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Variable Selection and Forecasting in High Dimensional Linear Regressions with Parameter Instability

Chudik, Alexander and Pesaran, Hashem and Sharifvaghefi, Mahrad (2021) Variable Selection and Forecasting in High Dimensional Linear Regressions with Parameter Instability. (Submitted)

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This paper is concerned with the problem of variable selection and forecasting in the presence of parameter instability. There are a number of approaches proposed for forecasting in the presence of time-varying parameters, including the use of rolling windows and exponential down-weighting. However, these studies start with a given model specification and do not consider the problem of variable selection, which is complicated by time variations in the effects of signals on target variables. In this study we investigate whether or not we should use weighted observations at the vari- able selection stage in the presence of parameter instability, particularly when the number of potential covariates is large. Amongst the extant variable selection approaches we focus on the recently developed One Covariate at a time Multiple Testing (OCMT) method. This procedure allows a natural distinction between the selection and forecasting stages. We establish three main theorems on selection, estimation post selection, and in-sample fit. These theorems provide justification for using the full (not down-weighted) sample at the selection stage of OCMT and down-weighting of observations only at the forecasting stage (if needed). The benefits of the proposed method are illustrated by empirical applications to forecasting monthly stock market returns and quarterly output growths.


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Item Type: Article
Status: Submitted
CreatorsEmailPitt UsernameORCID
Chudik, Alexander
Pesaran, Hashem
Sharifvaghefi, Mahradsharifvaghefi@pitt.edumas866
Date: 23 April 2021
Schools and Programs: Dietrich School of Arts and Sciences > Economics
Refereed: No
Uncontrolled Keywords: Time-varying parameters, high-dimensional, multiple testing, variable selection, Lasso, one covariate at a time multiple testing (OCMT), forecasting, monthly returns, Dow Jones
Article Type: Research Article
Other ID: C22, C52, C53, C55
Date Deposited: 16 May 2022 15:07
Last Modified: 16 May 2022 15:07


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