Variable Selection in Linear Regressions with Many Highly Correlated Covariates

Sharifvaghefi, Mahrad

doi:10.2139/ssrn.4159979

Cited by 3 publications

(6 citation statements)

References 52 publications

(41 reference statements)

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“…The condition on the number of pseudo-signals (k * T ) in the OCMT framework has been recently relaxed by Sharifvaghefi (2023). To illustrate how this is done, suppose there are no noise variables and hence the signals,…”

Section: Lasso and Ocmt Under Parameter Stabilitymentioning

confidence: 99%

“…When the common factors, f t , and idiosyncratic components, ε it , are known, this model would correspond to that presented in working paper version of our work, where common factors f t can be used as preselected variables. Since f t and ε it are not known, Sharifvaghefi (2023) shows that when both N and T are large the OCMT selection can be carried out using the principal component estimators of f t and ε it , denoted by ft and εit , using all the covariates in the active set. The large N is required for consistent estimation of the common factors.…”

Section: Lasso and Ocmt Under Parameter Stabilitymentioning

confidence: 99%

“…9 The predictions of these forecasters are highly correlated suggesting the presence of a common factor across these forecasts. To deal with this issue at the variable selection stage following Sharifvaghefi (2023) we also include the simple average of the 25 forecasts in the conditioning set, z t , as a proxy for the common factor in addition to the intercept. We consider 39 quarterly forecasts (from 2004Q3 and 2014Q1) for forecast evaluation, using expanding samples (weighted and unweighted) from 1999Q3.…”

Section: S-1 Technical and Financial Indicatorsmentioning

confidence: 99%

“…Finally, using Monte Carlo studies, they show that OCMT tends to perform better than penalized regression or boosting procedures under various designs. Sharifvaghefi (2022) has recently generalized the OCMT procedure to allow the covariates under consideration to be strongly correlated, while penalized regression methods require the covariates to be weakly correlated (see e.g. Zhao and Yu (2006)).…”

Section: Introductionmentioning

confidence: 99%

“…These conditions, and how they compare with the conditions that underlie OCMT, are discussed in Section 4 of the paper. Although Lasso does not directly impose any restrictions Sharifvaghefi (2023) shows that such common factors can be estimated from the principal components of the covariates in the active set and the OCMT condition on the number pseudo-signals, now defined in terms of the correlation of the residuals, is no longer restrictive. 1…”

Section: Introductionmentioning

confidence: 99%

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Variable Selection in High Dimensional Linear Regressions with Parameter Instability

Chudík¹,

Pesaran²,

Sharifvaghefi³

2023

gwp

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This paper is concerned with the problem of variable selection when the marginal effects of signals on the target variable as well as the correlation of the covariates in the active set are allowed to vary over time, without committing to any particular model of parameter instabilities. It poses the issue of whether weighted or unweighted observations should be used at the variable 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 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 unweighted observations at the selection stage of OCMT and down-weighting of observations only at the forecasting stage. The benefits of the proposed method as compared to Lasso, Adaptive Lasso and Boosting are illustrated by Monte Carlo studies and empirical applications to forecasting monthly stock market returns and quarterly output growths.

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Section: Lasso and Ocmt Under Parameter Stabilitymentioning

confidence: 99%

Section: Lasso and Ocmt Under Parameter Stabilitymentioning

confidence: 99%

Section: S-1 Technical and Financial Indicatorsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations