The Model Confidence Set
Abstract
This paper introduces the model confidence set (MCS) and applies it to the selection of models. A MCS is a set of models that is constructed such that it will contain the best model with a given level of confidence. The MCS is in this sense analogous to a confidence interval for a parameter. The MCS acknowledges the limitations of the data, such that uninformative data yield a MCS with many models, whereas informative data yield a MCS with only a few models. The MCS procedure does not assume that a particular model is the true model; in fact, the MCS procedure can be used to compare more general objects, beyond the comparison of models. We apply the MCS procedure to two empirical problems. First, we revisit the inflation forecasting problem posed by Stock and Watson (1999), and compute the MCS for their set of inflation forecasts. Second, we compare a number of Taylor rule regressions and determine the MCS of the best regression in terms of in‐sample likelihood criteria.
Citing Literature
Number of times cited according to CrossRef: 623
- Wang Chen, Feng Ma, Yu Wei, Jing Liu, Forecasting oil price volatility using high-frequency data: New evidence, International Review of Economics & Finance, 10.1016/j.iref.2019.10.014, 66, (1-12), (2020).
- Emawtee Bissoondoyal-Bheenick, Robert Brooks, Hung Xuan Do, Russell Smyth, Exploiting the heteroskedasticity in measurement error to improve volatility predictions in oil and biofuel feedstock markets, Energy Economics, 10.1016/j.eneco.2020.104689, (104689), (2020).
- Tim Bollerslev, Andrew J. Patton, Rogier Quaedvlieg, Multivariate leverage effects and realized semicovariance GARCH models, Journal of Econometrics, 10.1016/j.jeconom.2019.12.011, (2020).
- Manabu Asai, Rangan Gupta, Michael McAleer, Forecasting volatility and co-volatility of crude oil and gold futures: Effects of leverage, jumps, spillovers, and geopolitical risks, International Journal of Forecasting, 10.1016/j.ijforecast.2019.10.003, (2020).
- Nirodha I. Jayawardena, Neda Todorova, Bin Li, Jen-Je Su, Volatility forecasting using related markets’ information for the Tokyo stock exchange, Economic Modelling, 10.1016/j.econmod.2020.05.008, (2020).
- Jiawen Luo, Qiang Ji, Tony Klein, Neda Todorova, Dayong Zhang, On realized volatility of crude oil futures markets: Forecasting with exogenous predictors under structural breaks, Energy Economics, 10.1016/j.eneco.2020.104781, (104781), (2020).
- Yaojie Zhang, Likun Lei, Yu Wei, Forecasting the Chinese stock market volatility with international market volatilities: The role of regime switching, The North American Journal of Economics and Finance, 10.1016/j.najef.2020.101145, (101145), (2020).
- Malvina Marchese, Ioannis Kyriakou, Michael Tamvakis, Francesca Di Iorio, Forecasting crude oil and refined products volatilities and correlations: New evidence from fractionally integrated multivariate GARCH models, Energy Economics, 10.1016/j.eneco.2020.104757, (104757), (2020).
- Anders Bredahl Kock, Marcelo Medeiros, Gabriel Vasconcelos, Penalized Time Series Regression, Macroeconomic Forecasting in the Era of Big Data, 10.1007/978-3-030-31150-6_7, (193-228), (2020).
- Jussi Klemelä, Nonparametric volatility prediction, WIREs Computational Statistics , 10.1002/wics.1491, 12, 3, (2020).
- Akram Shavkatovich Hasanov, Mohammed Sharaf Shaiban, Ajab Al-Freedi, Forecasting volatility in the petroleum futures markets: A re-examination and extension, Energy Economics, 10.1016/j.eneco.2019.104626, (104626), (2020).
- Nima Nonejad, Crude oil price changes and the United Kingdom real gross domestic product growth rate: An out-of-sample investigation, The Journal of Economic Asymmetries, 10.1016/j.jeca.2020.e00154, 21, (e00154), (2020).
- Emese Lazar, Xiaohan Xue, Forecasting risk measures using intraday data in a generalized autoregressive score framework, International Journal of Forecasting, 10.1016/j.ijforecast.2019.10.007, (2020).
- Lu Wang, Feng Ma, Guoshan Liu, Forecasting stock volatility in the presence of extreme shocks: Short‐term and long‐term effects, Journal of Forecasting, 10.1002/for.2668, 39, 5, (797-810), (2020).
- Angelica Gianfreda, Francesco Ravazzolo, Luca Rossini, Comparing the forecasting performances of linear models for electricity prices with high RES penetration, International Journal of Forecasting, 10.1016/j.ijforecast.2019.11.002, (2020).
- Yan Cui, Yun Feng, Composite hedge and utility maximization for optimal futures hedging, International Review of Economics & Finance, 10.1016/j.iref.2020.03.002, (2020).
- Byounghyun Jeon, Sung Won Seo, Jun Sik Kim, Uncertainty and the volatility forecasting power of option‐implied volatility, Journal of Futures Markets, 10.1002/fut.22116, 40, 7, (1109-1126), (2020).
- Wei Chen, Huilin Xu, Lifen Jia, Ying Gao, Machine learning model for Bitcoin exchange rate prediction using economic and technology determinants, International Journal of Forecasting, 10.1016/j.ijforecast.2020.02.008, (2020).
- Sarantis Tsiaplias, Time-Varying Consumer Disagreement and Future Inflation, Journal of Economic Dynamics and Control, 10.1016/j.jedc.2020.103903, (103903), (2020).
- G. Albano, D. De Gaetano, HAR-type Models for Volatility Forecasting: An Empirical Investigation, Computer Aided Systems Theory – EUROCAST 2019, 10.1007/978-3-030-45093-9_23, (185-194), (2020).
- G. Albano, Michele La Rocca, C. Perna, Volatility Modelling for Air Pollution Time Series, Computer Aided Systems Theory – EUROCAST 2019, 10.1007/978-3-030-45093-9_22, (176-184), (2020).
- Campbell R Harvey, Yan Liu, Alessio Saretto, An Evaluation of Alternative Multiple Testing Methods for Finance Applications*, The Review of Asset Pricing Studies, 10.1093/rapstu/raaa003, 10, 2, (199-248), (2020).
- Wentao Gu, Suhao Zheng, Ru Wang, Cui Dong, Forecasting Realized Volatility Based on Sentiment Index and GRU Model, Journal of Advanced Computational Intelligence and Intelligent Informatics, 10.20965/jaciii.2020.p0299, 24, 3, (299-306), (2020).
- Y. Dendramis, G. Kapetanios, M. Marcellino, A similarity‐based approach for macroeconomic forecasting, Journal of the Royal Statistical Society: Series A (Statistics in Society), 10.1111/rssa.12574, 183, 3, (801-827), (2020).
- Giuseppe Buccheri, Gael Mboussa Anga, Parametric Estimation of Large Realized Covariance Matrices: Revisiting the Method of Corsi et al. (2015), SSRN Electronic Journal, 10.2139/ssrn.3541883, (2020).
- Eric Hillebrand, Manuel Lukas, Wei Wei, Bagging weak predictors, International Journal of Forecasting, 10.1016/j.ijforecast.2020.05.002, (2020).
- Mariarosaria Coppola, Maria Russolillo, Rosaria Simone, On the management of retirement age indexed to life expectancy: a scenario analysis of the Italian longevity experience, The Journal of Risk Finance, 10.1108/JRF-01-2020-0012, ahead-of-print, ahead-of-print, (2020).
- Alessandra Amendola, Manuela Braione, Vincenzo Candila, Giuseppe Storti, A Model Confidence Set approach to the combination of multivariate volatility forecasts, International Journal of Forecasting, 10.1016/j.ijforecast.2019.10.001, (2020).
- Wei Liu, Artur Semeyutin, Chi Keung Marco Lau, Giray Gozgor, Forecasting Value-at-Risk of Cryptocurrencies with RiskMetrics Type Models, Research in International Business and Finance, 10.1016/j.ribaf.2020.101259, (101259), (2020).
- Andres Algaba, David Ardia, Keven Bluteau, Samuel Borms, Kris Boudt, ECONOMETRICS MEETS SENTIMENT: AN OVERVIEW OF METHODOLOGY AND APPLICATIONS, Journal of Economic Surveys, 10.1111/joes.12370, 34, 3, (512-547), (2020).
- Faisal Nazir Zargar, Dilip Kumar, Modeling unbiased extreme value volatility estimator in presence of heterogeneity and jumps: A study with economic significance analysis, International Review of Economics & Finance, 10.1016/j.iref.2019.12.011, (2020).
- Saúl Alonso-Monsalve, Andrés L. Suárez-Cetrulo, Alejandro Cervantes, David Quintana, Convolution on Neural Networks for High-Frequency Trend Prediction of Cryptocurrency Exchange Rates Using Technical Indicators, Expert Systems with Applications, 10.1016/j.eswa.2020.113250, (113250), (2020).
- Raffaello Seri, Mario Martinoli, Davide Secchi, Samuele Centorrino, Model Calibration and Validation via Confidence Sets, Econometrics and Statistics, 10.1016/j.ecosta.2020.01.001, (2020).
- Min Liu, James W. Taylor, Wei-Chong Choo, Further empirical evidence on the forecasting of volatility with smooth transition exponential smoothing, Economic Modelling, 10.1016/j.econmod.2020.02.021, (2020).
- Jiawen Luo, Langnan Chen, Realized volatility forecast with the Bayesian random compressed multivariate HAR model, International Journal of Forecasting, 10.1016/j.ijforecast.2019.09.002, (2020).
- Yu You, Xiaochun Liu, Forecasting Short-Run Exchange Rate Volatility with Monetary Fundamentals: A GARCH-MIDAS Approach, Journal of Banking & Finance, 10.1016/j.jbankfin.2020.105849, (105849), (2020).
- Jian Zhou, Combining realized measures to forecast REIT volatility, Journal of European Real Estate Research, 10.1108/JERER-03-2020-0021, ahead-of-print, ahead-of-print, (2020).
- Christian Conrad, Onno Kleen, Two are better than one: Volatility forecasting using multiplicative component GARCH‐MIDAS models , Journal of Applied Econometrics, 10.1002/jae.2742, 35, 1, (19-45), (2020).
- Gregory Rice, Tony Wirjanto, Yuqian Zhao, Forecasting value at risk with intra-day return curves, International Journal of Forecasting, 10.1016/j.ijforecast.2019.10.006, (2020).
- Yu Lin, Yang Xiao, Fuxing Li, Forecasting crude oil price volatility via a HM-EGARCH model, Energy Economics, 10.1016/j.eneco.2020.104693, (104693), (2020).
- Danilo Vassallo, Giuseppe Buccheri, Fulvio Corsi, A DCC-type approach for realized covariance modeling with score-driven dynamics, International Journal of Forecasting, 10.1016/j.ijforecast.2020.07.006, (2020).
- Fabrizio Cipollini, Giampiero M. Gallo, Edoardo Otranto, Realized volatility forecasting: Robustness to measurement errors, International Journal of Forecasting, 10.1016/j.ijforecast.2020.02.009, (2020).
- Stavros Degiannakis, George Filis, Tony Klein, Thomas Walther, Forecasting realized volatility of agricultural commodities, International Journal of Forecasting, 10.1016/j.ijforecast.2019.08.011, (2020).
- Jiqian Wang, Yisu Huang, Feng Ma, Julien Chevallier, Does high-frequency crude oil futures data contain useful information for predicting volatility in the US stock market? New evidence, Energy Economics, 10.1016/j.eneco.2020.104897, (104897), (2020).
- Ying Yuan, Tonghui Zhang, Forecasting stock market in high and low volatility periods: a modified multifractal volatility approach, Chaos, Solitons & Fractals, 10.1016/j.chaos.2020.110252, 140, (110252), (2020).
- Xinjie Lu, Feng Ma, Jiqian Wang, Jianqiong Wang, Examining the predictive information of CBOE OVX on China’s oil futures volatility: Evidence from MS-MIDAS models, Energy, 10.1016/j.energy.2020.118743, (118743), (2020).
- Adam Clements, Mark Bernard Doolan, Combining multivariate volatility forecasts using weighted losses, Journal of Forecasting, 10.1002/for.2647, 39, 4, (628-641), (2020).
- Mark F. J. Steel, Model Averaging and Its Use in Economics, Journal of Economic Literature, 10.1257/jel.20191385, 58, 3, (644), (2020).
- Feng Ma, Chao Liang, Qing Zeng, Haibo Li, Jumps and oil futures volatility forecasting: a new insight, Quantitative Finance, 10.1080/14697688.2020.1805505, (1), (2020).
- Anthony Bellotti, Damiano Brigo, Paolo Gambetti, Frédéric Vrins, Forecasting recovery rates on non-performing loans with machine learning, International Journal of Forecasting, 10.1016/j.ijforecast.2020.06.009, (2020).
- Han Lin Shang, Heather Booth, Synergy in fertility forecasting: improving forecast accuracy through model averaging, Genus, 10.1186/s41118-020-00099-y, 76, 1, (2020).
- Yan Li, Chao Liang, Feng Ma, Jiqian Wang, The role of the IDEMV in predicting European stock market volatility during the COVID-19 pandemic, Finance Research Letters, 10.1016/j.frl.2020.101749, 36, (101749), (2020).
- Yaojie Zhang, Feng Ma, Yin Liao, Forecasting global equity market volatilities, International Journal of Forecasting, 10.1016/j.ijforecast.2020.02.007, (2020).
- Dooruj Rambaccussing, Andrzej Kwiatkowski, Forecasting with news sentiment: Evidence with UK newspapers, International Journal of Forecasting, 10.1016/j.ijforecast.2020.04.002, (2020).
- Trung H. Le, Forecasting value at risk and expected shortfall with mixed data sampling, International Journal of Forecasting, 10.1016/j.ijforecast.2020.01.008, (2020).
- Leopoldo Catania, Tommaso Proietti, Forecasting volatility with time-varying leverage and volatility of volatility effects, International Journal of Forecasting, 10.1016/j.ijforecast.2020.01.003, (2020).
- Elena Andreou, Patrick Gagliardini, Eric Ghysels, Mirco Rubin, Mixed-Frequency Macro–Finance Factor Models: Theory and Applications*, Journal of Financial Econometrics, 10.1093/jjfinec/nbaa015, 18, 3, (585-628), (2020).
- Leopoldo Catania, A Stochastic Volatility Model with a General Leverage Specification, SSRN Electronic Journal, 10.2139/ssrn.3642613, (2020).
- Linh Nguyen, Vilém Novák, Soheyla Mirshahi, Trend‐cycle Estimation Using Fuzzy Transform and Its Application for Identifying Bull and Bear Phases in Markets, Intelligent Systems in Accounting, Finance and Management, 10.1002/isaf.1473, 27, 3, (111-124), (2020).
- Timo Dimitriadis, Julie Schnaitmann, Forecast encompassing tests for the expected shortfall, International Journal of Forecasting, 10.1016/j.ijforecast.2020.07.008, (2020).
- Yue Liu, Huaping Sun, Jijian Zhang, Farhad Taghizadeh-Hesary, Detection of volatility regime-switching for crude oil price modeling and forecasting, Resources Policy, 10.1016/j.resourpol.2020.101669, 69, (101669), (2020).
- Jiqian Wang, Xinjie Lu, Feng He, Feng Ma, Which popular predictor is more useful to forecast international stock markets during the coronavirus pandemic: VIX vs EPU?, International Review of Financial Analysis, 10.1016/j.irfa.2020.101596, (101596), (2020).
- Meriam Dahmene, Adel Boughrara, Skander Slim, Nonlinearity in stock returns: Do risk aversion, investor sentiment and, monetary policy shocks matter?, International Review of Economics & Finance, 10.1016/j.iref.2020.10.002, (2020).
- Štefan Lyócsa, Tomáš Plíhal, Modeling realized volatility of the EUR/USD exchange rate: Does implied volatility really matter?, International Review of Economics & Finance, 10.1016/j.iref.2020.10.001, (2020).
- Manh Cuong Pham, Heather Margot Anderson, Huu Nhan Duong, Paul Lajbcygier, The effects of trade size and market depth on immediate price impact in a limit order book market, Journal of Economic Dynamics and Control, 10.1016/j.jedc.2020.103992, (103992), (2020).
- Štefan Lyócsa, Tomáš Píhal, Tomáš Výrost, FX Market Volatility Modelling: Can we use low-frequency data?, Finance Research Letters, 10.1016/j.frl.2020.101776, (101776), (2020).
- Zhihong Jian, Xupei Li, Zhican Zhu, Sequential forecasting of downside extreme risk during overnight and daytime: Evidence from the Chinese Stock Market, Pacific-Basin Finance Journal, 10.1016/j.pacfin.2020.101454, (101454), (2020).
- Li Liu, Feng Ma, Qing Zeng, Yaojie Zhang, Forecasting the aggregate stock market volatility in a data-rich world, Applied Economics, 10.1080/00036846.2020.1713291, (1-16), (2020).
- Chao Liang, Yu Wei, Yaojie Zhang, Is implied volatility more informative for forecasting realized volatility: An international perspective, Journal of Forecasting, 10.1002/for.2686, 0, 0, (2020).
- Silvia Muzzioli, Luca Gambarelli, Bernard De Baets, Option implied moments obtained through fuzzy regression, Fuzzy Optimization and Decision Making, 10.1007/s10700-020-09316-x, (2020).
- Erdinc Akyildirim, Ahmet Goncu, Ahmet Sensoy, Prediction of cryptocurrency returns using machine learning, Annals of Operations Research, 10.1007/s10479-020-03575-y, (2020).
- Feng Ma, Chao Liang, Yuanhui Ma, M.I.M. Wahab, Cryptocurrency volatility forecasting: A Markov regime‐switching MIDAS approach, Journal of Forecasting, 10.1002/for.2691, 0, 0, (2020).
- Ren-jie Han, Zhuo-ran Zeng, Qian Li, Qing Yan, CSI300 volatility predicting by internet users’ searching behavior, Current Psychology, 10.1007/s12144-020-00812-2, (2020).
- Mawuli Segnon, Rangan Gupta, Keagile Lesame, Mark E. Wohar, High-Frequency Volatility Forecasting of US Housing Markets, The Journal of Real Estate Finance and Economics, 10.1007/s11146-020-09745-w, (2020).
- Diaa Noureldin, Volatility Prediction Using a Realized-Measure-Based Component Model*, Journal of Financial Econometrics, 10.1093/jjfinec/nbz041, (2020).
- James Lightwood, Steve Anderson, Stanton A. Glantz, Predictive validation and forecasts of short-term changes in healthcare expenditure associated with changes in smoking behavior in the United States, PLOS ONE, 10.1371/journal.pone.0227493, 15, 1, (e0227493), (2020).
- Bastian Gribisch, Michael Stollenwerk, Dynamic principal component CAW models for high-dimensional realized covariance matrices, Quantitative Finance, 10.1080/14697688.2019.1701197, (1-23), (2020).
- Ufuk Beyaztas, Han Lin Shang, On function-on-function regression: partial least squares approach, Environmental and Ecological Statistics, 10.1007/s10651-019-00436-1, (2020).
- Giorgio Calzolari, Roxana Halbleib, Aygul Zagidullina, A Latent Factor Model for Forecasting Realized Variances, Journal of Financial Econometrics, 10.1093/jjfinec/nbz036, (2020).
- Zhiyuan Pan, Ruijun Bu, Li Liu, Yudong Wang, Macroeconomic fundamentals, jump dynamics and expected volatility, Quantitative Finance, 10.1080/14697688.2020.1736317, (1-27), (2020).
- Mawuli Segnon, Stelios Bekiros, Forecasting volatility in bitcoin market, Annals of Finance, 10.1007/s10436-020-00368-y, (2020).
- P. De Zea Bermudez, J. Miguel Marín, Helena Veiga, Data cloning estimation for asymmetric stochastic volatility models, Econometric Reviews, 10.1080/07474938.2020.1770997, (1-18), (2020).
- Xinyu Wu, Xiaona Wang, Haiyun Wang, Forecasting stock market volatility using implied volatility: evidence from extended realized EGARCH-MIDAS model, Applied Economics Letters, 10.1080/13504851.2020.1785617, (1-6), (2020).
- Laura Garcia‐Jorcano, Alfonso Novales, Volatility specifications versus probability distributions in VaR forecasting, Journal of Forecasting, 10.1002/for.2697, 0, 0, (2020).
- OUP accepted manuscript, Journal Of Financial Econometrics, 10.1093/jjfinec/nbaa002, (2020).
- Yu Wei, Lan Bai, Kun Yang, Guiwu Wei, Are industry‐level indicators more helpful to forecast industrial stock volatility? Evidence from Chinese manufacturing purchasing managers index, Journal of Forecasting, 10.1002/for.2696, 0, 0, (2020).
- Jack Fosten, Daniel Gutknecht, Horizon confidence sets, Empirical Economics, 10.1007/s00181-020-01891-7, (2020).
- Rafael B. Barbosa, Roberto Tatiwa Ferreira, Thibério Mota da Silva, Previsão de Variáveis Macroeconômicas Brasileiras usando Modelos de Séries Temporais de Alta Dimensão, Estudos Econômicos (São Paulo), 10.1590/0101-41615013rrt, 50, 1, (67-98), (2020).
- Isabel Casas, Helena Veiga, Exploring Option Pricing and Hedging via Volatility Asymmetry, Computational Economics, 10.1007/s10614-020-10005-5, (2020).
- Tunc Oygur, Gazanfer Unal, Traces of the Multifractal Nature of the Financial Crises in Turkey: Co-Movement of the Hölder Exponents and Large-Scale Forecast, Fluctuation and Noise Letters, 10.1142/S0219477520500297, (2050029), (2020).
- Daniel Borup, Erik Christian Montes Schütte, In Search of a Job: Forecasting Employment Growth Using Google Trends, Journal of Business & Economic Statistics, 10.1080/07350015.2020.1791133, (1-15), (2020).
- Anne Opschoor, André Lucas, István Barra, Dick van Dijk, Closed-Form Multi-Factor Copula Models With Observation-Driven Dynamic Factor Loadings, Journal of Business & Economic Statistics, 10.1080/07350015.2020.1763806, (1-14), (2020).
- Giuseppe Buccheri, Giacomo Bormetti, Fulvio Corsi, Fabrizio Lillo, A Score-Driven Conditional Correlation Model for Noisy and Asynchronous Data: an Application to High-Frequency Covariance Dynamics*, Journal of Business & Economic Statistics, 10.1080/07350015.2020.1739530, (1-39), (2020).
- Firat Melih Yilmaz, Ozer Arabaci, Should Deep Learning Models be in High Demand, or Should They Simply be a Very Hot Topic? A Comprehensive Study for Exchange Rate Forecasting, Computational Economics, 10.1007/s10614-020-10047-9, (2020).
- Richard Gerlach, Antonio Naimoli, Giuseppe Storti, Time-varying parameters realized GARCH models for tracking attenuation bias in volatility dynamics, Quantitative Finance, 10.1080/14697688.2020.1751257, (1-30), (2020).
- Fabrizio Cipollini, Giampiero M Gallo, Alessandro Palandri, Realized Variance Modeling: Decoupling Forecasting from Estimation*, Journal of Financial Econometrics, 10.1093/jjfinec/nbaa009, (2020).
- Jiling Cao, Xinfeng Ruan, Shu Su, Wenjun Zhang, Pricing VIX derivatives with infinite‐activity jumps, Journal of Futures Markets, 10.1002/fut.22074, 40, 3, (329-354), (2019).
- Erhard Reschenhofer, Manveer Kaur Mangat, Christian Zwatz, Sándor Guzmics, Evaluation of current research on stock return predictability, Journal of Forecasting, 10.1002/for.2629, 39, 2, (334-351), (2019).
- Duc Khuong Nguyen, Thomas Walther, Modeling and forecasting commodity market volatility with long‐term economic and financial variables, Journal of Forecasting, 10.1002/for.2617, 39, 2, (126-142), (2019).
- Stavroula P. Fameliti, Vasiliki D. Skintzi, Predictive ability and economic gains from volatility forecast combinations, Journal of Forecasting, 10.1002/for.2622, 39, 2, (200-219), (2019).
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