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GARCH Modeling

  • Reference work entry
Complex Systems in Finance and Econometrics

  • 3554 Accesses

Article Outline

Glossary

Definition of the Subject

Introduction

Properties of the GARCH(1,1) Model

Estimation and Inference

Testing for ARCH

Asymmetry, Long Memory, GARCH-in-Mean

Non- and Semi-parametric Models

Multivariate GARCH Models

Stochastic Volatility

Aggregation

Future Directions

Bibliography

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Abbreviations

ACF:

Autocorrelation Function

ARMA:

Autoregressive Moving Average

BEKK:

A multivariate GARCH model named after an early unpublished paper by Baba, Engle, Kraft and Kroner.

CCC:

Constant Conditional Correlation

DCC:

Dynamic Conditional Correlation

CAPM:

Capital Asset Pricing Model

GARCH:

Generalized Autoregressive Conditional Heteroskedasticity

Heteroskedasticity:

A non‐constant variance that depends on the observation or on time.

i.i.d.:

independent, identically distributed

Kurtosis:

A standardized fourth moment of a random variable that tells something about the shape of the distribution. A Gaussian distribution has a kurtosis of three. If the kurtosis is larger than three, then typically the distribution will have tails that are thicker than those of the Gaussian distribution.

Lag:

An operation that shifts the time index of a time series. For example, the first lag of y t is \({y_{t-1}}\).

Long memory:

Property of covariance stationary processes without absolutely summable ACF, meaning that the ACF decays slowly.

Realized volatility:

Sum of intra-day squared returns as a measure for daily volatility.

Skewness:

A standardized third moment of a random variable that tells something about the asymmetry of the distribution. Symmetric distributions have skewness equal to zero.

Volatility:

Degree of fluctuation of a time series around its mean.

Bibliography

Primary Literature

  1. Ait‐Sahalia Y, Mykland P, Zhang L (2005) A tale of two time scales: Determining integrated volatility with noisy high‐frequency data. J Am Stat Assoc 100:1394–1411

    Google Scholar 

  2. Ait‐Sahalia Y, Mykland P, Zhang L (2005) How often to sample a continuous time process in the presence of market microstructure noise. Rev Financial Stud 18:351–416

    Google Scholar 

  3. Alexander C (2001) Orthogonal GARCH. In: Mastering Risk, Financial Times, vol 2. Prentice Hall, London, pp 21–38

    Google Scholar 

  4. Andersen TG, Bollerslev T (1998) Answering the skeptics: Yes, standard volatility models do provide accurate forecasts. Int Econ Rev 39:885–905

    Article  Google Scholar 

  5. Andersen TG, Bollerslev T, Diebold FX, Labys P (2003) Modeling and forecasting realized volatility. Econometrica 71:579–625

    Google Scholar 

  6. Andrews DWK (1999) Estimation when a parameter is on a boundary. Econometrica 67:1341–1383

    Article  Google Scholar 

  7. Baillie RT (1996) Long memory processes and fractional integration in econometrics. J Econom 73:5–59

    Article  Google Scholar 

  8. Baillie RT, Bollerslev T, Mikkelsen HO (1996) Fractionally integrated generalized autoregressive conditional heteroskedasticity. J Econom 74:3–30

    Article  Google Scholar 

  9. Barndorff‐Nielsen O, Shephard N (2002) Econometric analysis of realized volatility and its use in estimating stochastic volatility models. J Roy Stat Soc 64:253–280

    Google Scholar 

  10. Barndorff‐Nielsen O, Shephard N (2004) Econometric analysis of realized covariation: high frequency covariance, regression and correlation in financial economics. Econometrica 72:885–925

    Google Scholar 

  11. Barndorff‐Nielsen O, Shephard N (2004) Power and bipower variation with stochastic volatility and jumps (with discussion). J Financial Econom 2:1–48

    Google Scholar 

  12. Bauwens L, Lubrano M (1998) Bayesian inference on garch models using the gibbs sampler. Econom J 1:C23–C46

    Article  Google Scholar 

  13. Bauwens L, Laurent S, Rombouts J (2006) Multivariate garch models: a survey. J Appl Econom 21:79–109

    Article  Google Scholar 

  14. Bera A, Higgins M (1993) A survey of ARCH models: properties, estimation and testing. J Econ Surv 7:305–366

    Article  Google Scholar 

  15. Berndt EK, Hall BH, Hall RE, Hausman JA (1974) Estimation and inference in nonlinear structural models. Ann Econ Soc Meas 3:653–665

    Google Scholar 

  16. Bickel PJ (1982) On adaptive estimation. Ann Stat 10:647–671

    Article  Google Scholar 

  17. Black F (1976) Studies in stock price volatility changes. In: Proceedings of the 1976 Meeting of the Business and Economic Statistics Section, American Statistical Association, pp 177–181

    Google Scholar 

  18. Black F, Scholes M (1973) The pricing of options and corporate liabilities. J Political Econ 81:637–654

    Article  Google Scholar 

  19. Bollerslev T, Mikkelsen HO (1996) Modeling and pricing long‐memory in stock market volatility. J Econom 73:151–184

    Article  Google Scholar 

  20. Bollerslev T, Engle R, Nelson D (1994) ARCH models. In: Engle R, McFadden D (eds) Handbook of Econometrics. North Holland, Amsterdam, pp 2959–3038

    Google Scholar 

  21. Bollerslev TP (1986) Generalized autoregressive conditional heteroscedasticity. J Econom 31:307–327

    Article  Google Scholar 

  22. Bollerslev TP (1990) Modelling the coherence in short-run nominal exchange rates: A multivariate generalized arch model. Rev Econ Stat 72:498–505

    Article  Google Scholar 

  23. Bollerslev TP, Wooldridge JM (1992) Quasi maximum likelihood estimation of dynamic models with time‐varying covariances. Econom Rev 11:143–172

    Article  Google Scholar 

  24. Bollerslev TP, Engle RF, Wooldridge JM (1988) A capital asset pricing model with time‐varying covariances. J Political Econ 96:116–131

    Article  Google Scholar 

  25. Bougerol P, Picard N (1992) Stationarity of garch processes and some nonnegative time series. J Econom 52:115–127

    Article  Google Scholar 

  26. Bühlmann P, McNeil AJ (2002) An algorithm for nonparametric GARCH modelling. Comput Stat Data Anal 40:665–683

    Google Scholar 

  27. Carnero MA, Pena D, Ruiz E (2004) Persistence and kurtosis in GARCH and stochastic volatility models. J Financial Econom 2:319–342

    Article  Google Scholar 

  28. Carrasco M, Chen X (2002) Mixing and moment properties of various garch and stochastic volatility models. Econom Theory 18:17–39

    Article  Google Scholar 

  29. Carroll R, Härdle W, Mammen E (2002) Estimation in an additive model when the components are linked parametrically. Econom Theory 18:886–912

    Google Scholar 

  30. Chan LKC, Karceski J, Lakonishok J (1999) On portfolio optimization: Forecasting covariances and choosing the risk model. Rev Financial Stud 12:937–674

    Article  Google Scholar 

  31. Comte F, Lieberman O (2003) Asymptotic theory for multivariate garch processes. J Multivar Anal 84:61–84

    Article  Google Scholar 

  32. Concepcion Ausian M, Galeano P (2007) Bayesian estimation of the gaussian mixture GARCH model. Comput Stat Data Anal 51:2636–2652

    Article  Google Scholar 

  33. Danielsson J (1998) Multivariate stochastic volatility models: Estimation and a comparison with vgarch models. J Empir Finance 5:155–174

    Article  Google Scholar 

  34. Diebold FX, Nerlove M (1989) The dynamics of exchange rate volatility: A multivariate latent factor arch model. J Appl Econom 4:1–21

    Article  Google Scholar 

  35. Ding Z, Granger C (1996) Modelling volatility persistence of speculative returns: a new approach. J Econom 73:185–215

    Article  Google Scholar 

  36. Ding Z, Granger CWJ, Engle RF (1993) A long memory property of stock market returns and a new model. J Empir Finance 1:83–106

    Article  Google Scholar 

  37. Drost FC, Klaassen CAJ (1997) Efficient estimation in semiparametric garch models. J Econom 81:193–221

    Article  Google Scholar 

  38. Drost FC, Nijman T (1993) Temporal aggregation of GARCH processes. Econometrica 61:909–927

    Article  Google Scholar 

  39. Drost FC, Werker BJM (1996) Closing the garch gap: Continuous garch modeling. J Econom 74:31–57

    Article  Google Scholar 

  40. Drost FC, Klaassen CAJ, Werker BJM (1997) Adaptive estimation in time series models. Ann Stat 25:786–817

    Article  Google Scholar 

  41. Duan JC (1995) The GARCH option pricing model. Math Finance 5:13–32

    Article  Google Scholar 

  42. Duan JC (1997) Augmented garch(p, q) process and its diffusion limit. J Econom 79:97–127

    Article  Google Scholar 

  43. Embrechts P, Klüppelberg C, Mikosch T (1997) Modelling Extremal Events. Springer, Berlin

    Google Scholar 

  44. Engle RF (1982) Autoregressive conditional heteroscedasticity with estimates of the variance of U.K. inflation. Econometrica 50:987–1008

    Article  Google Scholar 

  45. Engle RF (2002) Dynamic conditional correlation – a simple class of multivariate garch models. J Bus Econ Stat 20:339–350

    Article  Google Scholar 

  46. Engle RF (2002) New frontiers of ARCH models. J Appl Econom 17:425–446

    Article  Google Scholar 

  47. Engle RF, Bollerslev TP (1986) Modelling the persistence of conditional variances. Econom Rev 5:1–50, 81–87

    Google Scholar 

  48. Engle RF, Gonzalez‐Rivera G (1991) Semiparametric ARCH models. J Bus Econ Stat 9:345–360

    Google Scholar 

  49. Engle RF, Kroner KF (1995) Multivariate simultaneous generalized arch. Econom Theory 11:122–150

    Article  Google Scholar 

  50. Engle RF, Mezrich J (1996) GARCH for groups. RISK 9:36–40

    Google Scholar 

  51. Engle RF, Ng VK (1993) Measuring and testing the impact of news on volatility. J Finance 48:1749–1778

    Article  Google Scholar 

  52. Engle RF, Lilien DM, Robins RP (1987) Estimating time varying risk premia in the term structure: The ARCH-M model. Econometrica 55:391–407

    Article  Google Scholar 

  53. Engle RF, Ng VK, Rothschild M (1990) Asset pricing with a factor-ARCH covariance structure. J Econom 45:213–237

    Article  Google Scholar 

  54. Fama EF (1965) The behavior of stock market prices. J Bus 38:34–105

    Article  Google Scholar 

  55. Fan J, Wang M, Yao Q (2008) Modelling multivariate volatilities via conditionally uncorrelated components. J Royal Stat Soc Ser B 70:679–702

    Article  Google Scholar 

  56. Fiorentini G, Sentana E, Shephard N (2004) Likelihood‐based estimation of latent generalized ARCH structures. Econometrica 72:1481–1517

    Article  Google Scholar 

  57. Francq C, Zakoian JM (2004) Maximum likelihood estimation of pure garch and arma-garch processes. Bernoulli 10:605–637

    Article  Google Scholar 

  58. Fridman M, Harris L (1998) A maximum likelihood approach for non‐gaussian stochastic volatility models. J Bus Econ Stat 16:284–291

    Article  Google Scholar 

  59. Glosten LR, Jagannathan R, Runkle DE (1993) On the relation between the expected value and the volatility of the nominal excess return on stocks. J Finance 48:1779–1801

    Article  Google Scholar 

  60. Gouriéroux C (1992) Modèles ARCH et Applications Financières. Economica

    Google Scholar 

  61. Gouriéroux C, Monfort A (1992) Qualitative threshold ARCH models. J Econom 52:159–199

    Google Scholar 

  62. Granger CWJ (1980) Long memory relationships and the aggregation of dynamic models. J Econom 14:227–238

    Article  Google Scholar 

  63. Hafner CM (1998) Estimating high frequency foreign exchange rate volatility with nonparametric ARCH models. J Stat Plan Inference 68:247–269

    Article  Google Scholar 

  64. Hafner CM (2008) Temporal aggregation of multivariate GARCH processes. J Econom 142:467–483

    Article  Google Scholar 

  65. Hafner CM, Rombouts JVK (2007) Semiparametric multivariate volatility models. Econom Theory 23:251–280

    Article  Google Scholar 

  66. Hall P, Yao P (2003) Inference in ARCH and GARCH models with heavy‐tailed errors. Econometrica 71:285–317

    Article  Google Scholar 

  67. Hansen PR, Lunde A (2006) Realized variance and market microstructure noise, with comments and rejoinder. J Bus Econ Stat 24:127–218

    Article  Google Scholar 

  68. Härdle W, Tsybakov A (1997) Local polynomial estimation of the volatility function. J Econom 81:223–242

    Google Scholar 

  69. Harvey AC, Ruiz E, Shepard N (1994) Multivariate stochastic variance models. Rev Econ Stud 61:247–264

    Article  Google Scholar 

  70. He C, Teräsvirta T (1999) Statistical Properties of the Asymmetric Power ARCH Process. In: Engle RF, White H (eds) Cointegration, Causality, and Forecasting. Festschrift in honour of Clive W.J. Granger, Oxford University Press, pp 462–474

    Google Scholar 

  71. Hentschel L (1995) All in the family: Nesting symmetric and asymmetric garch models. J Financial Econ 39:71104

    Article  Google Scholar 

  72. Hill B (1975) A simple general approach to inference about the tail of a distribution. Ann Stat 3:1163–1174

    Article  Google Scholar 

  73. Hong Y, Tu J, Zhou G (2007) Asymmetries in stock returns: Statistical tests and economic evaluation. Rev Financial Stud 20:1547–1581

    Article  Google Scholar 

  74. Hull J, White A (1987) The pricing of options on assets with stochastic volatilities. J Finance 42:281–300

    Article  Google Scholar 

  75. Jacquier E, Polson NG, Rossi PE (1994) Bayesian analysis of stochastic volatility models (with discussion). J Bus Econ Stat 12:371–417

    Article  Google Scholar 

  76. Jacquier E, Polson NG, Rossi PE (2004) Bayesian analysis of stochastic volatility models with fat-tails and correlated errors. J Econom 122:185–212

    Article  Google Scholar 

  77. Jeantheau T (1998) Strong consistency of estimators for multivariate arch models. Econom Theory 14:70–86

    Article  Google Scholar 

  78. Jorion P (2000) Value-at-Risk: The New Benchmark for Managing Financial Risk. McGraw‐Hill, New York

    Google Scholar 

  79. Kawakatsu H (2006) Matrix exponential GARCH. J Econom 134:95–128

    Article  Google Scholar 

  80. Kim S, Shephard N, Chib S (1998) Stocahstic volatility: likelihood inference and comparison with ARCH models. Rev Econ Stud 65:361–393

    Article  Google Scholar 

  81. King M, Sentana E, Wadhwani S (1994) Volatility and links between national stock markets. Econometrica 62:901–933

    Article  Google Scholar 

  82. Kristensen D, Linton O (2006) A closed‐form estimator for the garch(1,1) model. Econom Theory 323–337

    Google Scholar 

  83. Lanne M, Saikkonen P (2007) A multivariate generalized orthogonal factor GARCH model. J Bus Econ Stat 25:61–75

    Article  Google Scholar 

  84. Ledoit O, Santa-Clara P, Wolf M (2003) Flexible multivariate GARCH modeling with an application to international stock markets. Rev Econs Stat 85:735–747

    Article  Google Scholar 

  85. Lee SW, Hansen BE (1994) Asymptotic properties of the maximum likelihood estimator and test of the stability of parameters of the GARCH and IGARCH models. Econom Theory 10:29–52

    Article  Google Scholar 

  86. Ling S, McAleer M (2003) Asymptotic theory for a vector ARMA-GARCH model. Econom Theory 19:280–310

    Google Scholar 

  87. Lintner J (1965) Security prices, risk and maximal gains from diversification. J Finance 20:587–615

    Article  Google Scholar 

  88. Linton O (1993) Adaptive estimation in ARCH models. Econom Theory 9:539–569

    Article  Google Scholar 

  89. Linton O, Mammen E (2005) Estimating semiparametric ARCH models by kernel smoothing methods. Econometrica 73:771–836

    Article  Google Scholar 

  90. Lo A, Wang J (1995) Implementing option pricing models when asset returns are predictable. J Finance 50:87–129

    Article  Google Scholar 

  91. Lumsdaine RL (1996) Asymptotic properties of the quasi maximum likelihood estimator in GARCH(1,1) and IGARCH(1,1) models. Econometrica 64:575–596

    Article  Google Scholar 

  92. Mahieu R, Schotman P (1998) An empirical application of stochastic volatility models. J Appl Econom 13:333–360

    Article  Google Scholar 

  93. Mandelbrot B (1963) The variation of certain speculative prices. J Bus 36:394–419

    Article  Google Scholar 

  94. Meddahi N, Renault E (2004) Temporal aggregation of volatility models. J of Econom 119:355–379

    Article  Google Scholar 

  95. Morgan JP (1996) Riskmetrics Technical Document, 4th edn. J.P. Morgan, New York

    Google Scholar 

  96. Morillo D, Pohlman L (2002) Large scale multivariate GARCH risk modelling for long‐horizon international equity portfolios. Proceedings of the 2002 Forecasting Financial Markets conference, London

    Google Scholar 

  97. Nelson DB (1990) ARCH models as diffusion approximations. J Econom 45:7–38

    Article  Google Scholar 

  98. Nelson DB (1990) Stationarity and persistence in the GARCH(1,1) model. Econom Theory 6:318–334

    Article  Google Scholar 

  99. Nelson DB (1991) Conditional heteroskedasticity in asset returns: A new approach. Econometrica 59:347–370

    Article  Google Scholar 

  100. Nelson DB, Cao CQ (1992) Inequality constraints in the univariate garch model. J Bus Econ Stat 10:229–235

    Article  Google Scholar 

  101. Newey WK, Steigerwald DS (1997) Asymptotic bias for quasi maximum likelihood estimators in conditional heteroskedasticity models. Econometrica 3:587–599

    Article  Google Scholar 

  102. Nijman T, Sentana E (1996) Marginalization and contemporaneous aggregation in multivariate GARCH processes. J Econom 71:71–87

    Article  Google Scholar 

  103. Pantula SG (1988) Estimation of autoregressive models with ARCH errors. Sankhya Indian J Stat B 50:119–138

    Google Scholar 

  104. Peng L, Yao Q (2003) Least absolute deviations estimation for ARCH and GARCH models. Biometrika 90:967–975

    Article  Google Scholar 

  105. Robinson PM (1991) Testing for strong serial correlation and dynamic conditional heteroskedasticity in multiple regression. J Econom 47:67–84

    Article  Google Scholar 

  106. Ross SA (1976) The arbitrage theory of capital asset pricing. J Econ Theory 13:341–360

    Article  Google Scholar 

  107. Sentana E, Fiorentini G (2001) Identification, estimation and testing of conditionally heteroskedastic factor models. J Econom 102:143–164

    Article  Google Scholar 

  108. Sharpe WF (1964) Capital asset prices: A theory of market equilibrium under conditions of risk. J Finance 19:425–442

    Article  Google Scholar 

  109. Shephard N (2005) Stochastic Volatility: Selected Readings. Oxford University Press, Oxford

    Google Scholar 

  110. Straumann D, Mikosch T (2006) Quasi-mle in heteroscedastic times series: a stochastic recurrence equations approach. Ann Stat 34:2449–2495

    Article  Google Scholar 

  111. Taylor SJ (1986) Modelling Financial Time Series. Wiley, New York

    Google Scholar 

  112. Tse YK (2000) A test for constant correlations in a multivariate GARCH model. J Econom 98:107–127

    Article  Google Scholar 

  113. Tse YK, Tsui AKC (2002) A multivariate GARCH model with time‐varying correlations. J Bus Econ Stat 20:351–362

    Article  Google Scholar 

  114. van der Weide R (2002) Go-garch: A multivariate generalized orthogonal GARCH model. J Appl Econom 17:549–564

    Article  Google Scholar 

  115. Vrontos ID, Dellaportas P, Politis DN (2000) Full bayesian inference for GARCH and EGARCH models. J Bus Econ Stat 18:187198

    Article  Google Scholar 

  116. Vrontos ID, Dellaportas P, Politis D (2003) A full‐factor multivariate garch model. Econom J 6:311–333

    Article  Google Scholar 

  117. Wang Y (2002) Asymptotic nonequivalence of GARCH models and diffusions. Ann Stat 30:754–783

    Article  Google Scholar 

  118. Weiss AA (1986) Asymptotic theory for ARCH models: Estimation and testing. Econom Theory 2:107–131

    Article  Google Scholar 

  119. Yang L (2006) A semiparametric GARCH model for foreign exchange volatility. J Econom 130:365–384

    Article  Google Scholar 

  120. Yang L, Härdle W, Nielsen P (1999) Nonparametric autoregression with multiplicative volatility and additive mean. J Time Ser Anal 20:579–604

    Google Scholar 

  121. Zaffaroni P (2007) Aggregation and memory of models of changing volatility. J Econom 136:237–249

    Article  Google Scholar 

  122. Zaffaroni P (2007) Contemporaneous aggregation of GARCH processes. J Time Series Anal 28:521–544

    Article  Google Scholar 

  123. Zakoian JM (1994) Threshold heteroskedastic functions. J Econ Dyn Control 18:931–955

    Article  Google Scholar 

Books and Reviews

  1. Andersen T, Bollerslev T, Diebold F (2004) Parametric and nonparametric measurement of volatility. In: Ait‐Sahalia L, Hansen LP (eds) Handbook of Financial Economtrics. Amsterdam (forthcoming)

    Google Scholar 

  2. Bauwens L, Laurent S, Rombouts J (2006) Multivariate GARCH models: A survey. J Appl Econom 21:79–109

    Article  Google Scholar 

  3. Bera A, Higgins M (1993) A survey of ARCH models: properties, estimation and testing. J Econ Surv 7:305–366

    Article  Google Scholar 

  4. Bollerslev T, Chou R, Kroner K (1992) ARCH modelling in finance: a review of the theory and empirical evidence. J Econom 52:5–59

    Article  Google Scholar 

  5. Bollerslev T, Engle R, Nelson D (1994) ARCH models. In: Engle R, McFadden D (eds) Handbook of Econometrics. North Holland Press, Amsterdam, pp 2959–3038

    Google Scholar 

  6. Engle R (1995) ARCH: Selected Readings. Oxford University Press, Oxford

    Google Scholar 

  7. Gouriéroux C (1997) ARCH Models and Financial Applications. Springer, New York

    Google Scholar 

  8. Shephard N (1996) Statistical aspects of ARCH and stochastic volatility. In: Cox DR, Hinkley DV, Barndorff‐Nielsen OE (eds) Time Series Models in Econometrics, Finance and Other Fields. Chapman & Hall, London, pp 1–67

    Google Scholar 

  9. Shephard N (2005) Stochastic Volatility: Selected Readings. Oxford University Press, Oxford

    Google Scholar 

  10. Taylor S (1986) Modelling Financial Time Series. Wiley, Chichester

    Google Scholar 

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Authors and Affiliations

  1. Université catholique de Louvain, Louvain-la-Neuve, Belgium

    Christian M. Hafner

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  1. RAMTECH LIMITED, 122 Escalle Lane, Larkspur, CA, 94939, USA

    Robert A. Meyers Ph. D. (Editor-in-Chief) (Editor-in-Chief)

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Hafner, C.M. (2009). GARCH Modeling. In: Meyers, R. (eds) Complex Systems in Finance and Econometrics. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-7701-4_26

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