{"id":11985,"date":"2021-03-03T19:33:52","date_gmt":"2021-03-03T19:33:52","guid":{"rendered":"https:\/\/analystprep.com\/study-notes\/?p=11985"},"modified":"2026-01-26T18:50:09","modified_gmt":"2026-01-26T18:50:09","slug":"model-misspecification","status":"publish","type":"post","link":"https:\/\/analystprep.com\/study-notes\/cfa-level-2\/model-misspecification\/","title":{"rendered":"Model Misspecification"},"content":{"rendered":"<p><script type=\"application\/ld+json\">\n{\n  \"@context\": \"https:\/\/schema.org\",\n  \"@type\": \"QAPage\",\n  \"mainEntity\": {\n    \"@type\": \"Question\",\n    \"name\": \"What causes time-series model misspecification when independent variables correlate with the error term?\",\n    \"text\": \"The correlation of the independent variables with the error term may result in model misspecification. This type of time-series misspecification is most likely created by:\\n\\nA. Using independent variables that are measured with an error.\\n\\nB. The omission of some important variables from the regression.\\n\\nC. Use of improperly pooled data.\",\n    \"answerCount\": 1,\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The correct answer is A. Measuring independent variables with error creates time-series model misspecification because the measurement error can be correlated with the regression error term. An example is using forward rates instead of spot rates. Other causes include using lagged dependent variables as independent variables in the presence of serial correlation, or using a function of the dependent variable as an independent variable. Choices B and C relate to incorrect functional form rather than this type of time-series misspecification.\"\n    }\n  }\n}\n<\/script><br \/>\n<script type=\"application\/ld+json\">\n{\n  \"@context\": \"https:\/\/schema.org\",\n  \"@type\": \"VideoObject\",\n  \"name\": \"Multiple Regression (2022 Level II CFA\u00ae Exam \u2013 Reading 2)\",\n  \"description\": \"Professor James Forjan, PhD, CFA, explains multiple regression for the CFA Level II Quantitative Methods curriculum. This lesson builds on simple linear regression and shows how to evaluate multiple independent variables, interpret coefficients, and assess statistical significance.\",\n  \"uploadDate\": \"2021-12-23\",\n  \"thumbnailUrl\": \"https:\/\/img.youtube.com\/vi\/8E2AbtAb0a8\/maxresdefault.jpg\",\n  \"contentUrl\": \"https:\/\/www.youtube.com\/watch?v=8E2AbtAb0a8\",\n  \"embedUrl\": \"https:\/\/www.youtube.com\/embed\/8E2AbtAb0a8\",\n  \"duration\": \"PT55M42S\",\n  \"publisher\": {\n    \"@type\": \"Organization\",\n    \"name\": \"AnalystPrep\",\n    \"url\": \"https:\/\/analystprep.com\/\",\n    \"logo\": {\n      \"@type\": \"ImageObject\",\n      \"url\": \"https:\/\/analystprep.com\/wp-content\/uploads\/2023\/01\/analystprep-logo.png\"\n    }\n  },\n  \"creator\": {\n    \"@type\": \"Person\",\n    \"name\": \"James Forjan\",\n    \"honorificSuffix\": \"PhD, CFA\"\n  }\n}\n<\/script><\/p>\n<p><iframe loading=\"lazy\" width=\"560\" height=\"315\" src=\"https:\/\/www.youtube.com\/embed\/8E2AbtAb0a8?si=4ZPlKKh7lN1JTtdA\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe><\/p>\n<p>Model specification involves selecting independent variables to include in the regression and the functional form of the regression equation. We say that a model is <strong>misspecified<\/strong> when it violates the assumptions underlying linear regression, its functional form is incorrect, or it contains time series specification problems.<\/p>\n<h2>Categories of Model Misspecification<\/h2>\n<h4>Misspecified Functional Form<\/h4>\n<p>This type of model misspecification occurs when the regression formula is incorrect. Misspecification functional form can result from:<\/p>\n<ul>\n<li>The omission of important variables from the regression.<\/li>\n<li>Use of the wrong form of data in the regression. This may be due to failure to transform variables that are non-linear.<\/li>\n<li>Use of improperly pooled data.<\/li>\n<\/ul>\n<h4>Misspecified Time Series Data<\/h4>\n<p>This type of model misspecification occurs when there is a correlation between the independent variables and the error term. This is a violation of the multiple regression assumption that the error term has a mean of 0, conditioned on the independent variable results to biased and inconsistent estimated regression coefficients.<\/p>\n<p>Time series model misspecification is created by:<\/p>\n<p>\u00a0i. Using lagged dependent variables as independent variables in regressions with serially correlated errors.<\/p>\n<p>\u00a0ii. Using a function of the dependent variable as an independent variable, for example, forecasting the past.<\/p>\n<p>\u00a0iii. Measuring independent variables with an error. An example is using forward rates instead of spot rates.<\/p>\n<p><strong>Nonstationarity <\/strong>is a type of time series misspecification that arises when a variable\u2019s mean and variance vary with time.<\/p>\n<h2>Effects of Model Misspecification<\/h2>\n<p>Misspecification of the main dependent variable and other covariates is very common. This has a great impact on tests of association between the dependent and the independent variables. More specifically, model misspecification leads to the following:<\/p>\n<p>\u00a0 \u00a0 \u00a0i. Biased and inconsistent regression coefficients<\/p>\n<p>\u00a0 \u00a0 ii. Unreliable hypothesis test results<\/p>\n<p>\u00a0 \u00a0 iii. Inaccurate predictions<\/p>\n<h2>Avoiding Model Misspecification<\/h2>\n<p>\u00a0 \u00a0 \u00a0 i. Transform non-linear variables to a linear form\u2014for example, the use of log-based transformations.<\/p>\n<p>\u00a0 \u00a0 \u00a0ii. Avoid independent variables that are mathematical functions of dependent variables.<\/p>\n<p>\u00a0 \u00a0 iii. Omit spurious independent variables.<\/p>\n<p>\u00a0 \u00a0iv. Validate model estimations out-of-sample.<\/p>\n<p>\u00a0 \u00a0 v. Use good samples when collecting data.<\/p>\n<p>\u00a0 \u00a0vi. Check for violations of linear regression assumptions using diagnostic tests.<\/p>\n<blockquote>\n<h2>Question<\/h2>\n<p>The correlation of the independent variables with the error term may result in model misspecification. This type of time-series misspecification is <em>most likely<\/em> created by:<\/p>\n<p>\u00a0 \u00a0 \u00a0 A. Using independent variables that are measured with an error.<\/p>\n<p>\u00a0 \u00a0 \u00a0 B. The omission of some important variables from the regression.<\/p>\n<p>\u00a0 \u00a0 \u00a0 C. Use of improperly pooled data.<\/p>\n<h3>Solution<\/h3>\n<p><strong>The correct answer is A.<\/strong><\/p>\n<p>Measuring independent variables with an error creates time-series model misspecification. An example is using forward rates instead of spot rates.<\/p>\n<p>Other common problems that create this type of time-series misspecification are:<\/p>\n<p>\u00a0 \u00a0 \u00a0 i. Using lagged dependent variables as independent variables in regressions with serially correlated errors.<\/p>\n<p>\u00a0 \u00a0 \u00a0ii. Using a function of the dependent variable as an independent variable, for example, forecasting the past.<\/p>\n<p><strong>B and C are incorrect.<\/strong>\u00a0They violate the assumption that a model has the correct functional form, when in fact, it does not, thus creating functional form model misspecification.<\/p>\n<\/blockquote>\n<p>Reading 2: Multiple Regression<\/p>\n<p><em>LOS 2 (m) Describe how model misspecification affects the results of regression analysis and describe how to avoid common forms of misspecification.<\/em><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Model specification involves selecting independent variables to include in the regression and the functional form of the regression equation. We say that a model is misspecified when it violates the assumptions underlying linear regression, its functional form is incorrect, or&#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":[216,250,230],"class_list":["post-11985","post","type-post","status-publish","format-standard","hentry","category-cfa-level-2","category-quantitative-method","tag-cfa-level-2","tag-model-misspecification","tag-quantitative-method","blog-post","no-post-thumbnail","animate"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v26.9 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Model Misspecification | CFA Level II Quantitative<\/title>\n<meta name=\"description\" content=\"Learn what model misspecification is and how it arises in regression analysis, including functional form 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