佳作分享|模型偏差在预测波动率中的作用:来自美国股市的证据

The role of model bias in predicting volatility: evidence from the US equity markets

模型偏差在预测波动率中的作用:来自美国股市的证据

Authors

Yan Li 

Southwest Jiaotong University, Chengdu, China,and,

Lian Luo 

Southwest Jiaotong University, Chengdu, China,and,

Chao Liang 

Southwest Jiaotong University, Chengdu, China,and,

Feng Ma 

Southwest Jiaotong University, Chengdu, China

Citation

Li, Y., Luo, L., Liang, C. and Ma, F. (2020), "The role of model bias in predicting volatility: evidence from the US equity markets", China Finance Review International, Vol. ahead-of-print No. ahead-of-print. https://doi.org/10.1108/CFRI-04-2020-0037

摘要

我们使用流行的异质自回归已实现波动率（HAR-RV）框架和高频数据分析了样本外模型偏差对道琼斯工业平均指数（DJI）和标普500（SPX）指数的已实现波动率（RV）的预测能力。首先，样本内结果表明，包含模型偏差的预测模型可以获得较大的R2，这意味着模型偏差包含了预测RV的有用信息。其次，基于几种评估方法的样本外实证结果表明，结合模型偏差的预测模型（即：HAR-RV-L-RES）可以提高DJI和SPX指数的RV的预测准确性。最后，我们的结果对于不同的评估方法、不同的预测窗口和替代的波动率估计都具有鲁棒性。

Abstract

Purpose

The purpose of this paper is to explore whether the out-of-sample model bias plays an important role in predicting volatility.

Design/methodology/approach

Under the heterogeneous autoregressive realized volatility (HAR-RV) framework, we analyze the predictive power of out-of-sample model bias for the realized volatility (RV) of the Dow Jones Industrial Average (DJI) and the S&P 500 (SPX) indices from in-sample and out-of-sample perspectives respectively.

Findings

The in-sample results reveal that the prediction model including the model bias can obtain bigger R2, and the out-of-sample empirical results based on several evaluation methods suggest that the prediction model incorporating model bias can improve forecast accuracy for the RV of the DJI and the SPX indices. That is, model bias can enhance the predictability of original HAR family models.

Originality/value

The author introduce out-of-sample model bias into HAR family models to enhance model capability in predicting realized volatility.

Keywords

Realized volatility, Model bias, Volatility forecasting, Equity markets

文章结构

1. Introduction

2. Methodology and data

   2.1 Benchmark models

   2.2 The definition of model bias

   2.3 Prediction models considering model bias

   2.4 Forecast evaluation methods

   2.5 Data and descriptive statistic
   

3. Empirical results

   3.1 In-sample estimation results

   3.2 Out-of-sample forecasting results

4. Robustness checks

   4.1 Direction-of-change test

   4.2 Different forecasting window

   4.3 Different evaluation method

   4.4 Realized kernel

5. Conclusions

研究成果

Descriptive statistics.

Full sample estimation results.

MCS test results.

DM test results.

Direction-of-Change test results.

MCS test results with the rolling window length is 1500.

DM test results with the rolling window length is 1500.

Out-of-sample R2 results for the DJI index.

Out-of-sample R2 results for the SPX index.

Time series evolution of the cumulative difference between the squared one-day-ahead forecast errors from the HAR-RV-L model and the HAR-RV-L-RES model on DJI.

Time series evolution of the cumulative difference between the squared one-day-ahead forecast errors from the HAR-RV-L model and the HAR-RV-L-RES model on SPX.

MCS test results using the RK.

主要结论

In this paper, the main purpose is to investigate whether the model bias contains additional predictive power for the RV of DJI and SPX indices. We use the prevailing HAR-RV framework and high-frequency data from the Oxford-Man Realized Library. The sample spans from January 3, 2000 to March 5, 2019. There are several important findings. First, the full sample estimation results suggest that the estimated coefficient for model bias is 0.553 (0.524) and significant at the 1% level, implying that higher level of model bias predicts a subsequent increase in RV of the DJI (SPX) index. And the HAR-RV-L-RES can obtain bigger R2, implying model bias contains useful information for predicting the RVs. Second, the out-of-sample empirical results based on two popular evaluation methods of MCS and DM test suggest that the prediction model incorporating model bias can improve forecast accuracy for the RVs of the DJI and the SPX indices. Finally, the empirical results of DoC test, different evaluation methods, different forecasting windows and alternative volatility estimators confirm that our results are robust. Our findings have important implications for scholars, market participants, as well as policymakers in practical applications.

作者简介

李岩，西南交通大学经济管理学院博士生，研究方向包括金融预测及风险管理、实证金融、机器学习和能源经济。曾在《International Review of Financial Analysis》、《Economic Modelling》、《Finance Research Letters》等期刊发表论文。

罗炼，西南交通大学经济管理学院硕士研究生，研究领域为金融预测。

梁超，西南交通大学经济管理学院讲师，研究方向为金融工程、金融预测，主要研究工作发表在《系统工程理论与实践》、《中国管理科学》、《International Review of Financial Analysis》、《Journal of Forecasting》、《Quantitative Finance》、《Energy Economics》、《International Journal of Finance & Economics》、《Economic Modelling》、《Applied Economics》、《Finance Research Letters》、《Resources Policy》及《Management Decision》等期刊，1篇ECONOMICS & BUSINESS（经济与商学）ESI高被引论文。

马锋，西南交通大学经济管理学院副教授、博导，研究方向为金融计量、预测及风险管理。2019年12月入选四川省“天府万人计划”，2020年6月入选学校“雏鹰计划”。2021年3月，入选第十三批四川省学术和技术带头人后备人选。现主持国家自然科学基金面上、青年及教育部人文社科项目各一项,参与国家级课题多项。现发表学术期刊80余篇,主要研究工作发表在《Journal of Banking & Finance》、《Journal of Empirical Finance》、《International Journal of Forecasting》、《Journal of Forecasting》、《Quantitative Finance》、《Energy Economics》、《International Review of Financial Analysis》、《Pacific-basin Finance Journal》、《Economic Modelling》、《Applied Economics》、《Empirical Economics》、《Studies in Nonlinear Dynamics & Econometrics》、《管理科学学报》、《系统工程理论与实践》及《系统管理学报》等期刊, 4篇ECONOMICS & BUSINESS（经济与商学）ESI高被引论文。2021年4月，入选2020年爱思唯尔中国高被引学者（应用经济学）。

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