10,"Lifestyle","lifestyle",{"id":136,"doc_module":4,"doc_module_name":46,"category_name":137,"show_sort_weight":106,"slug":138},19,"General","general"]