{"title":"关于高维预测回归的 LASSO 推论","authors":"Zhan Gao, Ji Hyung Lee, Ziwei Mei, Zhentao Shi","doi":"arxiv-2409.10030","DOIUrl":null,"url":null,"abstract":"LASSO introduces shrinkage bias into estimated coefficients, which can\nadversely affect the desirable asymptotic normality and invalidate the standard\ninferential procedure based on the $t$-statistic. The desparsified LASSO has\nemerged as a well-known remedy for this issue. In the context of high\ndimensional predictive regression, the desparsified LASSO faces an additional\nchallenge: the Stambaugh bias arising from nonstationary regressors. To restore\nthe standard inferential procedure, we propose a novel estimator called\nIVX-desparsified LASSO (XDlasso). XDlasso eliminates the shrinkage bias and the\nStambaugh bias simultaneously and does not require prior knowledge about the\nidentities of nonstationary and stationary regressors. We establish the\nasymptotic properties of XDlasso for hypothesis testing, and our theoretical\nfindings are supported by Monte Carlo simulations. Applying our method to\nreal-world applications from the FRED-MD database -- which includes a rich set\nof control variables -- we investigate two important empirical questions: (i)\nthe predictability of the U.S. stock returns based on the earnings-price ratio,\nand (ii) the predictability of the U.S. inflation using the unemployment rate.","PeriodicalId":501293,"journal":{"name":"arXiv - ECON - Econometrics","volume":"26 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On LASSO Inference for High Dimensional Predictive Regression\",\"authors\":\"Zhan Gao, Ji Hyung Lee, Ziwei Mei, Zhentao Shi\",\"doi\":\"arxiv-2409.10030\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"LASSO introduces shrinkage bias into estimated coefficients, which can\\nadversely affect the desirable asymptotic normality and invalidate the standard\\ninferential procedure based on the $t$-statistic. The desparsified LASSO has\\nemerged as a well-known remedy for this issue. In the context of high\\ndimensional predictive regression, the desparsified LASSO faces an additional\\nchallenge: the Stambaugh bias arising from nonstationary regressors. To restore\\nthe standard inferential procedure, we propose a novel estimator called\\nIVX-desparsified LASSO (XDlasso). XDlasso eliminates the shrinkage bias and the\\nStambaugh bias simultaneously and does not require prior knowledge about the\\nidentities of nonstationary and stationary regressors. We establish the\\nasymptotic properties of XDlasso for hypothesis testing, and our theoretical\\nfindings are supported by Monte Carlo simulations. Applying our method to\\nreal-world applications from the FRED-MD database -- which includes a rich set\\nof control variables -- we investigate two important empirical questions: (i)\\nthe predictability of the U.S. stock returns based on the earnings-price ratio,\\nand (ii) the predictability of the U.S. inflation using the unemployment rate.\",\"PeriodicalId\":501293,\"journal\":{\"name\":\"arXiv - ECON - Econometrics\",\"volume\":\"26 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-09-16\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - ECON - Econometrics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2409.10030\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - ECON - Econometrics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.10030","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
On LASSO Inference for High Dimensional Predictive Regression
LASSO introduces shrinkage bias into estimated coefficients, which can
adversely affect the desirable asymptotic normality and invalidate the standard
inferential procedure based on the $t$-statistic. The desparsified LASSO has
emerged as a well-known remedy for this issue. In the context of high
dimensional predictive regression, the desparsified LASSO faces an additional
challenge: the Stambaugh bias arising from nonstationary regressors. To restore
the standard inferential procedure, we propose a novel estimator called
IVX-desparsified LASSO (XDlasso). XDlasso eliminates the shrinkage bias and the
Stambaugh bias simultaneously and does not require prior knowledge about the
identities of nonstationary and stationary regressors. We establish the
asymptotic properties of XDlasso for hypothesis testing, and our theoretical
findings are supported by Monte Carlo simulations. Applying our method to
real-world applications from the FRED-MD database -- which includes a rich set
of control variables -- we investigate two important empirical questions: (i)
the predictability of the U.S. stock returns based on the earnings-price ratio,
and (ii) the predictability of the U.S. inflation using the unemployment rate.