{"title":"长期可预测性测试比你想象的还要糟糕","authors":"Erik Hjalmarsson, Tamas Kiss","doi":"10.1002/jae.2930","DOIUrl":null,"url":null,"abstract":"<p>We derive asymptotic results for the long-horizon ordinary least squares (OLS) estimator and corresponding \n<math>\n <semantics>\n <mrow>\n <mi>t</mi>\n </mrow>\n <annotation>$$ t $$</annotation>\n </semantics></math>-statistic for stationary autoregressive predictors. The \n<math>\n <semantics>\n <mrow>\n <mi>t</mi>\n </mrow>\n <annotation>$$ t $$</annotation>\n </semantics></math>-statistic—formed using the correct asymptotic variance—together with standard-normal critical values result in a correctly-sized test for exogenous predictors. For endogenous predictors, the test is size distorted regardless of the persistence in the predictor and adjusted critical values are necessary. The endogeneity problem stems from the long-run estimation and is distinct from the ordinary persistence-dependent “Stambaugh” bias. The bias for fully stationary predictors appears not to have been previously noted and adds further difficulty to inference in long-run predictive regressions.</p>","PeriodicalId":48363,"journal":{"name":"Journal of Applied Econometrics","volume":"37 7","pages":"1334-1355"},"PeriodicalIF":2.3000,"publicationDate":"2022-08-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/jae.2930","citationCount":"1","resultStr":"{\"title\":\"Long-run predictability tests are even worse than you thought\",\"authors\":\"Erik Hjalmarsson, Tamas Kiss\",\"doi\":\"10.1002/jae.2930\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>We derive asymptotic results for the long-horizon ordinary least squares (OLS) estimator and corresponding \\n<math>\\n <semantics>\\n <mrow>\\n <mi>t</mi>\\n </mrow>\\n <annotation>$$ t $$</annotation>\\n </semantics></math>-statistic for stationary autoregressive predictors. The \\n<math>\\n <semantics>\\n <mrow>\\n <mi>t</mi>\\n </mrow>\\n <annotation>$$ t $$</annotation>\\n </semantics></math>-statistic—formed using the correct asymptotic variance—together with standard-normal critical values result in a correctly-sized test for exogenous predictors. For endogenous predictors, the test is size distorted regardless of the persistence in the predictor and adjusted critical values are necessary. The endogeneity problem stems from the long-run estimation and is distinct from the ordinary persistence-dependent “Stambaugh” bias. The bias for fully stationary predictors appears not to have been previously noted and adds further difficulty to inference in long-run predictive regressions.</p>\",\"PeriodicalId\":48363,\"journal\":{\"name\":\"Journal of Applied Econometrics\",\"volume\":\"37 7\",\"pages\":\"1334-1355\"},\"PeriodicalIF\":2.3000,\"publicationDate\":\"2022-08-18\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://onlinelibrary.wiley.com/doi/epdf/10.1002/jae.2930\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Applied Econometrics\",\"FirstCategoryId\":\"96\",\"ListUrlMain\":\"https://onlinelibrary.wiley.com/doi/10.1002/jae.2930\",\"RegionNum\":3,\"RegionCategory\":\"经济学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"ECONOMICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Applied Econometrics","FirstCategoryId":"96","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1002/jae.2930","RegionNum":3,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"ECONOMICS","Score":null,"Total":0}
引用次数: 1
摘要
我们得到了平稳自回归预测量的长期视界普通最小二乘(OLS)估计量和相应的t $$ t $$统计量的渐近结果。t $$ t $$ -使用正确的渐近方差形成的统计-与标准正态临界值一起导致外生预测因子的正确大小的检验。对于内源性预测因子,无论预测因子的持久性如何,测试都是大小扭曲的,调整临界值是必要的。内生性问题源于长期估计,与普通的持久性依赖的“斯坦博”偏差不同。完全平稳预测因子的偏差似乎以前没有被注意到,这进一步增加了长期预测回归推理的难度。
Long-run predictability tests are even worse than you thought
We derive asymptotic results for the long-horizon ordinary least squares (OLS) estimator and corresponding
-statistic for stationary autoregressive predictors. The
-statistic—formed using the correct asymptotic variance—together with standard-normal critical values result in a correctly-sized test for exogenous predictors. For endogenous predictors, the test is size distorted regardless of the persistence in the predictor and adjusted critical values are necessary. The endogeneity problem stems from the long-run estimation and is distinct from the ordinary persistence-dependent “Stambaugh” bias. The bias for fully stationary predictors appears not to have been previously noted and adds further difficulty to inference in long-run predictive regressions.
期刊介绍:
The Journal of Applied Econometrics is an international journal published bi-monthly, plus 1 additional issue (total 7 issues). It aims to publish articles of high quality dealing with the application of existing as well as new econometric techniques to a wide variety of problems in economics and related subjects, covering topics in measurement, estimation, testing, forecasting, and policy analysis. The emphasis is on the careful and rigorous application of econometric techniques and the appropriate interpretation of the results. The economic content of the articles is stressed. A special feature of the Journal is its emphasis on the replicability of results by other researchers. To achieve this aim, authors are expected to make available a complete set of the data used as well as any specialised computer programs employed through a readily accessible medium, preferably in a machine-readable form. The use of microcomputers in applied research and transferability of data is emphasised. The Journal also features occasional sections of short papers re-evaluating previously published papers. The intention of the Journal of Applied Econometrics is to provide an outlet for innovative, quantitative research in economics which cuts across areas of specialisation, involves transferable techniques, and is easily replicable by other researchers. Contributions that introduce statistical methods that are applicable to a variety of economic problems are actively encouraged. The Journal also aims to publish review and survey articles that make recent developments in the field of theoretical and applied econometrics more readily accessible to applied economists in general.