1/f noise bib: math of long-memory processes

Mathematical Studies of Long-Memory Processes

Note: Papers listed here are not necessarily related to 1/f noise. 1/f noise is a special case of long-memory process, but a long memory may not be a 1/f noise. The purpose of this page is to collect papers on long-memory processes which may end up useful in explaining 1/f noise.

2001

P Doukhan, G Oppenheim, MS Taqqu (2001), eds.
Long-range Dependence: Theory and Applications,
(Birkhauser, Boston)
J Gao, V Anh, C Heyde, Q Tieng (2001),
"Parameter estimation of stochastic processes with long-range dependence and intermittency",
Journal of Time Series Analysis, 22(5):517-539.
L Giraitis, P Kokoszka, R Leipus (2001),
"Testing for long memory in the presence of a general trend",
preprint.
P Kokoszka (2001),
"Predicting of long memory time series: an overview",
Estadistica, in press.

2000

CWJ Granger (2000?)
"Current perspectives on long-memory processes",
Academia Economic Paper, ?:?-?.
L Giraitis, PM Robinson, D Surgailis (2000),
"A model for long memory conditional heteroskedasticity",
Annals of Applied Probability, 10:1002-1024.
V Pipiras, MS Taqqu (2000),
"Convergence of weighted sums of random variables with long-range dependence",
Stochastic Processes and their Applications, 90:157-174.
V Pipiras, MS Taqqu (2000),
"Integration questions related to fractional Brownian motion",
Probability Theory and their Applications, 118:251-291.
Wen-Jen Tsay, Ching-Fan Chung (2000),
"The spurious regression of fractionally integrated processes",
Journal of Econometrics, 96(1):155-182.

1999

J Beran , S Ghosh (1999),
"Estimation of the dominating frequency for stationary and nonstationary fractional autoregressive processes",
Journal of Time Series Analysis, ?:?-?.
FX Diebold, A Inoue (1999),
"Long memory and structual change",
Working Paper (NYU).
[ PDF]
L Giraitis, MS Taqqu (1999),
"Whittle estimator for non-Gaussian long-memory time series",
Annals of Statistics, 27:178-203.
CWJ Granger, N Hyung (1999),
"Occasional structural breaks and long memory",
Discussion Paper 99-14 (UCSD).
P Kokoszka, MS Taqqu (1999),
"Discrete time parametic models with long memory and infinite variance",
Mathematical and Computer Modelling, 29:203-215.
Ignacio N Lobato (1999),
"A semiparametric two-step estimator in a multivariate long memory model",
Journal of Econometrics, 90(1):129-153.
Y Meyer, F Sellan, MS Taqqu (1999),
"Wavelets, generalized white noise and fractional integration: the synthesis of fractional Brownian motion",
Journal of Fourier Analysis and Applications, 5:466-494.
A Montanari, V Teverovsky, MS Taqqu (1999),
"Estimating long-range dependence in the presence of periodicity: an empirical study",
Mathematical and Computer Modelling, 29:217-228.
V Teverovsky, MS Taqqu, W Willinger (1999),
"A critical look at Lo's modified R/S statistic",
Journal of Statistical Planning and Inference, 80:211-227.

1998

RJ Adler, RE Feldman, MS Taqqu (1998),
A Practical Guide to Heavy Tails: Statistical Techniques and Applications
(Birkhauser, Boston)
J Beran (1998),
"Fractional ARIMA models",
in Encyclopedia of Statistical Sciences, eds. S Kotz, CB Read, DL Banks, NL Johnson (Wiley), Vol 2.
J Beran, RJ Bhansali, D Ocker (1998),
"On unified model selection for stationary and nonstationary short- and long-memory autoregressive processes",
Biometrika, 85:921-934.

1997

J Beran (1997),
"Long-range dependence",
in Encyclopedia of Statistical Sciences, eds. S Kotz, CB Read, DL Banks, NL Johnson (Wiley), Vol 1, pp.385-390.
S Ghosh, J Beran , J Innes (1997),
"Nonparametric conditional quantile estimation in the presence of long memory",
Student, 2(2):109-117.
P Hall (1997),
"Defining and measuring long-range dependence",
Fields Institute Communications, 11:153-160.
CC Heyde, Y Yang (1997),
"On defining long-range dependence",
Journal of Applied Probability, 34:939-944.
P Kokoszka, L Horvath (1997),
"The effect of long-range dependence on change point estimators",
Journal of Statistical Planning and Inference, 64:57-81.
MS Taqqu V Teverovsky (1997),
"Robustness of Whittle-type estimators for time series with long-range dependence",
Stochastic Models, 13:723-757.
V Teverovsky, MS Taqqu (1997),
"Testing for long-range dependence in the presence of shifting means or a slowly declining trend, using a variance-type estimator",
Journal of Time Series Analysis, 18:279-304.

1996

J Beran, N Terrin (1996),
"Testing for a change of the long-memory parameter",
Biometrika, 83(3):627-638.
Ching-Fan Chung (1996),
"Estimating a generalized long memory process,",
Journal of Econometrics, 73(1):237-259.
F Comte, E Renault (1996),
"Long memory continuous time models",
Journal of Econometrics, 73(1):101-149.
CWJ Granger, Z Ding (1996),
"Varieties of long-memory models",
Journal of Econometrics, 73:61-77.
Javier Hidalgo, Peter M Robinson (1996),
"Testing for structural change in a long-memory environment",
Journal of Econometrics, 70(1):59-174.
P Kokoszka, MS Taqqu (1996),
"Infinite variance stable moving averages with long memory",
Journal of Econometrics, 73(1):79-99
Dongin Lee, Peter Schmidt (1996),
"On the power of the KPSS test of stationarity against fractionally-integrated alternatives",
Journal of Econometrics, 73(1):285-302.
I Lobato, PM Robinson (1996),
"Averaged periodogram estimation of long memory",
Journal of Econometrics, 73(1):303-324.
Margie A Tieslau, Peter Schmidt, Richard T Baillie (1996),
"A minimum distance estimator for long-memory processes",
Journal of Econometrics, 71(1-2):249-264.

1995

J Beran (1995),
"Maximum likelihood estimation of the differencing parameter for invertible short- and long-memory ARIMA models",
Journal of Royal Society of Statistics, Series B, 57(4):659-672.
Ngai Hang Chan, Norma Terrin (1995),
"Inference for unstable long-memory processes with applications to fractional unit root autoregressions",
Annals of Statistics, 23(5):1662-1683.
CWJ Granger, J Gonzalo (1995),
"Estimation of common long-memory components in cointegrated systems",
Journal of Business and Economic Statistics, 13:27-36.
PM Robinson (1995),
"Gaussian semiparametric estimation of long range dependence",
Annals of Statistics, 23(5):1630-1661.

1994

Jan Beran (1994),
Statistics for Long-Memory Processes (Chapman and Hall)
Jan Beran (1994),
"On a class of M-estimators for long-memory Gaussian models",
Biometrika, 81(4):755-766.
Jan Beran, N Terrin (1994),
"Estimation of the long-memory parameter, based on a multivariate central limit theorem",
Journal of Time Series Analysis, 15(3):269-278.
Bing Cheng, PM Robinson (1994),
"Semiparametric estimation from time series with long-range dependence",
Journal of Econometrics, 64(1-2):335-353
PM Robinson (1994),
"Semiparametric analysis of long-memory time series",
Annals of Statistics, 22(1):515-539.

1993

J Beran (1993),
"Fitting long-memory models by generalized linear regression",
Biometrika, 80:817-822.
J Beran (1993),
"Fitting long-memory models by generalized linear regression",
Biometrika, 80(4):817-822.
H Kunsch, J Beran, F Hampel (1993),
"Contrasts under long-range correlations",
Annals of Statistics, 21:943-964.

1992

Jan Beran (1992),
"Statistical methods for data with long-range dependence",
Statistical Science, 7(4):404-427.
[ PDF ]
[see also the comments by:
AP Dempster, JS Hwang, "Short-range consequences of long-range dependence", pp.416-420;
E Parzen, "Comments", p.420;
AE Raftery, "Computational aspects of fractionally differenced ARIMA modeling for long-memory time series", pp.421-422;
RL Smith, "Comment", pp.422-425;
J Beran, "Rejoinder", pp.425-427.]
J Beran (1992),
"A goodness of fit test for time series with long-range dependence",
Journal of Royal Society of Statistics, Series B, 54(3):749-760.

1991

J Beran (1991),
"M-estimators of location for data with slowly decaying serial correlations",
Journal of the American Statistical Association, 86:704-708.
J Beran, S Ghosh (1991),
"Slowly decaying correlations, testing normality, nuisance parameters",
Journal of the American Statistical Association, 86:785-791.
CWJ Granger, J Hallman (1991),
"Long memory processes with attractors",
Oxford Bulletin of Economics and Statistics, 53:11-26.

1990

J Beran (1990),
"Akaike's model choice criterion, long-range dependence and approximate maximum likelihood estimation",
Technical Report, No. 96 (Texas A&M).

1989

J Beran (1989),
"A test of location for data with slowly decaying serial correlations",
Biometrika, 76:261-269.
J Beran (1989),
"Statistical aspects of stationary processes with long-range dependence",
preprint (U North Carolina).

1986

J Beran (1986),
Estimation, Testing and Prediction for Self-Similar and Related Processes,
Ph.D Thesis (Swiss Federal Institute of Techlonogy).
H Kunsch (1986),
"Discrimination between monotonic and long-range dependence",
Journal of Applied Probability, 23:1025-1030.

1983

RN Bhattacharya, VK Gupta, E Waymire (1983),
"The Hurst effect under trends",
Journal of Applied Probability, 20:649-662.

1981

JRM Hosking (1981),
"Fractional differencing",
Biometrika, 68(1):165-176.

1980

CWJ Granger (1980),
"Long-memory relationships and the aggregation of dynamic models",
Journal of Econometrics, 14:227-238.
CWJ Granger, R Joyeux (1980),
"An introduction to long-memory time series",
Journal of Time Series Analysis, 1:15-30.

1969

BB Mandelbrot, JM Wallis (1969),
"Robustness of the rescaled range R/S in the measurement of noncyclic long run statistical dependence",
Water Resources Research, 5:967-988.