{"id":13252,"date":"2021-04-11T05:44:46","date_gmt":"2021-04-11T05:44:46","guid":{"rendered":"https:\/\/analystprep.com\/study-notes\/?p=13252"},"modified":"2026-01-26T18:02:17","modified_gmt":"2026-01-26T18:02:17","slug":"residual-autocorrelation","status":"publish","type":"post","link":"https:\/\/analystprep.com\/study-notes\/cfa-level-2\/residual-autocorrelation\/","title":{"rendered":"Residual Autocorrelation"},"content":{"rendered":"<script type=\"application\/ld+json\">\r\n{\r\n  \"@context\": \"https:\/\/schema.org\",\r\n  \"@type\": \"QAPage\",\r\n  \"mainEntity\": {\r\n    \"@type\": \"Question\",\r\n    \"name\": \"Is the AR(1) model correctly specified based on residual autocorrelations?\",\r\n    \"text\": \"Consider an AR(1) model relating to 100 observations with residual autocorrelations at lags 1 to 4 given as \u22120.0584, \u22120.0492, 0.0625, and 0.1455. At the 5% significance level, which statement is most appropriate regarding the model specification?\",\r\n    \"answerCount\": 1,\r\n    \"acceptedAnswer\": {\r\n      \"@type\": \"Answer\",\r\n      \"text\": \"The AR(1) model is correctly specified. With 100 observations, the standard error of the residual autocorrelation is 1\/\u221a100 = 0.10. All reported residual autocorrelations are within \u00b11.96 \u00d7 0.10, so none are statistically different from zero at the 5% significance level. This indicates no remaining serial correlation in the residuals.\",\r\n      \"dateCreated\": \"2026-01-21\"\r\n    }\r\n  }\r\n}\r\n<\/script>\r\n\r\n\r\n<h3 id=\"mce_22\" class=\"editor-rich-text__tinymce mce-content-body\" data-is-placeholder-visible=\"false\"><iframe loading=\"lazy\"\r\n  width=\"611\"\r\n  height=\"344\"\r\n  src=\"https:\/\/www.youtube.com\/embed\/-SilFtkpBK8\"\r\n  title=\"YouTube video player\"\r\n  frameborder=\"0\"\r\n  allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\"\r\n  referrerpolicy=\"strict-origin-when-cross-origin\"\r\n  allowfullscreen>\r\n<\/iframe><\/h3>\r\n<p>The autocorrelation of a time series refers to the correlation of that time series with its past values. The k<sup>th<\/sup> order autocorrelation is the autocorrelation between <strong>one time series observation<\/strong> and the value <em>k<\/em> periods before.<\/p>\r\n<p>We cannot use the Durbin-Watson statistic to test for serial correlation in autoregressive models. This is because the test becomes invalid when the independent variables include past values of the dependent variable. Nevertheless, we can use the t-test to check whether the autocorrelations of the error terms are significantly different from zero. (Recall that serial correlation refers to the positive or negative correlation of the error terms.)<\/p>\r\n<p>An accurately specified autoregressive model will have residual autocorrelations that do not vary significantly from zero.<\/p>\r\n<p>To test whether an AR model is correctly specified, the following steps are followed:<\/p>\r\n<ul style=\"list-style-type: disc;\">\r\n\t<li>Estimate the autoregressive model and calculate the residuals;<\/li>\r\n\t<li>Calculate the autocorrelations of the residuals; and<\/li>\r\n\t<li>Perform a t-test to check if the autocorrelations are statistically different from 0.<\/li>\r\n<\/ul>\r\n<p>$$\\text{t}_{\\text{statistic}}=\\frac{\\text{Residual Autocorrelation}}{\\frac{1}{\\sqrt{\\text{T}}}}$$<\/p>\r\n<p>i.e.<\/p>\r\n<p>$$\\text{t}=\\frac{\\rho_{\\epsilon_{\\text{t}}}, \\epsilon_{\\text{t}-\\text{k}}}{\\frac{1}{\\sqrt{\\text{T}}}}$$<\/p>\r\n<p>Where:<\/p>\r\n<ul>\r\n\t<li>\\(\\frac{1}{\\sqrt{\\text{T}}}\\)= Standard Error<\/li>\r\n\t<li>T= number of observations<\/li>\r\n\t<li>\\(\\rho_{\\epsilon_{\\text{t}}}, \\epsilon_{\\text{t}-\\text{k}}\\) = Correlation of the Error Term \\(t\\) with the k<sup>th<\/sup> lagged error term.<\/li>\r\n<\/ul>\r\n<p>Note:\u00a0<\/p>\r\n<ul style=\"list-style-type: circle;\">\r\n\t<li>The null hypothesis, \\(\\text{H}_{0}\\) is that there is no autocorrelation.<\/li>\r\n\t<li>Reject the null hypothesis if \\(\\text{t}_{\\text{statistic}}\\) is greater than the critical value of t at the specified significance level and T-2 degrees of freedom.\u00a0<\/li>\r\n<\/ul>\r\n<p>Rejection of the null hypothesis implies that the model is not correctly specified and should be modified. On the other hand, failure to reject the null hypothesis implies that the model is statistically valid.<\/p>\r\n<h3>Example: Testing an Autoregressive Model<\/h3>\r\n<p>Consider the following AR(1) model:<\/p>\r\n<p>$$\\text{x}_{\\text{t}}=\\text{b}_{0}+\\text{b}_{1}\\text{x}_{\\text{t}-1}+\\epsilon_{\\text{t}}$$<\/p>\r\n<p>The following table shows the autocorrelations of the residuals from the estimation of the model using a sample of 23 observations.<\/p>\r\n<p>$$\\small{\\begin{array}{c|c|c} \\textbf{Lag} &amp; \\textbf{Autocorrelation} &amp; \\textbf{t-statistic} \\\\ \\hline1 &amp; 0.3834 &amp; 1.8388 \\\\ \\hline 2 &amp; 0.3483 &amp; 1.6705 \\\\ \\hline3 &amp; 0.2897 &amp; 1.3894 \\\\ \\hline 4 &amp; -0.1722 &amp; -0.8259 \\\\ \\hline 5 &amp; -0.0725 &amp; -0.3477 \\\\ \\hline6 &amp; -0.3952 &amp; -1.8954 \\\\\u00a0 \\end{array}}$$<\/p>\r\n<p>Check whether the model is correctly specified at the 5% level of significance.<\/p>\r\n<p>$$\\text{Standard error}= \\frac{1}{\\sqrt{T}}=\\frac{1}{\\sqrt{23}}=0.2085$$<\/p>\r\n<p>We can compute the t-statistic for lag one as:\u00a0<\/p>\r\n<p>$$\\begin{align*}\\text{t}_{\\text{statistic}}&amp;=\\frac{\\text{Residual Autocorrelation}}{\\frac{1}{\\sqrt{\\text{T}}}}\\\\&amp;=\\frac{0.3834}{0.2085}=1.8388\\end{align*}$$<\/p>\r\n<p>The critical two-tail t-value using 21 degrees of freedom at the 5% level of significance is 2.08.<\/p>\r\n<p>Notice that all the absolute values of the t-statistics corresponding to the residual autocorrelations are less than 2.08. This implies that none of them is statistically different from zero.<\/p>\r\n<p>Therefore, we can conclude that the error terms from the AR(1) model are not serially correlated, and thus the model is correctly specified.<\/p>\r\n<blockquote>\r\n<h2>Question<\/h2>\r\n<p>Consider an AR(1) model relating to 100 observations with residual autocorrelations as presented in the following table:<\/p>\r\n<p>$$\\small{\\begin{array}{c|c} \\textbf{Lag} &amp; \\textbf{Autocorrelation} \\\\\\hline1 &amp; -0.0584 \\\\ \\hline 2 &amp; -0.0492 \\\\ \\hline 3 &amp; 0.0625 \\\\ \\hline4 &amp; 0.1455 \\\\\u00a0 \\end{array}}$$<\/p>\r\n<p>At the 5% significance level, the <em>most appropriate<\/em> statement is that:<\/p>\r\n<ol style=\"list-style-type: upper-alpha;\">\r\n\t<li>The AR(1) model is correctly specified.<\/li>\r\n\t<li>The AR model is not correctly specified because the autocorrelations of the residuals for lag 1 are statistically different from 0.<\/li>\r\n\t<li>The AR model is not correctly specified because the autocorrelations of the residuals for lag 4 are statistically different from 0.<\/li>\r\n<\/ol>\r\n<h4>Solution<\/h4>\r\n<p><strong>The correct answer is A.<\/strong><\/p>\r\n<p>$$\\text{Standard error}=\\frac{1}{\\sqrt{\\text{T}}}=\\frac{1}{\\sqrt{100}}=0.10$$<\/p>\r\n<p>We can compute the t-statistic for lag one as:\u00a0<\/p>\r\n<p>$$\\text{t}_{\\text{statistic}}=\\frac{\\text{Residual autocorrelation}}{\\frac{1}{\\sqrt{\\text{T}}}}$$<\/p>\r\n<p>$$\\text{t}_{\\text{Statistic}}=\\frac{-0.0584}{0.10}=-0.584$$<\/p>\r\n<p>Repeating this for all the lags gives:\u00a0<\/p>\r\n<p>$$\\small{\\begin{array}{c|c|c} \\textbf{Lag} &amp; \\textbf{Autocorrelation} &amp; \\textbf{t-Statistic} \\\\ \\hline 1 &amp; -0.0584 &amp; -0.584 \\\\ \\hline2 &amp; -0.0492 &amp; -0.492 \\\\ \\hline3 &amp; 0.0625 &amp; 0.625 \\\\ \\hline 4 &amp; 0.1455 &amp; 1.455 \\\\\u00a0 \\end{array}}$$<\/p>\r\n<p>The critical two-tail t-value using 98 degrees of freedom at the 5% level of significance is 1.98.<\/p>\r\n<p>Notice that all the absolute values of the t-statistics corresponding to the residual autocorrelations are less than 1.98, which implies that none of them is statistically different from zero.<\/p>\r\n<p>Therefore, we can conclude that the error terms from the AR(1) model are not serially correlated, implying that the model is correctly specified.<\/p>\r\n<\/blockquote>\r\n<p>Reading 5: Time Series Analysis<\/p>\r\n<p><em>LOS 5 (e) Explain how autocorrelations of the residuals can be used to test whether the autoregressive model fits the time series.<\/em><\/p>\r\n<p>&nbsp;<\/p>\r\n","protected":false},"excerpt":{"rendered":"<p>The autocorrelation of a time series refers to the correlation of that time series with its past values. The kth order autocorrelation is the autocorrelation between one time series observation and the value k periods before. We cannot use the&#8230;<\/p>\n","protected":false},"author":5,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[102,229],"tags":[216,230,291],"class_list":["post-13252","post","type-post","status-publish","format-standard","hentry","category-cfa-level-2","category-quantitative-method","tag-cfa-level-2","tag-quantitative-method","tag-residual-autocorrelation","blog-post","no-post-thumbnail","animate"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.4 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Residual Autocorrelation in Time Series | CFA Level II<\/title>\n<meta name=\"description\" content=\"Learn how residual autocorrelation is used to test model fit in time series analysis, including autocorrelation of residuals and diagnostic testing methods.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/analystprep.com\/study-notes\/cfa-level-2\/residual-autocorrelation\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Residual Autocorrelation in Time Series | CFA Level II\" \/>\n<meta property=\"og:description\" content=\"Learn how residual autocorrelation is used to test model fit in time series analysis, including autocorrelation of residuals and diagnostic testing methods.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/analystprep.com\/study-notes\/cfa-level-2\/residual-autocorrelation\/\" \/>\n<meta property=\"og:site_name\" content=\"CFA, FRM, and Actuarial Exams Study Notes\" \/>\n<meta property=\"article:published_time\" content=\"2021-04-11T05:44:46+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2026-01-26T18:02:17+00:00\" \/>\n<meta name=\"author\" content=\"Irene R\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"Irene R\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"2 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\\\/\\\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\\\/\\\/analystprep.com\\\/study-notes\\\/cfa-level-2\\\/residual-autocorrelation\\\/#article\",\"isPartOf\":{\"@id\":\"https:\\\/\\\/analystprep.com\\\/study-notes\\\/cfa-level-2\\\/residual-autocorrelation\\\/\"},\"author\":{\"name\":\"Irene R\",\"@id\":\"https:\\\/\\\/analystprep.com\\\/study-notes\\\/#\\\/schema\\\/person\\\/7002f30d8f174958802c1c30b167eaf5\"},\"headline\":\"Residual Autocorrelation\",\"datePublished\":\"2021-04-11T05:44:46+00:00\",\"dateModified\":\"2026-01-26T18:02:17+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\\\/\\\/analystprep.com\\\/study-notes\\\/cfa-level-2\\\/residual-autocorrelation\\\/\"},\"wordCount\":764,\"keywords\":[\"CFA-level-2\",\"Quantitative Method\",\"Residual Autocorrelation\"],\"articleSection\":[\"CFA Level II Study Notes\",\"Quantitative Method\"],\"inLanguage\":\"en-US\"},{\"@type\":\"WebPage\",\"@id\":\"https:\\\/\\\/analystprep.com\\\/study-notes\\\/cfa-level-2\\\/residual-autocorrelation\\\/\",\"url\":\"https:\\\/\\\/analystprep.com\\\/study-notes\\\/cfa-level-2\\\/residual-autocorrelation\\\/\",\"name\":\"Residual Autocorrelation in Time Series | CFA Level II\",\"isPartOf\":{\"@id\":\"https:\\\/\\\/analystprep.com\\\/study-notes\\\/#website\"},\"datePublished\":\"2021-04-11T05:44:46+00:00\",\"dateModified\":\"2026-01-26T18:02:17+00:00\",\"author\":{\"@id\":\"https:\\\/\\\/analystprep.com\\\/study-notes\\\/#\\\/schema\\\/person\\\/7002f30d8f174958802c1c30b167eaf5\"},\"description\":\"Learn how residual autocorrelation is used to test model fit in time series analysis, including autocorrelation of residuals and diagnostic testing methods.\",\"breadcrumb\":{\"@id\":\"https:\\\/\\\/analystprep.com\\\/study-notes\\\/cfa-level-2\\\/residual-autocorrelation\\\/#breadcrumb\"},\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\\\/\\\/analystprep.com\\\/study-notes\\\/cfa-level-2\\\/residual-autocorrelation\\\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\\\/\\\/analystprep.com\\\/study-notes\\\/cfa-level-2\\\/residual-autocorrelation\\\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\\\/\\\/analystprep.com\\\/study-notes\\\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Residual Autocorrelation\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\\\/\\\/analystprep.com\\\/study-notes\\\/#website\",\"url\":\"https:\\\/\\\/analystprep.com\\\/study-notes\\\/\",\"name\":\"CFA, FRM, and Actuarial Exams Study Notes\",\"description\":\"Question Bank and Study Notes for the CFA, FRM, and Actuarial exams\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\\\/\\\/analystprep.com\\\/study-notes\\\/?s={search_term_string}\"},\"query-input\":{\"@type\":\"PropertyValueSpecification\",\"valueRequired\":true,\"valueName\":\"search_term_string\"}}],\"inLanguage\":\"en-US\"},{\"@type\":\"Person\",\"@id\":\"https:\\\/\\\/analystprep.com\\\/study-notes\\\/#\\\/schema\\\/person\\\/7002f30d8f174958802c1c30b167eaf5\",\"name\":\"Irene R\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\\\/\\\/secure.gravatar.com\\\/avatar\\\/33caf1e1bcb63ee970b36351f165c7bc714b19614993ab9c2c8bf36273b7df48?s=96&d=mm&r=g\",\"url\":\"https:\\\/\\\/secure.gravatar.com\\\/avatar\\\/33caf1e1bcb63ee970b36351f165c7bc714b19614993ab9c2c8bf36273b7df48?s=96&d=mm&r=g\",\"contentUrl\":\"https:\\\/\\\/secure.gravatar.com\\\/avatar\\\/33caf1e1bcb63ee970b36351f165c7bc714b19614993ab9c2c8bf36273b7df48?s=96&d=mm&r=g\",\"caption\":\"Irene R\"},\"url\":\"https:\\\/\\\/analystprep.com\\\/study-notes\\\/author\\\/irene\\\/\"}]}<\/script>\n<meta property=\"og:video\" content=\"https:\/\/www.youtube.com\/embed\/-SilFtkpBK8\" \/>\n<meta property=\"og:video:type\" content=\"text\/html\" \/>\n<meta property=\"og:video:duration\" content=\"3302\" \/>\n<meta property=\"og:video:width\" content=\"480\" \/>\n<meta property=\"og:video:height\" content=\"270\" \/>\n<meta property=\"ya:ovs:adult\" content=\"false\" \/>\n<meta property=\"ya:ovs:upload_date\" content=\"2021-04-11T05:44:46+00:00\" \/>\n<meta property=\"ya:ovs:allow_embed\" content=\"true\" \/>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"Residual Autocorrelation in Time Series | CFA Level II","description":"Learn how residual autocorrelation is used to test model fit in time series analysis, including autocorrelation of residuals and diagnostic testing methods.","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:\/\/analystprep.com\/study-notes\/cfa-level-2\/residual-autocorrelation\/","og_locale":"en_US","og_type":"article","og_title":"Residual Autocorrelation in Time Series | CFA Level II","og_description":"Learn how residual autocorrelation is used to test model fit in time series analysis, including autocorrelation of residuals and diagnostic testing methods.","og_url":"https:\/\/analystprep.com\/study-notes\/cfa-level-2\/residual-autocorrelation\/","og_site_name":"CFA, FRM, and Actuarial Exams Study Notes","article_published_time":"2021-04-11T05:44:46+00:00","article_modified_time":"2026-01-26T18:02:17+00:00","author":"Irene R","twitter_card":"summary_large_image","twitter_misc":{"Written by":"Irene R","Est. reading time":"2 minutes"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Article","@id":"https:\/\/analystprep.com\/study-notes\/cfa-level-2\/residual-autocorrelation\/#article","isPartOf":{"@id":"https:\/\/analystprep.com\/study-notes\/cfa-level-2\/residual-autocorrelation\/"},"author":{"name":"Irene R","@id":"https:\/\/analystprep.com\/study-notes\/#\/schema\/person\/7002f30d8f174958802c1c30b167eaf5"},"headline":"Residual Autocorrelation","datePublished":"2021-04-11T05:44:46+00:00","dateModified":"2026-01-26T18:02:17+00:00","mainEntityOfPage":{"@id":"https:\/\/analystprep.com\/study-notes\/cfa-level-2\/residual-autocorrelation\/"},"wordCount":764,"keywords":["CFA-level-2","Quantitative Method","Residual Autocorrelation"],"articleSection":["CFA Level II Study Notes","Quantitative Method"],"inLanguage":"en-US"},{"@type":"WebPage","@id":"https:\/\/analystprep.com\/study-notes\/cfa-level-2\/residual-autocorrelation\/","url":"https:\/\/analystprep.com\/study-notes\/cfa-level-2\/residual-autocorrelation\/","name":"Residual Autocorrelation in Time Series | CFA Level II","isPartOf":{"@id":"https:\/\/analystprep.com\/study-notes\/#website"},"datePublished":"2021-04-11T05:44:46+00:00","dateModified":"2026-01-26T18:02:17+00:00","author":{"@id":"https:\/\/analystprep.com\/study-notes\/#\/schema\/person\/7002f30d8f174958802c1c30b167eaf5"},"description":"Learn how residual autocorrelation is used to test model fit in time series analysis, including autocorrelation of residuals and diagnostic testing methods.","breadcrumb":{"@id":"https:\/\/analystprep.com\/study-notes\/cfa-level-2\/residual-autocorrelation\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/analystprep.com\/study-notes\/cfa-level-2\/residual-autocorrelation\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/analystprep.com\/study-notes\/cfa-level-2\/residual-autocorrelation\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/analystprep.com\/study-notes\/"},{"@type":"ListItem","position":2,"name":"Residual Autocorrelation"}]},{"@type":"WebSite","@id":"https:\/\/analystprep.com\/study-notes\/#website","url":"https:\/\/analystprep.com\/study-notes\/","name":"CFA, FRM, and Actuarial Exams Study Notes","description":"Question Bank and Study Notes for the CFA, FRM, and Actuarial exams","potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/analystprep.com\/study-notes\/?s={search_term_string}"},"query-input":{"@type":"PropertyValueSpecification","valueRequired":true,"valueName":"search_term_string"}}],"inLanguage":"en-US"},{"@type":"Person","@id":"https:\/\/analystprep.com\/study-notes\/#\/schema\/person\/7002f30d8f174958802c1c30b167eaf5","name":"Irene R","image":{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/secure.gravatar.com\/avatar\/33caf1e1bcb63ee970b36351f165c7bc714b19614993ab9c2c8bf36273b7df48?s=96&d=mm&r=g","url":"https:\/\/secure.gravatar.com\/avatar\/33caf1e1bcb63ee970b36351f165c7bc714b19614993ab9c2c8bf36273b7df48?s=96&d=mm&r=g","contentUrl":"https:\/\/secure.gravatar.com\/avatar\/33caf1e1bcb63ee970b36351f165c7bc714b19614993ab9c2c8bf36273b7df48?s=96&d=mm&r=g","caption":"Irene R"},"url":"https:\/\/analystprep.com\/study-notes\/author\/irene\/"}]},"og_video":"https:\/\/www.youtube.com\/embed\/-SilFtkpBK8","og_video_type":"text\/html","og_video_duration":"3302","og_video_width":"480","og_video_height":"270","ya_ovs_adult":"false","ya_ovs_upload_date":"2021-04-11T05:44:46+00:00","ya_ovs_allow_embed":"true"},"_links":{"self":[{"href":"https:\/\/analystprep.com\/study-notes\/wp-json\/wp\/v2\/posts\/13252","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/analystprep.com\/study-notes\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/analystprep.com\/study-notes\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/analystprep.com\/study-notes\/wp-json\/wp\/v2\/users\/5"}],"replies":[{"embeddable":true,"href":"https:\/\/analystprep.com\/study-notes\/wp-json\/wp\/v2\/comments?post=13252"}],"version-history":[{"count":32,"href":"https:\/\/analystprep.com\/study-notes\/wp-json\/wp\/v2\/posts\/13252\/revisions"}],"predecessor-version":[{"id":42111,"href":"https:\/\/analystprep.com\/study-notes\/wp-json\/wp\/v2\/posts\/13252\/revisions\/42111"}],"wp:attachment":[{"href":"https:\/\/analystprep.com\/study-notes\/wp-json\/wp\/v2\/media?parent=13252"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/analystprep.com\/study-notes\/wp-json\/wp\/v2\/categories?post=13252"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/analystprep.com\/study-notes\/wp-json\/wp\/v2\/tags?post=13252"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}