Penalized regression models with autoregressive error terms

Yoon, Young Il; Park, Cheolwoo; Lee, Taewook

doi:10.1080/00949655.2012.669383

Cited by 26 publications

(26 citation statements)

References 23 publications

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“…1, we consider the REGAR model with the autoregressive order q = 4, which corresponds to Yoon et al (2013). For our analysis, we randomly split all the 87 observations into training, tuning and testing data sets of size 20, 30, and 37 respectively.…”

Section: Real Data Examplementioning

confidence: 99%

“…This data has been used by Wang et al (2007) and Yoon et al (2013) for REGAR model analysis. We have 87 quarterly observations from the second quarter of 1972 through fourth quarter of 1993, and the response variable is the electricity consumption as measured by the logarithm of the kwh sales per residential customer (LKWH).…”

Section: Real Data Examplementioning

confidence: 99%

“…To overcome this limitation, Wang, Li, and Tsai (2007) and Yoon, Park, and Lee (2013) extended the scope of penalized regression to linear regression with autoregressive error (REGAR) model of Tsay (1984). They considered various penalty functions not only on regression coefficients but also on autoregression coefficients, which results in selecting important covariates and some of the autoregression error terms.…”

Section: Introductionmentioning

confidence: 99%

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Variable selection in quantile regression when the models have autoregressive errors

Lim

2014

Journal of the Korean Statistical Society

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a b s t r a c tThis paper considers a problem of variable selection in quantile regression with autoregressive errors. Recently, Wu and Liu (2009) investigated the oracle properties of the SCAD and adaptive-LASSO penalized quantile regressions under non identical but independent error assumption. We further relax the error assumptions so that the regression model can hold autoregressive errors, and then investigate theoretical properties for our proposed penalized quantile estimators under the relaxed assumption. Optimizing the objective function is often challenging because both quantile loss and penalty functions may be non-differentiable and/or non-concave. We adopt the concept of pseudo data by Oh et al. (2007) to implement a practical algorithm for the quantile estimate. In addition, we discuss the convergence property of the proposed algorithm. The performance of the proposed method is compared with those of the majorization-minimization algorithm (Hunter and Li, 2005) and the difference convex algorithm (Wu and Liu, 2009) through numerical and real examples.

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Section: Real Data Examplementioning

confidence: 99%

Section: Real Data Examplementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Variable selection in quantile regression when the models have autoregressive errors

Lim

2014

Journal of the Korean Statistical Society

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“…Without going into detail, it is clear that the estimators might be improved if the structure of the conditional heteroscedasticity in the data is used. Furthermore, Yoon et al (2013) analysed the lasso estimator in an autoregressive regression model. Additionally, they formulated the lasso problem in a time series setting with ARCH errors.…”

Section: Introductionmentioning

confidence: 99%

“…However, we restrict ourself to 1 -penalised regressions as they are popular in time series settings (see e.g. Wang et al (2007b), Nardi and Rinaldo (2011) and Yoon et al (2013)). In general, other q -penalty could also be considered, e.g.…”

Section: Introductionmentioning

confidence: 99%

Iteratively reweighted adaptive lasso for conditional heteroscedastic time series with applications to AR–ARCH type processes

Ziel

2016

Computational Statistics & Data Analysis

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Shrinkage algorithms are of great importance in almost every area of statistics due to the increasing impact of big data. Especially time series analysis benefits from efficient and rapid estimation techniques such as the lasso. However, currently lasso type estimators for autoregressive time series models still focus on models with homoscedastic residuals. Therefore, an iteratively reweighted adaptive lasso algorithm for the estimation of time series models under conditional heteroscedasticity is presented in a high-dimensional setting. The asymptotic behaviour of the resulting estimator is analysed. It is found that the proposed estimation procedure performs substantially better than its homoscedastic counterpart. A special case of the algorithm is suitable to compute the estimated multivariate AR-ARCH type models efficiently. Extensions to the model like periodic AR-ARCH, threshold AR-ARCH or ARMA-GARCH are discussed. Finally, different simulation results and applications to electricity market data and returns of metal prices are shown.

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