Improved Breitung and Roling estimator for mixed-frequency models with application to forecasting inflation rates

IF 1.2 3区数学 Q2 STATISTICS & PROBABILITY

Statistical Papers Pub Date : 2024-01-04 DOI:10.1007/s00362-023-01520-2

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引用次数: 0

Abstract

Instead of applying the commonly used parametric Almon or Beta lag distribution of MIDAS, Breitung and Roling (J Forecast 34:588–603, 2015) suggested a nonparametric smoothed least-squares shrinkage estimator (henceforth \({SLS}_{1}\) ) for estimating mixed-frequency models. This \({SLS}_{1}\) approach ensures a flexible smooth trending lag distribution. However, even if the biasing parameter in \({SLS}_{1}\) solves the overparameterization problem, the cost is a decreased goodness-of-fit. Therefore, we suggest a modification of this shrinkage regression into a two-parameter smoothed least-squares estimator ( \({SLS}_{2}\) ). This estimator solves the overparameterization problem, and it has superior properties since it ensures that the orthogonality assumption between residuals and the predicted dependent variable holds, which leads to an increased goodness-of-fit. Our theoretical comparisons, supported by simulations, demonstrate that the increase in goodness-of-fit of the proposed two-parameter estimator also leads to a decrease in the mean square error of \({SLS}_{2},\) compared to that of \({SLS}_{1}\) . Empirical results, where the inflation rate is forecasted based on the oil returns, demonstrate that our proposed \({SLS}_{2}\) estimator for mixed-frequency models provides better estimates in terms of decreased MSE and improved R², which in turn leads to better forecasts.

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混合频率模型的改进 Breitung 和 Roling 估计器在预测通货膨胀率中的应用

摘要 Breitung和Roling（J Forecast 34:588-603，2015）提出了一种非参数平滑最小二乘收缩估计器（以下简称\({SLS}_{1}\)）来估计混合频率模型，而不是应用MIDAS常用的参数Almon或Beta滞后分布。这种（{SLS}_{1}\）方法确保了灵活平滑的趋势滞后分布。然而，即使 \({SLS}_{1}\) 中的偏置参数解决了过参数化问题，其代价也是拟合优度的下降。因此，我们建议将这种收缩回归修改为双参数平滑最小二乘估计器（\({SLS}_{2}\) ）。这种估计方法解决了过参数化问题，而且具有更优越的特性，因为它确保了残差与预测因变量之间的正交假设成立，从而提高了拟合优度。我们的理论比较和模拟证明，与 \（{SLS}_{1}\）相比，所提出的双参数估计器拟合优度的提高也导致了 \（{SLS}_{2},\）均方误差的减小。基于石油收益率预测通货膨胀率的实证结果表明，我们为混合频率模型提出的（{SLS}_{2}\）估计器在减少均方误差和提高 R2 方面提供了更好的估计，从而带来更好的预测。

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来源期刊

Statistical Papers 数学-统计学与概率论

CiteScore

2.80

自引率

7.70%

发文量

审稿时长

6-12 weeks

期刊介绍： The journal Statistical Papers addresses itself to all persons and organizations that have to deal with statistical methods in their own field of work. It attempts to provide a forum for the presentation and critical assessment of statistical methods, in particular for the discussion of their methodological foundations as well as their potential applications. Methods that have broad applications will be preferred. However, special attention is given to those statistical methods which are relevant to the economic and social sciences. In addition to original research papers, readers will find survey articles, short notes, reports on statistical software, problem section, and book reviews.