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.

2003

Paul Doukhan, George Oppenheim, Murad S Taqqu (2003), eds. Theory and Applications of Long-Range Dependence (Birkhauser, Boston). [ISBN 0-8176-4168-8]
G Rangarajan, M Ding (2003), Processes with Long Range Correlations: Theory and Applications (Springer Lecture Notes in Physics 621) (Springer-Verlag).
[table of contents]

2001

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", Journal of Applied Probability, 38:1033-1054.
P Kokoszka (2001), "Predicting of long memory time series: an overview", Estadistica, 53:41-96.

2000

J Beran , S Ghosh (2000), "Estimation of the dominating frequency for stationary and nonstationary fractional autoregressive processes", Journal of Time Series Analysis, 21:513-533.
CWJ Granger (2000) "Current perspectives on long-memory processes", Academia Economic Papers, 28:1-16.
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.
G Rangarajan, M Ding (2000), "Integrated approach to the assessment of long range correlation in time series data", Physical Review E, 61:4991-5001.
Wen-Jen Tsay, Ching-Fan Chung (2000), "The spurious regression of fractionally integrated processes", Journal of Econometrics, 96(1):155-182.

1999

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) [ISBN 0-8176-3951-9]
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) [ISBN 0-4120-4901-5]
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.