{"id":13212,"date":"2021-04-11T02:05:58","date_gmt":"2021-04-11T02:05:58","guid":{"rendered":"https:\/\/analystprep.com\/study-notes\/?p=13212"},"modified":"2026-03-26T07:00:20","modified_gmt":"2026-03-26T07:00:20","slug":"covariance-stationary-property","status":"publish","type":"post","link":"https:\/\/analystprep.com\/study-notes\/cfa-level-2\/covariance-stationary-property\/","title":{"rendered":"Covariance Stationary Property"},"content":{"rendered":"<p><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\": \"Which condition is least likely required for covariance stationarity?\",\r\n    \"text\": \"Which of the following is least likely a condition for covariance stationary property?\\n\\nA. The expected value of the time series is constant and finite over time.\\n\\nB. The volatility of the time series around its mean varies at a constant rate with time.\\n\\nC. The covariance of the time series with leading or lagged values of itself is constant.\",\r\n    \"answerCount\": 1,\r\n    \"acceptedAnswer\": {\r\n      \"@type\": \"Answer\",\r\n      \"text\": \"The correct answer is B.\\n\\nA time series is covariance stationary if its mean is constant and finite, its variance is constant over time, and the covariance between values depends only on the lag and not on time. Statement B is incorrect because it implies that volatility varies over time, whereas covariance stationarity requires constant variance.\\n\\nOptions A and C describe valid conditions for covariance stationarity.\"\r\n    }\r\n  }\r\n}\r\n<\/script><\/p>\r\n\r\n<h3 class=\"editor-rich-text__tinymce mce-content-body\" data-is-placeholder-visible=\"false\">\u00a0<\/h3>\r\n<p><iframe loading=\"lazy\" src=\"https:\/\/www.youtube.com\/embed\/-SilFtkpBK8\" width=\"611\" height=\"343\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\r\n<h3 id=\"mce_22\" class=\"editor-rich-text__tinymce mce-content-body\" data-is-placeholder-visible=\"false\">\u00a0<\/h3>\r\n<p>A time series is said to be covariance stationary if its properties, such as the mean and variance, remain constant over time. A time series that is nonstationary leads to invalid linear regression estimates with no economic meaning.<\/p>\r\n<p>A time series is covariance stationary if it satisfies the following three conditions:<\/p>\r\n<ul style=\"list-style-type: disc;\">\r\n\t<li>The expected value of the time series is constant and finite over time;<\/li>\r\n\t<li>The volatility of the time series around its mean is constant and finite in all periods; and<\/li>\r\n\t<li>The covariance of the time series with leading or lagged values of itself is constant.<\/li>\r\n<\/ul>\r\n<p>Covariance stationarity can be detected by plotting the time series. We may assume covariance stationarity if the time series appears to have the same mean and variance, with no apparent seasonality.<\/p>\r\n<blockquote>\r\n<h1>Question<\/h1>\r\n<p>Which of the following is <em>least likely<\/em> a condition for covariance stationary property?<\/p>\r\n<ol style=\"list-style-type: upper-alpha;\">\r\n\t<li>The expected value of the time series is constant and finite overtime.<\/li>\r\n\t<li>The volatility of the time series around its mean varies at a constant rate with time.<\/li>\r\n\t<li>The covariance of the time series with leading or lagged values of itself is constant.<\/li>\r\n<\/ol>\r\n<h3>Solution<\/h3>\r\n<p><strong>The correct answer is B. <\/strong><\/p>\r\n<p>A time series is covariance stationary if its volatility around its mean is constant and finite in all periods<\/p>\r\n<p>Options A and C are true statements.<\/p>\r\n<\/blockquote>\r\n<p>Reading 5: Time Series Analysis<\/p>\r\n<p><em>LOS 5 (c) Explain the requirement for a time series to be covariance stationary and describe the significance of a series that is not stationary.<\/em><\/p>\r\n\r\n<div style=\"text-align: center; margin: 40px 0;\"><a style=\"display: inline-flex; align-items: center; justify-content: center; padding: 12px 20px; border-radius: 999px; background-color: #1a73e8; color: #ffffff; text-decoration: none; font-weight: 600;\" href=\"https:\/\/analystprep.com\/free-trial\/\" target=\"_blank\" rel=\"noopener\"> Start Free Trial \u2192 <\/a>\r\n<p style=\"font-size: 15px; margin-top: 12px; color: #555;\">Practice identifying stationary time series and applying CFA Level II concepts with AnalystPrep.<\/p>\r\n<\/div>","protected":false},"excerpt":{"rendered":"<p>\u00a0 \u00a0 A time series is said to be covariance stationary if its properties, such as the mean and variance, remain constant over time. A time series that is nonstationary leads to invalid linear regression estimates with no economic meaning&#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":[216,289,230],"class_list":["post-13212","post","type-post","status-publish","format-standard","hentry","category-cfa-level-2","category-quantitative-method","tag-cfa-level-2","tag-covariance-stationary-property","tag-quantitative-method","blog-post","no-post-thumbnail","animate"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.6 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Covariance Stationary Time Series Conditions<\/title>\n<meta name=\"description\" content=\"Learn what covariance stationarity means, the conditions required for a time series, and how to identify stationary processes in 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