[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-84139-en":3,"doc-seo-84139-105":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":20,"is_deleted":4,"is_public":21,"is_downloadable":21,"audit_status":21,"page_count":22,"language":23,"language_code":24,"site_id":25,"html_lang":24,"table_of_contents":26,"faqs":27,"seo_title":13,"seo_description":14,"update_tm":28,"read_time":29},84139,2336464648746,"Skyler","https://ap-avatar.wpscdn.com/davatar_276721f389ce27ea32af1340a28f341c",8,"Research & Report","tsbootstrap Distribution-Free Uncertainty Quantification and Conformal Prediction for Time Series","tsbootstrap addresses time-series problems where financial, sensing, and demand streams break the exchangeability assumed by IID conformal prediction and IID bootstrap. It unifies dependence-aware resampling (block, residual, sieve, wild) with classical bootstrap confidence intervals and adaptive conformal calibrators such as EnbPI, ACI, NexCP, and AgACI via a single typed API. Coverage studies show sharp IID undercoverage under dependence; dependence-aware methods reduce the deficit. A compiled backend accelerates fixed-statistic execution and a streaming reduce limits peak extra memory to O(B).","arXiv :2607 .06690v1 [ stat .ME] 7 Jul 2026  \ntsbootstrap: Distribution-Free Uncertainty Quantification and Conformal Prediction for Time Series  \nSankalp Gilda  \nDeep Thought Solutions  \nORCID: 0000-0002-3645-4501  \nEditor:  \nAbstract  \nFinance, sensing, and demand streams violate the exchangeability that IID conformal prediction and the IID bootstrap assume, and existing libraries implement either a general resampling engine or conformal calibration without the other. tsbootstrap provides block, residual, sieve, and wild resampling, classical bootstrap confidence intervals, and adaptive conformal calibrators (EnbPI, ACI, NexCP, AgACI) through a single typed API in which a specification object selects each method. In a controlled coverage study the IID bootstrap undercovers sharply under dependence; dependence-aware methods reduce the coverage deficit, the sieve nearest to nominal under short-memory linear dependence. On the shared fixed-statistic path a compiled backend runs several times faster than arch, and a streaming reduce avoids materializing the O(Bn) replicate tensor, limiting peak extra memory to O (B) for the statistic array. The software is MIT licensed (v0.6.1) .  \nKeywords: conformal prediction, uncertainty quantification, bootstrap, time series, distribution-free inference  \n1 Introduction and Statement of Need  \nPractitioners pair point forecasts with calibrated intervals, but the two distribution-free tools that would supply one assume away temporal structure: split conformal prediction assumes exchangeable calibration data, the ordinary bootstrap assumes IID observations, and both undercover on autoregressive streams. The time series bootstrap restores validity under dependence, and conformal calibration supplies the finite-sample coverage guarantee. Prior libraries supply one piece: forecasting toolkits (skforecast, darts, statsforecast, neuralforecast) attach residual-bootstrap or split-conformal intervals to their own forecasters, conformal libraries (MAPIE, TorchCP, puncc) calibrate a fitted predictor, and resampling libraries (arch) stop at classical intervals. To our knowledge, no existing library combines a general dependence-aware resampling engine (block, residual, sieve, and wild methods with typed specs, for arbitrary statistics) with an adaptive conformal layer and a streaming reduce in one API; tsbootstrap provides this combination. Derivations appear in the companion methods manuscript (arXiv:2404.15227) .  \n2 Design and API  \nThe single typed entry point bootstrap(X, *, method=spec, . . .) selects the method by a concrete specification object whose type identifies it, visible to editors and type checkers. A typical analysis consists of three calls: diagnose(X) to recom-  \n©2026 Sankalp Gilda.  \nLicense: CC-BY 4.0, see [https://creativecommons.org/licenses/by/4.0/](https://creativecommons.org/licenses/by/4.0/. Attribution)[. Attribution](https://creativecommons.org/licenses/by/4.0/. Attribution) requirements are provided  \nat [http://jmlr.org/papers/v27/.html](http://jmlr.org/papers/v27/.html).  \nGilda  \nmend a spec, bootstrap(X, method=spec, n bootstraps=999, random state=0), and conf   int(res, statistic=\"mean\") .  \nThe call returns a structured BootstrapResult: samples (the replicate array), provenance (spec, seed, backend), out-of-bag (the held-out index EnbPI calibrates on), and in-bag (the drawn index, for jackknife-after-bootstrap and studentized errors) . Inputs are handled by a narwhals layer (a lightweight compatibility layer over dataframe libraries): NumPy arrays, Python lists, and frames or series from pandas, Polars, and PyArrow. Each spec carries a MethodMetadata record (metadata for(spec)) declaring assumptions, capabilities, references, cost, and failure modes; diagnose(X) reads the lag-one autocorrelation and an ADF stationarity test and returns a frozen Diagnosis naming recommended specs with an auto-selected block length.  \nResults are deterministic per backend for a fixed ","cbCail7EtYey3jpx","https://ap.wps.com/l/cbCail7EtYey3jpx","pdf",219724,4,1,6,"English","en",105,"# Abstract\n# Introduction and Statement of Need\n# Design and API\n## Typed specification object API\n## Determinism and backend behavior\n# Methods and UQ Coverage\n## Dependence-aware bootstrap methods\n## Classical bootstrap intervals\n## Conformal and adaptive intervals","[{\"question\":\"Why do standard IID conformal prediction and IID bootstrap fail for time series?\",\"answer\":\"They assume exchangeability or IID observations, which temporal dependence in time series violates. This leads to undercoverage on autoregressive streams.\"},{\"question\":\"What uncertainty quantification methods does tsbootstrap provide in one API?\",\"answer\":\"It supports block, residual, sieve, and wild resampling; classical bootstrap confidence intervals; and adaptive conformal calibration methods including EnbPI, ACI, NexCP, and AgACI.\"},{\"question\":\"How does tsbootstrap manage coverage calibration under dependence?\",\"answer\":\"It uses dependence-aware resampling to restore validity under dependence, while conformal calibration supplies finite-sample coverage guarantees through adaptive calibrators such as EnbPI.\"}]",1784193284,15,{"code":4,"msg":31,"data":32},"ok",{"site_id":25,"language":24,"slug":33,"title":13,"keywords":34,"description":14,"schema_data":35,"social_meta":86,"head_meta":88,"extra_data":90,"updated_unix":28},"tsbootstrap-distribution-free-uncertainty-quantification-and-conformal-prediction-for-time-series","",{"@graph":36,"@context":85},[37,53,68],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,48,51],{"item":41,"name":42,"@type":43,"position":21},"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":20},"https://docshare.wps.com/document/tsbootstrap-distribution-free-uncertainty-quantification-and-conformal-prediction-for-time-series/84139/",{"url":52,"name":13,"@type":54,"author":55,"headline":13,"publisher":57,"fileFormat":60,"inLanguage":24,"description":14,"dateModified":61,"datePublished":62,"encodingFormat":60,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":56},"Person",{"url":41,"name":58,"@type":59},"DocShare","Organization","application/pdf","2026-07-26","2026-07-16",true,{"@type":65,"interactionType":66,"userInteractionCount":20},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71,77,81],{"name":72,"@type":73,"acceptedAnswer":74},"Why do standard IID conformal prediction and IID bootstrap fail for time series?","Question",{"text":75,"@type":76},"They assume exchangeability or IID observations, which temporal dependence in time series violates. This leads to undercoverage on autoregressive streams.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"What uncertainty quantification methods does tsbootstrap provide in one API?",{"text":80,"@type":76},"It supports block, residual, sieve, and wild resampling; classical bootstrap confidence intervals; and adaptive conformal calibration methods including EnbPI, ACI, NexCP, and AgACI.",{"name":82,"@type":73,"acceptedAnswer":83},"How does tsbootstrap manage coverage calibration under dependence?",{"text":84,"@type":76},"It uses dependence-aware resampling to restore validity under dependence, while conformal calibration supplies finite-sample coverage guarantees through adaptive calibrators such as EnbPI.","https://schema.org",{"og:url":52,"og:type":87,"og:title":13,"og:site_name":58,"og:description":14},"article",{"robots":89,"canonical":52},"index,follow",{"doc_id":7,"site_id":25},{"code":4,"msg":5,"data":92},[93,97,101,105,110,114,119,122,127,130,134],{"id":21,"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":20,"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":22,"doc_module":4,"doc_module_name":46,"category_name":111,"show_sort_weight":112,"slug":113},"Technology",50,"technology",{"id":115,"doc_module":4,"doc_module_name":46,"category_name":116,"show_sort_weight":117,"slug":118},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":46,"category_name":12,"show_sort_weight":120,"slug":121},30,"research-report",{"id":123,"doc_module":4,"doc_module_name":46,"category_name":124,"show_sort_weight":125,"slug":126},9,"Religion & Spirituality",20,"religion-spirituality",{"id":125,"doc_module":4,"doc_module_name":46,"category_name":128,"show_sort_weight":125,"slug":129},"World Cup","world-cup",{"id":131,"doc_module":4,"doc_module_name":46,"category_name":132,"show_sort_weight":131,"slug":133},10,"Lifestyle","lifestyle",{"id":135,"doc_module":4,"doc_module_name":46,"category_name":136,"show_sort_weight":106,"slug":137},19,"General","general"]