Document Zbl 1273.62222

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Time Ser. Anal.</a> <a href="/?q=in%3A322015" title="Articles in this Issue">32, No. 6, 587-597 (2011)</a>. </div> <div class="abstract">Summary: The article considers the Yule-Walker estimator of the autoregressive coefficient based on the observed time series that contains an unknown trend function and an autoregressive error term. The trend function is estimated by means of B-splines and then subtracted from the observations. The Yule-Walker estimator is obtained from the residual sequence. Asymptotic properties of this estimator are derived. The performance of the estimator is illustrated by simulation studies and real data analysis.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A6213605">Cited in <strong>12</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A62M10" title="MSC2020">62M10</a> </td> <td class="space"> Time series, auto-correlation, regression, etc. in statistics (GARCH) </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A62M09" title="MSC2020">62M09</a> </td> <td class="space"> Non-Markovian processes: estimation </td> </tr><tr> <td class="mono"> 65C60 </td> <td class="space"> Computational problems in statistics (MSC2010) </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A62F12" title="MSC2020">62F12</a> </td> <td class="space"> Asymptotic properties of parametric estimators </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A62G05" title="MSC2020">62G05</a> </td> <td class="space"> Nonparametric estimation </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A65D07" title="MSC2020">65D07</a> </td> <td class="space"> Numerical computation using splines </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Aautoregressive+time+series">autoregressive time series</a>; <a href="/?q=ut%3AYule-Walker+estimator">Yule-Walker estimator</a>; <a href="/?q=ut%3AB-splines">B-splines</a></div>  <div class="modal fade" id="metadataModal" tabindex="-1" role="dialog" aria-labelledby="myModalLabel"> <div class="modal-dialog" role="document"> <div class="modal-content"> <div class="modal-header"> <button type="button" class="close" data-dismiss="modal" aria-label="Close"><span aria-hidden="true">×</span></button> <h4 class="modal-title" id="myModalLabel">Cite</h4> </div> <div class="modal-body"> <div class="form-group"> <label for="select-output" class="control-label">Format</label> <select id="select-output" class="form-control" aria-label="Select Metadata format"></select> </div> <div class="form-group"> <label for="metadataText" class="control-label">Result</label> <textarea class="form-control" id="metadataText" rows="10" style="min-width: 100%;max-width: 100%"></textarea> </div> <div id="metadata-alert" class="alert alert-danger" role="alert" style="display: none;">  </div> </div> <div class="modal-footer"> <button type="button" class="btn btn-primary" onclick="copyMetadata()">Copy to clipboard</button> <button type="button" class="btn btn-default" data-dismiss="modal">Close</button> </div> </div> </div> </div> <div class="functions clearfix"> <div class="function">  <a type="button" class="btn btn-default btn-xs pdf" data-toggle="modal" data-target="#metadataModal" data-itemtype="Zbl" data-itemname="Zbl 1273.62222" data-ciurl="/ci/06213605" data-biburl="/bibtex/06213605.bib" data-amsurl="/amsrefs/06213605.bib" data-xmlurl="/xml/06213605.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/06213605.pdf" title="Zbl 1273.62222 as PDF">Review PDF</a> </div> <div class="fulltexts"> <span class="fulltext">Full Text:</span> <a class="btn btn-default btn-xs" type="button" href="https://doi.org/10.1111/j.1467-9892.2010.00708.x" aria-label="DOI for “Autoregressive coefficient estimation in nonparametric analysis”" title="10.1111/j.1467-9892.2010.00708.x">DOI</a> </div> <div class="sfx" style="float: right;"> </div> </div> <div class="references"> <h3>References:</h3> <table><tr> <td>[1]</td> <td class="space">Altman, Estimating error correlation in non-parametric regression, Statistics & Probability Letters 18 pp 213– (1993) · <a href="/0788.62033" class="nowrap">Zbl 0788.62033</a> · <a href="https://doi.org/10.1016/0167-7152(93)90219-9" class="nowrap">doi:10.1016/0167-7152(93)90219-9</a></td> </tr><tr> <td>[2]</td> <td class="space">Brockwell, Time Series: Theory and Methods, 2nd ed (1991) · <a href="/0709.62080" class="nowrap">Zbl 0709.62080</a> · <a href="https://doi.org/10.1007/978-1-4419-0320-4" class="nowrap">doi:10.1007/978-1-4419-0320-4</a></td> </tr><tr> <td>[3]</td> <td class="space">Fan, Polynomial Modeling and Its Applications (1996)</td> </tr><tr> <td>[4]</td> <td class="space">Fuller, Introduction to Statistical Time Series (1996) · <a href="/0851.62057" class="nowrap">Zbl 0851.62057</a></td> </tr><tr> <td>[5]</td> <td class="space">Hall, Using difference-based methods for inference in non-parametric regression with time series errors, Journal of the Royal Statistical Society Series B 65 pp 443– (2003) · <a href="/1065.62067" class="nowrap">Zbl 1065.62067</a> · <a href="https://doi.org/10.1111/1467-9868.00395" class="nowrap">doi:10.1111/1467-9868.00395</a></td> </tr><tr> <td>[6]</td> <td class="space">Huang, Local asymptotics for polynomial spline regression, Annals of Statistics 31 pp 1600– (2003) · <a 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stationary and nonstationary ARMA models, Journal of the American Statistical Association 79 pp 84– (1984) · <a href="/0537.62071" class="nowrap">Zbl 0537.62071</a> · <a href="https://doi.org/10.2307/2288340" class="nowrap">doi:10.2307/2288340</a></td> </tr><tr> <td>[10]</td> <td class="space">Wang, Spline-backfitted kernel smoothing of nonlinear additive autoregression model, Annals of Statistics 35 pp 2474– (2007) · <a href="/1129.62038" class="nowrap">Zbl 1129.62038</a> · <a href="https://doi.org/10.1214/009053607000000488" class="nowrap">doi:10.1214/009053607000000488</a></td> </tr><tr> <td>[11]</td> <td class="space">Wang, Polynomial spline confidence bands for regression curves, Statistica Sinica 19 pp 325– (2009) · <a href="/1225.62055" class="nowrap">Zbl 1225.62055</a></td> </tr><tr> <td>[12]</td> <td class="space">Xue, Additive coefficient modelling via polynomial spline, Statistica Sinica 16 pp 1423– (2006) · <a href="/1109.62030" class="nowrap">Zbl 1109.62030</a></td> </tr><tr> <td>[13]</td> <td class="space">Yang, Multivariate bandwidth selection for local linear regression, Journal of the Royal Statistical Society Series B 61 pp 793– (1999) · <a href="/0952.62039" class="nowrap">Zbl 0952.62039</a> · <a href="https://doi.org/10.1111/1467-9868.00203" class="nowrap">doi:10.1111/1467-9868.00203</a></td> </tr></table> <div class="reference_disclaimer"> This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching. </div> </div></article> </div></div> </div> </div> <div class="clearfix"></div> </div> </div> <div id="foot"><div class="copyright"> © 2025 <a target="fiz" href="https://www.fiz-karlsruhe.de/en">FIZ Karlsruhe GmbH</a> <a href="/privacy-policy/">Privacy Policy</a> <a href="/legal-notices/">Legal Notices</a> <a href="/terms-conditions/">Terms & Conditions</a> <div class="info"> <ul class="nav"> <li class="mastodon"> <a href="https://mathstodon.xyz/@zbMATH" target="_blank" class="no-new-tab-icon"> <img src="/static/mastodon.png" title="zbMATH at Mathstodon (opens in new tab)" alt="Mastodon logo"> </a> </li> </ul> </div> </div> <div class="clearfix" style="height: 0px;"></div> </div> </div> <script src="https://static.zbmath.org/contrib/jquery/1.9.1/jquery.min.js"></script> <script src="https://static.zbmath.org/contrib/jquery-caret/1.5.2/jquery.caret.min.js"></script> <script src="/static/js/jquery-ui-1.10.1.custom.min.js"></script> <script src="https://static.zbmath.org/contrib/bootstrap/v3.3.7zb1/js/bootstrap.min.js"></script> <script src="https://static.zbmath.org/contrib/bootstrap-lightbox/v0.7.0/bootstrap-lightbox.min.js"></script> <script src="https://static.zbmath.org/contrib/retina/unknown/retina.js"></script> <script src="https://static.zbmath.org/contrib/bootstrap-select/v1.13.14/js/bootstrap-select.min.js"></script> <script> var SCRIPT_ROOT = ""; </script> <script src="/static/scripts.js?v=20240926"> </script> <script src="https://static.zbmath.org/contrib/mathjax/2.7.1/MathJax.js?config=TeX-AMS-MML_HTMLorMML"></script> <script type="text/x-mathjax-config"> MathJax.Hub.Config({ "HTML-CSS": { preferredFont: "TeX", availableFonts: [ "STIX", "TeX" ], linebreaks: { automatic: true }, EqnChunk: (MathJax.Hub.Browser.isMobile ? 10 : 50) }, tex2jax: { processEscapes: true, ignoreClass: "tex2jax_ignore|dno" }, TeX: { Macros: { Aut: "\\operatorname{Aut}", Hom: "\\operatorname{Hom}" }, noUndefined: { attributes: { mathcolor: "#039", //"red", mathbackground: "white", //"#FFEEEE", mathsize: "90%" } } }, messageStyle: "none" }); </script> <script type="text/javascript"> $(document).ready(function() { $("#MathInput").stop(true, true).keyup(function() { $.ajax({ url: "/mwsq/", type: "POST", data: { query : $("#MathInput").val() }, dataType: "text" }) .done(function(xml) { $("#MathPreview").html(xml); $(window).resize(); }); }); var press = jQuery.Event("keyup"); press.ctrlKey = false; press.which = 40; $("#MathInput").trigger(press); }); </script> <div id="new_tab_icon" style="display: none"> <span class="glyphicon glyphicon-new-window" aria-hidden="true"></span><span class="sr-only">(opens in new tab)</span></div> </body> </html>

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