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Testing the Lag Structure of Assets’ Realized Volatility Dynamics

Department of Economics, University of St. Gallen, Bodanstrasse 6, 9000 St.Gallen, Switzerland

Special Issue: Financial Big Data Technology and Its Applications

A (conservative) test is applied to investigate the optimal lag structure for modelingrealized volatility dynamics. The testing procedure relies on the recent theoretical results that showthe ability of the adaptive least absolute shrinkage and selection operator (adaptive lasso) to combinee cient parameter estimation, variable selection, and valid inference for time series processes. In anapplication to several constituents of the S&P 500 index it is shown that (i) the optimal significantlag structure is time-varying and subject to drastic regime shifts that seem to happen across assetssimultaneously; (ii) in many cases the relevant information for prediction is included in the first 22lags, corroborating previous results concerning the accuracy and the diffculty of outperforming outof-sample the heterogeneous autoregressive (HAR) model; and (iii) some common features of theoptimal lag structure can be identified across assets belonging to the same market segment or showinga similar beta with respect to the market index.
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Keywords realized volatility; adaptive lasso; HAR model; test for false positives; lag structure

Citation: Francesco Audrino, Lorenzo Camponovo, Constantin Roth. Testing the Lag Structure of Assets’ Realized Volatility Dynamics. Quantitative Finance and Economics, 2017, 1(4): 363-387. doi: 10.3934/QFE.2017.4.363


  • 1.Andersen T, Bollerslev T, Diebold F (2003) Some like it smooth, and some like it rough: untangling continuous and jump components in measuring, modeling, and forecasting asset return volatility. Pier working paper 03-025, Northwestern University - Kellogg School of Management.
  • 2.Andersen TG, Bollerslev T, Diebold FX, et al. (2001) The distribution of realized stock return volatility. J Financ Econo 61: 43-76.    
  • 3.Andersen TG, Bollerslev T, Diebold FX, et al. (2001) The distribution of realized exchange rate volatility. J Am Stat Associ 96: 42-55.    
  • 4.Andersen TG, Bollerslev T, Diebold FX, et al. (2003) Modeling and forecasting realized volatility. Econom 71: 579-625.    
  • 5.Ang A, Bekaert G (2007) Stock return predictability: Is it there? Rev Financ Stud 20: 651-707.    
  • 6.Audrino F, Camponovo L (2015) Oracle properties, bias correction, and inference of the adaptive lasso for time series extremum estimators. SSRN working paper series, University of St. Gallen.
  • 7.Audrino F, Knaus SD (2016) Lassoing the har model: A model selection perspective on realized volatility dynamics. Econom Rev 35: 1485-1521.    
  • 8.Barndorff-Nielsen OE, Shephard N (2002) Estimating quadratic variation using realized variance. J Appl Econom 17: 457-477.    
  • 9.Benjamini Y, Hochberg Y (1995) Controlling the false discovery rate: A practical and powerful approach to multiple testing. J R Stat Soc, Ser B 57: 289-300.
  • 10.Bertram P, Kruse R, Sibbertsen P (2013) Fractional integration versus level shifts: the case of realized asset correlations. Stat Papers 54: 977-991.    
  • 11.Bollerslev T (1986) Generalized autoregressive conditional heteroskedasticity. J Econom 31: 307-327.    
  • 12.Bühlmann P, Rütimann P, Geer SVD, et al. (2013) Correlated variables in regression: clustering and sparse estimation. J Stat Plan Inference 143: 1835-1858.    
  • 13.Callot LAF, Kock AB (2014) Oracle effcient estimation and forecasting with the adaptive lasso and the adaptive group lasso in vector autoregressions. In: N. Haldrup, M. Meitz and P. Saikkonen (eds), Essays Nonlinear Time Ser Econom, Oxford University Press.
  • 14.Campbell JY, Yogo M (2006) Effcient tests of stock return predictability. J Financ Econ 81: 27-60.    
  • 15.Corsi F (2009) A simple approximate long-memory model of realized volatility. J Financ Econom 7: 174-196.
  • 16.Corsi F, Audrino F, Renò R (2012) HAR Modelling for Realized Volatility Forecasting. In Volatility Models Appl. Wiley.
  • 17.Craioveanu M, Hillebrand E (2012) Why it is ok to use the HAR-RV (1, 5, 21) model. Working paper, University of Central Missouri.
  • 18.Friedman JH, Hastie T, Tibshirani R (2010) Regularization paths for generalized linear models via coordinate descent. J Stat Softw 33: 1-22.
  • 19.Genovese CR, Roeder K, Wasserman L (2006) False discovery control with p-value weighting. Biom 93: 509-524.
  • 20.Goetzmann WN, Jorion P (1993) Testing the predictive power of dividend yields. J Financ 48: 663-679.    
  • 21.Hansen PR, Lunde A (2005) A forecast comparison of volatility models: does anything beat a garch (1, 1)? J Appl Econom 20: 873-889.    
  • 22.Hillebrand E, Medeiros MC (2016) Asymmetries, breaks, and long-range dependence. J Bus Econ Stat 34: 23-41.    
  • 23.Holm S (1979) A simple sequentially rejective multiple test procedure. Scand J Stat 6: 65-70.
  • 24.Hwang E, Shin D (2014) Infinite-order, long-memory heterogeneous autoregressive models. Comput Stat Data Anal 76: 339–358.    
  • 25.Kock AB (2016) Consistent and conservative model selection with the adaptive lasso in stationary and nonstationary autoregressions. Econom Theory 32: 243-259.    
  • 26.Kock AB, Callot LAF (2015) Oracle inequalities for high dimensional vector autoregressions. J Econom 186: 325-344.    
  • 27.Kothari SP, Shanken J (1997) Book-to-market, dividend yield, and expected market returns: A timeseries analysis. J Financ Econ 44: 169-203.    
  • 28.Leeb H, Pötscher BM (2006) Performance limits for estimators of the risk or distribution of shrinkagetype estimators, and some general lower risk-bound results. Econom Theory 22: 69–97.
  • 29.Leeb H, Pötscher BM (2008) Sparse estimators and the oracle property, or the return of hodges estimator. J Econom 142: 201-211.    
  • 30.McAleer M, Medeiros MC (2008) Realized volatility: A review. Econom Rev 27: 10-45.    
  • 31.Medeiros MC, Mendes E (2016) l1-regularization of high-dimensional time-series models with nongaussian and heteroskedastic innovations. J Econom 191: 255-271.    
  • 32.Nelson CR, Kim MJ (1993) Predictable stock returns: The role of small sample bias. J Financ 48: 641-661.    
  • 33.Pötscher BM, Schneider U (2009) On the distribution of the adaptive lasso estimator. J Stat Plan Inference 139: 2775-2790.    
  • 34.Romano JP, Wolf M (2005) Stepwise multiple testing as formalized data snooping. Econom 73: 1237-1282.    
  • 35.Stambaugh RF (1999) Predictive regressions. J Financ Econ 54: 375-421.    
  • 36.Tibshirani R (1996) Regression shrinkage and selection via the lasso. J R Stat Soc Ser B (Methodol) 58: 267-288.
  • 37.Torous W, Valkanov R, Yan S (2004) On predicting stock returns with nearly integrated explanatory variables. J Bus 77: 937-966.    
  • 38.Wang SH, Bauwens L, Hsiao C (2013) Forecasting a Long Memory Process subject to Structural Breaks. J Econom 177: 171-184.    
  • 39.Zhang L, Mykland PA, Aїt-Sahalia Y (2005) A tale of two time scales: Determining integrated volatility with noisy high-frequency data. J Am Stat Associ 100: 1394-1411.    
  • 40.Zou H (2006) The adaptive lasso and its oracle properties. J Am Stat Associ 101: 1418-1429.    


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