Empirical wavelet analysis of tail and memory properties of LARCH and FIGARCH models

Abry P, Taqqu MS, Pesquet-Popescu B (2000) Wavelet-based estimators for self-similar α-stable processes. In: International conference on signal processing, 16th World Computer Congress, Beijing, pp 369–375

Abry P, Flandrin P, Taqqu MS, Veitch D (2002) Self-similarity and long-range dependence through the wavelet lens. In: Doukhan P, Oppenheim G, Taqqu MS (eds) Theory and applications of long range dependence. Birkhäuser, Boston, pp 527–554

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

Baillie RT, Han YW, Myers RJ, Song J (2007) Long memory and FIGARCH models for daily and high frequency commodity prices. J Futures Mark 27: 643–668

Basrak B, Davis R, Mikosch T (2002) Regular variation of GARCH processes. Stoch Process Appl 99: 95–115

Beine M, Laurent S, Lecourt C (2002) Accounting for conditional leptokurtosis and closing days effects in FIGARCH models of daily exchange rates. Appl Financ Econ 12: 589–600

Brockwell P, Davis R (2002) Introduction to time series and forecasting, 2nd edn. Springer-Verlag, New York

Campbell JY, Lo AW, MacKinlay AC (1997) The econometrics of financial markets. Princeton University Press, New Jersey

Craigmile P, Guttorp P, Percival DB (2005) Wavelet-based parameter estimation for polynomial contaminated fractionally differenced process. IEEE Trans Signal Process 53: 3151–3161

Davis R, Mikosch T (2009) Extremes of stochastic volatility models. In: Andersen T, Davis R, Kreiß J, Mikosch T (eds) Handbook of financial time series. Springer, New York, pp 355–364

de Hann L, Resnick S, Rootzén H, de Vries CG (1989) Extremal behaviour of solutions to a stochastic difference equation with application to ARCH processes. Stoch Process Appl 32: 213–224

Douc R, Roueff F, Soulier P (2008) On the existence of some ARCH(∞) processes. Stoch Process Appl 118: 755–761

Embrechts P, Klüppelberg C, Mikosch T (1997) Modelling extremal events for insurance and finance. Springer-Verlag, Berlin

Geweke J, Porter-Hudak S (1983) The estimation and application of long memory time series models. J Time Ser Anal 4: 221–238

Giraitis L, Robinson P, Surgailis D (2000) A model for long memory conditional heteroskedasticity. Ann Appl Probab 10: 1002–1024

Giraitis L, Kokoszka P, Leipus R, Teyssière G (2003) Rescaled variance and related tests for long memory in volatility and levels. J Econom 112: 265–294

Giraitis L, Leipus R, Robinson P, Surgailis D (2004) LARCH, leverage and long memory. J Financ Econom 2: 177–210

Giraitis L, Leipus R, Surgailis D (2008) ARCH(∞) models and long memory properties. In: Andersen T, Davis R, Kreiß J, Mikosch T (eds) Handbook of financial time series. Springer, New York, pp 71–84

Gnedenko BV, Kolmogorov AN (1954) Limit distributions for sums of independent random variables. Addison-Wesley, Reading

Henry M (2001) Robust automatic bandwidth for long memory. J Time Ser Anal 22: 293–316

Hurvich CM, Deo R, Brodsky J (1998) The mean squared error of Geweke and Porter-Hudak’s estimator of the memory parameter of a long memory time series. J Time Ser Anal 19: 19–46

Jach A, Kokoszka P (2008) Robust wavelet-domain estimation of the fractional difference parameter in heavy-tailed time series: an empirical study. Methodol Comput Appl Probab. doi: 10.1007/s11009-008-9105-3

Kokoszka P, Maslova I, Sojka J, Zhu L (2006) Probability tails of wavelet coefficients of magnetometer records. J Geophys Res. doi: 10.1029/2005JA011321

Lardic S, Mignon V (2004) Term premium and long-range dependence in volatility: a FIGARCH-M estimation on some Asian countries. J Emerg Market Finance 3: 1–19

Lee SH (2005) Forecasting conditional volatility of returns by using the relationship among returns, trading volume, and open interest in commodity futures markets. PhD thesis, Purdue University

Mikosch T, Stărică C (2000) Limit theory for the sample autocorrelation and extremes of a GARCH(1, 1) process. Ann Stat 28: 1427–1451

Moulines E, Roueff E, Taqqu MS (2008) A wavelet Whittle estimator of the memory parameter of a nonstationary Gaussian time series. Ann Stat 36: 1925–1956

Palma W (2007) Long-memory time series: theory and methods. Wiley-Interscience, New Jersey

Percival DB, Walden AT (2000) Wavelet Methods for time series analysis. Cambridge University Press, Cambridge

Pipiras V, Taqqu MS, Abry P (2007) Bounds for the covariance of functions of infinite variance stable random variables with applications to central limit theorems and wavelet-based estimation. Bernoulli 13: 1091–1123

Robinson P (1991) Testing for strong serial correlation and dynamic conditional heteroskedasticity. J Econom 47: 67–84

Robinson P (1995) Gaussian semiparametric estimation of long range dependence. Ann Stat 23: 1630–1661

Samorodnitsky G, Taqqu MS (1994) Stable non-Gaussian random processes: stochastic models with infinite variance. Chapman and Hall, New York

Stoev S, Taqqu MS (2005) Asymptotic self-similarity and wavelet estimation for long-range dependent FARIMA time series with stable innovations. J Time Ser Anal 26: 211–249

Stoev S, Pipiras V, Taqqu MS (2002) Estimation of the self-similarity parameter in linear fractional stable motion. Signal Process 80: 1873–1901

Stoev S, Michailidis G, Taqqu MS (2006) Estimating heavy-tail exponents through max self-similarity. Techical report TR445, University of Michigan

Teyssière G, Abry P (2006) Wavelet analysis of nonlinear long-range dependent processes. Applications to financial time series. In: Teyssière G, Kirman A (eds) Long memory in economics. Springer, New York, pp 173–238