Skip to main content
Top

2010 | OriginalPaper | Chapter

5. Spectral Analysis

Author : Dr. Manfred Mudelsee

Published in: Climate Time Series Analysis

Publisher: Springer Netherlands

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

Spectral analysis investigates the noise component in the climate equation (Eq. 1.2). A Fourier transformation into the frequency domain makes it possible to separate short-term from long-term variations and to distinguish between cyclical forcing mechanisms of the climate system and broad-band resonances. Spectral analysis allows to learn about the climate physics.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Literature
go back to reference Abram NJ, Mulvaney R, Wolff EW, Mudelsee M (2007) Ice core records as sea ice proxies: An evaluation from the Weddell Sea region of Antarctica. Journal of Geophysical Research 112(D15): D15101. [doi:10.1029/2006JD008139] Abram NJ, Mulvaney R, Wolff EW, Mudelsee M (2007) Ice core records as sea ice proxies: An evaluation from the Weddell Sea region of Antarctica. Journal of Geophysical Research 112(D15): D15101. [doi:10.1029/2006JD008139]
go back to reference Akaike H (1960) Effect of timing-error on the power spectrum of sampled-data. Annals of the Institute of Statistical Mathematics 11: 145–165. Akaike H (1960) Effect of timing-error on the power spectrum of sampled-data. Annals of the Institute of Statistical Mathematics 11: 145–165.
go back to reference Angelini C, Cava D, Katul G, Vidakovic B (2005) Resampling hierarchical processes in the wavelet domain: A case study using atmospheric turbulence. Physica D 207(1–2): 24–40. Angelini C, Cava D, Katul G, Vidakovic B (2005) Resampling hierarchical processes in the wavelet domain: A case study using atmospheric turbulence. Physica D 207(1–2): 24–40.
go back to reference Bard E, Frank M (2006) Climate change and solar variability: What’s new under the sun? Earth and Planetary Science Letters 248(1–2): 1–14. Bard E, Frank M (2006) Climate change and solar variability: What’s new under the sun? Earth and Planetary Science Letters 248(1–2): 1–14.
go back to reference Bartlett MS (1950) Periodogram analysis and continuous spectra. Biometrika 37(1–2): 1–16. Bartlett MS (1950) Periodogram analysis and continuous spectra. Biometrika 37(1–2): 1–16.
go back to reference Bartlett MS (1955) An introduction to stochastic processes with special reference to methods and applications. Cambridge University Press, Cambridge, 312 pp. Bartlett MS (1955) An introduction to stochastic processes with special reference to methods and applications. Cambridge University Press, Cambridge, 312 pp.
go back to reference Belcher J, Hampton JS, Tunnicliffe Wilson G (1994) Parameterization of continuous time autoregressive models for irregularly sampled time series data. Journal of the Royal Statistical Society, Series B 56(1): 141–155. Belcher J, Hampton JS, Tunnicliffe Wilson G (1994) Parameterization of continuous time autoregressive models for irregularly sampled time series data. Journal of the Royal Statistical Society, Series B 56(1): 141–155.
go back to reference Bell B, Percival DB, Walden AT (1993) Calculating Thomson’s spectral multitapers by inverse iteration. Journal of Computational and Graphical Statistics 2(1): 119–130. Bell B, Percival DB, Walden AT (1993) Calculating Thomson’s spectral multitapers by inverse iteration. Journal of Computational and Graphical Statistics 2(1): 119–130.
go back to reference Bendat JS, Piersol AG (1986) Random Data: Analysis and Measurement Procedures. Second edition. Wiley, New York, 566 pp. Bendat JS, Piersol AG (1986) Random Data: Analysis and Measurement Procedures. Second edition. Wiley, New York, 566 pp.
go back to reference Berger A, Loutre MF (1991) Insolation values for the climate of the last 10 million years. Quaternary Science Reviews 10(4): 297–317. Berger A, Loutre MF (1991) Insolation values for the climate of the last 10 million years. Quaternary Science Reviews 10(4): 297–317.
go back to reference Berger A, Loutre MF, Mélice JL (1998) Instability of the astronomical periods from 1.5 Myr BP to 0.5 Myr AP. Paleoclimates 2(4): 239–280. Berger A, Loutre MF, Mélice JL (1998) Instability of the astronomical periods from 1.5 Myr BP to 0.5 Myr AP. Paleoclimates 2(4): 239–280.
go back to reference Beutler FJ (1970) Alias-free randomly timed sampling of stochastic processes. IEEE Transactions on Information Theory 16(2): 147–152. Beutler FJ (1970) Alias-free randomly timed sampling of stochastic processes. IEEE Transactions on Information Theory 16(2): 147–152.
go back to reference Bond G, Kromer B, Beer J, Muscheler R, Evans MN, Showers W, Hoffmann S, Lotti-Bond R, Hajdas I, Bonani G (2001) Persistent solar influence on North Atlantic climate during the Holocene. Science 294(5549): 2130–2136. Bond G, Kromer B, Beer J, Muscheler R, Evans MN, Showers W, Hoffmann S, Lotti-Bond R, Hajdas I, Bonani G (2001) Persistent solar influence on North Atlantic climate during the Holocene. Science 294(5549): 2130–2136.
go back to reference Brillinger DR (1975) Time Series: Data Analysis and Theory. Holt, Rinehart and Winston, New York, 500 pp. Brillinger DR (1975) Time Series: Data Analysis and Theory. Holt, Rinehart and Winston, New York, 500 pp.
go back to reference Bronez TP (1988) Spectral estimation of irregularly sampled multidimensional processes by generalized prolate spheroidal sequences. IEEE Transactions on Acoustics, Speech, and Signal Processing 36(12): 1862–1873. Bronez TP (1988) Spectral estimation of irregularly sampled multidimensional processes by generalized prolate spheroidal sequences. IEEE Transactions on Acoustics, Speech, and Signal Processing 36(12): 1862–1873.
go back to reference Chave AD, Luther DS, Filloux JH (1997) Observations of the boundary current system at 25.5°N in the subtropical North Atlantic Ocean. Journal of Physical Oceanography 27(9): 1827–1848. Chave AD, Luther DS, Filloux JH (1997) Observations of the boundary current system at 25.5°N in the subtropical North Atlantic Ocean. Journal of Physical Oceanography 27(9): 1827–1848.
go back to reference Cini Castagnoli G, Provenzale A (Eds) (1997) Past and Present Variability of the Solar–Terrestrial System: Measurement, Data Analysis and Theoretical Models. Società Italiana di Fisica, Bologna, 491 pp. Cini Castagnoli G, Provenzale A (Eds) (1997) Past and Present Variability of the Solar–Terrestrial System: Measurement, Data Analysis and Theoretical Models. Società Italiana di Fisica, Bologna, 491 pp.
go back to reference Cooley JW, Tukey JW (1965) An algorithm for the machine calculation of complex Fourier series. Mathematics of Computation 19(90): 297–301. Cooley JW, Tukey JW (1965) An algorithm for the machine calculation of complex Fourier series. Mathematics of Computation 19(90): 297–301.
go back to reference Crutzen PJ (2002) Geology of mankind. Nature 415(6867): 23. Crutzen PJ (2002) Geology of mankind. Nature 415(6867): 23.
go back to reference Crutzen PJ, Steffen W (2003) How long have we been in the Anthropocene era? Climatic Change 61(3): 251–257. Crutzen PJ, Steffen W (2003) How long have we been in the Anthropocene era? Climatic Change 61(3): 251–257.
go back to reference Daubechies I, Guskov I, Schröder P, Sweldens W (1999) Wavelets on irregular point sets. Philosophical Transactions of the Royal Society of London, Series A 357(1760): 2397–2413. Daubechies I, Guskov I, Schröder P, Sweldens W (1999) Wavelets on irregular point sets. Philosophical Transactions of the Royal Society of London, Series A 357(1760): 2397–2413.
go back to reference DeBlonde G, Peltier WR (1991) A one-dimensional model of continental ice volume fluctuations through the Pleistocene: Implications for the origin of the mid-Pleistocene climate transition. Journal of Climate 4(3): 318–344. DeBlonde G, Peltier WR (1991) A one-dimensional model of continental ice volume fluctuations through the Pleistocene: Implications for the origin of the mid-Pleistocene climate transition. Journal of Climate 4(3): 318–344.
go back to reference De Pol-Holz R, Ulloa O, Lamy F, Dezileau L, Sabatier P, Hebbeln D (2007) Late Quaternary variability of sedimentary nitrogen isotopes in the eastern South Pacific Ocean. Paleoceanography 22(2): PA2207. [doi:10.1029/2006PA001308] De Pol-Holz R, Ulloa O, Lamy F, Dezileau L, Sabatier P, Hebbeln D (2007) Late Quaternary variability of sedimentary nitrogen isotopes in the eastern South Pacific Ocean. Paleoceanography 22(2): PA2207. [doi:10.1029/2006PA001308]
go back to reference De Ridder F, de Brauwere A, Pintelon R, Schoukens J, Dehairs F (2006) Identification of the accretion rate for annually resolved archives. Biogeosciences Discussions 3(2): 321–344. De Ridder F, de Brauwere A, Pintelon R, Schoukens J, Dehairs F (2006) Identification of the accretion rate for annually resolved archives. Biogeosciences Discussions 3(2): 321–344.
go back to reference de Vries H (1958) Variation in concentration of radiocarbon with time and location on Earth. Proceedings of the Koninklijke Nederlandse Akademie van Wetenschappen, Series B 61(2): 94–102. de Vries H (1958) Variation in concentration of radiocarbon with time and location on Earth. Proceedings of the Koninklijke Nederlandse Akademie van Wetenschappen, Series B 61(2): 94–102.
go back to reference Diaz HF, Pulwarty RS (1994) An analysis of the time scales of variability in centuries-long ENSO-sensitive records in the last 1000 years. Climatic Change 26(2–3): 317–342. Diaz HF, Pulwarty RS (1994) An analysis of the time scales of variability in centuries-long ENSO-sensitive records in the last 1000 years. Climatic Change 26(2–3): 317–342.
go back to reference Einsele G, Ricken W, Seilacher A (Eds) (1991) Cycles and Events in Stratigraphy. Springer, Berlin, 955 pp. Einsele G, Ricken W, Seilacher A (Eds) (1991) Cycles and Events in Stratigraphy. Springer, Berlin, 955 pp.
go back to reference Ferraz-Mello S (1981) Estimation of periods from unequally spaced observations. The Astronomical Journal 86(4): 619–624. Ferraz-Mello S (1981) Estimation of periods from unequally spaced observations. The Astronomical Journal 86(4): 619–624.
go back to reference Fisher RA (1929) Tests of significance in harmonic analysis. Proceedings of the Royal Society of London, Series A 125(796): 54–59. Fisher RA (1929) Tests of significance in harmonic analysis. Proceedings of the Royal Society of London, Series A 125(796): 54–59.
go back to reference Fleitmann D (2001) Annual to millennial Indian Ocean monsoon variability recorded in Holocene and Pleistocene stalagmites from Oman. Ph.D. Dissertation. University of Bern, Bern, 236 pp. Fleitmann D (2001) Annual to millennial Indian Ocean monsoon variability recorded in Holocene and Pleistocene stalagmites from Oman. Ph.D. Dissertation. University of Bern, Bern, 236 pp.
go back to reference Fleitmann D, Burns SJ, Mangini A, Mudelsee M, Kramers J, Villa I, Neff U, Al-Subbary AA, Buettner A, Hippler D, Matter A (2007a) Holocene ITCZ and Indian monsoon dynamics recorded in stalagmites from Oman and Yemen (Socotra). Quaternary Science Reviews 26(1–2): 170–188. Fleitmann D, Burns SJ, Mangini A, Mudelsee M, Kramers J, Villa I, Neff U, Al-Subbary AA, Buettner A, Hippler D, Matter A (2007a) Holocene ITCZ and Indian monsoon dynamics recorded in stalagmites from Oman and Yemen (Socotra). Quaternary Science Reviews 26(1–2): 170–188.
go back to reference Fleitmann D, Burns SJ, Mudelsee M, Neff U, Kramers J, Mangini A, Matter A (2003) Holocene forcing of the Indian monsoon recorded in a stalagmite from southern Oman. Science 300(5626): 1737–1739. Fleitmann D, Burns SJ, Mudelsee M, Neff U, Kramers J, Mangini A, Matter A (2003) Holocene forcing of the Indian monsoon recorded in a stalagmite from southern Oman. Science 300(5626): 1737–1739.
go back to reference Fodor IK, Stark PB (2000) Multitaper spectrum estimation for time series with gaps. IEEE Transactions on Signal Processing 48(12): 3472–3483. Fodor IK, Stark PB (2000) Multitaper spectrum estimation for time series with gaps. IEEE Transactions on Signal Processing 48(12): 3472–3483.
go back to reference Foias C, Frazho AE, Sherman PJ (1988) A geometric approach to the maximum likelihood spectral estimator for sinusoids in noise. IEEE Transactions on Information Theory 34(5): 1066–1070. Foias C, Frazho AE, Sherman PJ (1988) A geometric approach to the maximum likelihood spectral estimator for sinusoids in noise. IEEE Transactions on Information Theory 34(5): 1066–1070.
go back to reference Foster G (1996a) Time series analysis by projection. I. Statistical properties of Fourier analysis. The Astronomical Journal 111(1): 541–554. Foster G (1996a) Time series analysis by projection. I. Statistical properties of Fourier analysis. The Astronomical Journal 111(1): 541–554.
go back to reference Genton MG, Hall P (2007) Statistical inference for evolving periodic functions. Journal of the Royal Statistical Society, Series B 69(4): 643–657. Genton MG, Hall P (2007) Statistical inference for evolving periodic functions. Journal of the Royal Statistical Society, Series B 69(4): 643–657.
go back to reference Ghil M, Allen MR, Dettinger MD, Ide K, Kondrashov D, Mann ME, Robertson AW, Saunders A, Tian Y, Varadi F, Yiou P (2002) Advanced spectral methods for climatic time series. Reviews of Geophysics 40(1): 1003. [doi:10.1029/2000RG000092] Ghil M, Allen MR, Dettinger MD, Ide K, Kondrashov D, Mann ME, Robertson AW, Saunders A, Tian Y, Varadi F, Yiou P (2002) Advanced spectral methods for climatic time series. Reviews of Geophysics 40(1): 1003. [doi:10.1029/2000RG000092]
go back to reference Gleissberg W (1965) The eighty-year solar cycle in auroral frequency numbers. Journal of the British Astronomical Association 75(4): 227–231. Gleissberg W (1965) The eighty-year solar cycle in auroral frequency numbers. Journal of the British Astronomical Association 75(4): 227–231.
go back to reference Grenander U (1958) Bandwidth and variance in estimation of the spectrum. Journal of the Royal Statistical Society, Series B 20(1): 152–157. Grenander U (1958) Bandwidth and variance in estimation of the spectrum. Journal of the Royal Statistical Society, Series B 20(1): 152–157.
go back to reference Grenander U, Rosenblatt M (1956) Statistical Analysis of Stationary Time Series. Almqvist & Wiksell, Stockholm, 300 pp. Grenander U, Rosenblatt M (1956) Statistical Analysis of Stationary Time Series. Almqvist & Wiksell, Stockholm, 300 pp.
go back to reference Hagelberg T, Pisias N, Elgar S (1991) Linear and nonlinear couplings between orbital forcing and the marine δ 18O record during the late Neogene. Paleoceanography 6(6): 729–746. Hagelberg T, Pisias N, Elgar S (1991) Linear and nonlinear couplings between orbital forcing and the marine δ 18O record during the late Neogene. Paleoceanography 6(6): 729–746.
go back to reference Hall P, Turlach BA (1997) Interpolation methods for nonlinear wavelet regression with irregularly spaced design. The Annals of Statistics 25(5): 1912–1925. Hall P, Turlach BA (1997) Interpolation methods for nonlinear wavelet regression with irregularly spaced design. The Annals of Statistics 25(5): 1912–1925.
go back to reference Hannan EJ (1960) Time Series Analysis. Methuen, London, 152 pp. Hannan EJ (1960) Time Series Analysis. Methuen, London, 152 pp.
go back to reference Hannan EJ (1961) Testing for a jump in the spectral function. Journal of the Royal Statistical Society, Series B 23(2): 394–404. Hannan EJ (1961) Testing for a jump in the spectral function. Journal of the Royal Statistical Society, Series B 23(2): 394–404.
go back to reference Hannan EJ, Quinn BG (1989) The resolution of closely adjacent spectral lines. Journal of Time Series Analysis 10(1): 13–31. Hannan EJ, Quinn BG (1989) The resolution of closely adjacent spectral lines. Journal of Time Series Analysis 10(1): 13–31.
go back to reference Hansen JE, Lacis AA (1990) Sun and dust versus greenhouse gases: An assessment of their relative roles in global climate change. Nature 346(6286): 713–719. Hansen JE, Lacis AA (1990) Sun and dust versus greenhouse gases: An assessment of their relative roles in global climate change. Nature 346(6286): 713–719.
go back to reference Harris FJ (1978) On the use of windows for harmonic analysis with the discrete Fourier transform. Proceedings of the IEEE 66(1): 51–83. Harris FJ (1978) On the use of windows for harmonic analysis with the discrete Fourier transform. Proceedings of the IEEE 66(1): 51–83.
go back to reference Hartley HO (1949) Tests of significance in harmonic analysis. Biometrika 36(1–2): 194–201. Hartley HO (1949) Tests of significance in harmonic analysis. Biometrika 36(1–2): 194–201.
go back to reference Hegerl GC, Zwiers FW, Braconnot P, Gillett NP, Luo Y, Marengo Orsini JA, Nicholls N, Penner JE, Stott PA (2007b) Understanding and attributing climate change. In: Solomon S, Qin D, Manning M, Marquis M, Averyt K, Tignor MMB, Miller Jr HL, Chen Z (Eds) Climate Change 2007: The Physical Science Basis. Contribution of Working Group I to the Fourth Assessment Report of the Intergovernmental Panel on Climate Change. Cambridge University Press, Cambridge, pp 663–745. Hegerl GC, Zwiers FW, Braconnot P, Gillett NP, Luo Y, Marengo Orsini JA, Nicholls N, Penner JE, Stott PA (2007b) Understanding and attributing climate change. In: Solomon S, Qin D, Manning M, Marquis M, Averyt K, Tignor MMB, Miller Jr HL, Chen Z (Eds) Climate Change 2007: The Physical Science Basis. Contribution of Working Group I to the Fourth Assessment Report of the Intergovernmental Panel on Climate Change. Cambridge University Press, Cambridge, pp 663–745.
go back to reference Heslop D, Dekkers MJ (2002) Spectral analysis of unevenly spaced climatic time series using CLEAN: Signal recovery and derivation of significance levels using a Monte Carlo simulation. Physics of the Earth and Planetary Interiors 130(1–2): 103–116. Heslop D, Dekkers MJ (2002) Spectral analysis of unevenly spaced climatic time series using CLEAN: Signal recovery and derivation of significance levels using a Monte Carlo simulation. Physics of the Earth and Planetary Interiors 130(1–2): 103–116.
go back to reference Hidalgo J (2003) An alternative bootstrap to moving blocks for time series regression models. Journal of Econometrics 117(2): 369–399. Hidalgo J (2003) An alternative bootstrap to moving blocks for time series regression models. Journal of Econometrics 117(2): 369–399.
go back to reference Hinnov LA, Schulz M, Yiou P (2002) Interhemispheric space–time attributes of the Dansgaard–Oeschger oscillations between 100 and 0 ka. Quaternary Science Reviews 21(10): 1213–1228. Hinnov LA, Schulz M, Yiou P (2002) Interhemispheric space–time attributes of the Dansgaard–Oeschger oscillations between 100 and 0 ka. Quaternary Science Reviews 21(10): 1213–1228.
go back to reference Holzkämper S, Mangini A, Spötl C, Mudelsee M (2004) Timing and progression of the last interglacial derived from a high Alpine stalagmite. Geophysical Research Letters 31(7): L07201. [doi:10.1029/2003GL019112] Holzkämper S, Mangini A, Spötl C, Mudelsee M (2004) Timing and progression of the last interglacial derived from a high Alpine stalagmite. Geophysical Research Letters 31(7): L07201. [doi:10.1029/2003GL019112]
go back to reference Horne JH, Baliunas SL (1986) A prescription for period analysis of unevenly sampled time series. The Astrophysical Journal 302(2): 757–763. Horne JH, Baliunas SL (1986) A prescription for period analysis of unevenly sampled time series. The Astrophysical Journal 302(2): 757–763.
go back to reference Hornstein C (1871) über die Abhängigkeit des Erdmagnetismus von der Rotation der Sonne. Sitzungsberichte der Kaiserlichen Akademie der Wissenschaften, Mathematisch-Naturwissenschaftliche Classe, Zweite Abtheilung 64(6): 62–74. Hornstein C (1871) über die Abhängigkeit des Erdmagnetismus von der Rotation der Sonne. Sitzungsberichte der Kaiserlichen Akademie der Wissenschaften, Mathematisch-Naturwissenschaftliche Classe, Zweite Abtheilung 64(6): 62–74.
go back to reference Horowitz LL (1974) The effects of spline interpolation on power spectral density. IEEE Transactions on Acoustics, Speech, and Signal Processing 22(1): 22–27. Horowitz LL (1974) The effects of spline interpolation on power spectral density. IEEE Transactions on Acoustics, Speech, and Signal Processing 22(1): 22–27.
go back to reference Hoyt DV, Schatten KH (1997) The Role of the Sun in Climate Change. Oxford University Press, New York, 279 pp. Hoyt DV, Schatten KH (1997) The Role of the Sun in Climate Change. Oxford University Press, New York, 279 pp.
go back to reference Huybers P, Wunsch C (2005) Obliquity pacing of the late Pleistocene glacial terminations. Nature 434(7032): 491–494. Huybers P, Wunsch C (2005) Obliquity pacing of the late Pleistocene glacial terminations. Nature 434(7032): 491–494.
go back to reference Imbrie J, Berger A, Boyle EA, Clemens SC, Duffy A, Howard WR, Kukla G, Kutzbach J, Martinson DG, McIntyre A, Mix AC, Molfino B, Morley JJ, Peterson LC, Pisias NG, Prell WL, Raymo ME, Shackleton NJ, Toggweiler JR (1993) On the structure and origin of major glaciation cycles 2. The 100,000-year cycle. Paleoceanography 8(6): 699–735. Imbrie J, Berger A, Boyle EA, Clemens SC, Duffy A, Howard WR, Kukla G, Kutzbach J, Martinson DG, McIntyre A, Mix AC, Molfino B, Morley JJ, Peterson LC, Pisias NG, Prell WL, Raymo ME, Shackleton NJ, Toggweiler JR (1993) On the structure and origin of major glaciation cycles 2. The 100,000-year cycle. Paleoceanography 8(6): 699–735.
go back to reference Imbrie J, Boyle EA, Clemens SC, Duffy A, Howard WR, Kukla G, Kutzbach J, Martinson DG, McIntyre A, Mix AC, Molfino B, Morley JJ, Peterson LC, Pisias NG, Prell WL, Raymo ME, Shackleton NJ, Toggweiler JR (1992) On the structure and origin of major glaciation cycles 1. Linear responses to Milankovitch forcing. Paleoceanography 7(6): 701–738. Imbrie J, Boyle EA, Clemens SC, Duffy A, Howard WR, Kukla G, Kutzbach J, Martinson DG, McIntyre A, Mix AC, Molfino B, Morley JJ, Peterson LC, Pisias NG, Prell WL, Raymo ME, Shackleton NJ, Toggweiler JR (1992) On the structure and origin of major glaciation cycles 1. Linear responses to Milankovitch forcing. Paleoceanography 7(6): 701–738.
go back to reference Jenkins GM, Watts DG (1968) Spectral Analysis and its Applications. Holden-Day, San Francisco, 525 pp. Jenkins GM, Watts DG (1968) Spectral Analysis and its Applications. Holden-Day, San Francisco, 525 pp.
go back to reference Jiménez-Moreno G, Anderson RS, Fawcett PJ (2007) Orbital- and millennial-scale vegetation and climate changes of the past 225 ka from Bear Lake, Utah–Idaho (USA). Quaternary Science Reviews 26(13–14): 1713–1724. Jiménez-Moreno G, Anderson RS, Fawcett PJ (2007) Orbital- and millennial-scale vegetation and climate changes of the past 225 ka from Bear Lake, Utah–Idaho (USA). Quaternary Science Reviews 26(13–14): 1713–1724.
go back to reference Johnson NL, Kotz S, Balakrishnan N (1995) Continuous Univariate Distributions, volume 2. Second edition. Wiley, New York, 719 pp. Johnson NL, Kotz S, Balakrishnan N (1995) Continuous Univariate Distributions, volume 2. Second edition. Wiley, New York, 719 pp.
go back to reference Kantz H, Schreiber T (1997) Nonlinear time series analysis. Cambridge University Press, Cambridge, 304 pp. Kantz H, Schreiber T (1997) Nonlinear time series analysis. Cambridge University Press, Cambridge, 304 pp.
go back to reference Kay SM, Marple Jr SL (1981) Spectrum analysis–-a modern perspective. Proceedings of the IEEE 69(11): 1380–1419. Kay SM, Marple Jr SL (1981) Spectrum analysis–-a modern perspective. Proceedings of the IEEE 69(11): 1380–1419.
go back to reference King T (1996) Quantifying nonlinearity and geometry in time series of climate. Quaternary Science Reviews 15(4): 247–266. King T (1996) Quantifying nonlinearity and geometry in time series of climate. Quaternary Science Reviews 15(4): 247–266.
go back to reference Lees JM, Park J (1995) Multiple-taper spectral analysis: A stand-alone C-subroutine. Computers and Geosciences 21(2): 199–236. Lees JM, Park J (1995) Multiple-taper spectral analysis: A stand-alone C-subroutine. Computers and Geosciences 21(2): 199–236.
go back to reference Linnell Nemec AF, Nemec JM (1985) A test of significance for periods derived using phase-dispersion-minimization techniques. The Astronomical Journal 90(11): 2317–2320. Linnell Nemec AF, Nemec JM (1985) A test of significance for periods derived using phase-dispersion-minimization techniques. The Astronomical Journal 90(11): 2317–2320.
go back to reference Lomb NR (1976) Least-squares frequency analysis of unequally spaced data. Astrophysics and Space Science 39(2): 447–462. Lomb NR (1976) Least-squares frequency analysis of unequally spaced data. Astrophysics and Space Science 39(2): 447–462.
go back to reference MacDonald GJ (1989) Spectral analysis of time series generated by nonlinear processes. Reviews of Geophysics 27(4): 449–469. MacDonald GJ (1989) Spectral analysis of time series generated by nonlinear processes. Reviews of Geophysics 27(4): 449–469.
go back to reference Madden RA, Jones RH (2001) A quantitative estimate of the effect of aliasing in climatological time series. Journal of Climate 14(19): 3987–3993. Madden RA, Jones RH (2001) A quantitative estimate of the effect of aliasing in climatological time series. Journal of Climate 14(19): 3987–3993.
go back to reference Mann ME, Lees JM (1996) Robust estimation of background noise and signal detection in climatic time series. Climatic Change 33(3): 409–445. Mann ME, Lees JM (1996) Robust estimation of background noise and signal detection in climatic time series. Climatic Change 33(3): 409–445.
go back to reference Masry E (1984) Spectral and probability density estimation from irregularly observed data. In: Parzen E (Ed) Time Series Analysis of Irregularly Observed Data. Springer, New York, pp 224–250. Masry E (1984) Spectral and probability density estimation from irregularly observed data. In: Parzen E (Ed) Time Series Analysis of Irregularly Observed Data. Springer, New York, pp 224–250.
go back to reference Mayewski PA, Meeker LD, Twickler MS, Whitlow S, Yang Q, Lyons WB, Prentice M (1997) Major features and forcing of high-latitude northern hemisphere atmospheric circulation using a 110,000-year-long glaciochemical series. Journal of Geophysical Research 102(C12): 26345–26366. Mayewski PA, Meeker LD, Twickler MS, Whitlow S, Yang Q, Lyons WB, Prentice M (1997) Major features and forcing of high-latitude northern hemisphere atmospheric circulation using a 110,000-year-long glaciochemical series. Journal of Geophysical Research 102(C12): 26345–26366.
go back to reference Meeker LD, Mayewski PA, Grootes PM, Alley RB, Bond GC (2001) Comment on “On sharp spectral lines in the climate record and the millennial peak” by Carl Wunsch. Paleoceanography 16(5): 544–547. Meeker LD, Mayewski PA, Grootes PM, Alley RB, Bond GC (2001) Comment on “On sharp spectral lines in the climate record and the millennial peak” by Carl Wunsch. Paleoceanography 16(5): 544–547.
go back to reference Miao X, Mason JA, Johnson WC, Wang H (2007) High-resolution proxy record of Holocene climate from a loess section in southwestern Nebraska, USA. Palaeogeography, Palaeoclimatology, Palaeoecology 245(3–4): 368–381. Miao X, Mason JA, Johnson WC, Wang H (2007) High-resolution proxy record of Holocene climate from a loess section in southwestern Nebraska, USA. Palaeogeography, Palaeoclimatology, Palaeoecology 245(3–4): 368–381.
go back to reference Milne AE, Lark RM (2009) Wavelet transforms applied to irregularly sampled soil data. Mathematical Geosciences 41(6): 661–678. Milne AE, Lark RM (2009) Wavelet transforms applied to irregularly sampled soil data. Mathematical Geosciences 41(6): 661–678.
go back to reference Moore MI, Thomson PJ (1991) Impact of jittered sampling on conventional spectral estimates. Journal of Geophysical Research 96(C10): 18519–18526. Moore MI, Thomson PJ (1991) Impact of jittered sampling on conventional spectral estimates. Journal of Geophysical Research 96(C10): 18519–18526.
go back to reference Mudelsee M, Scholz D, Röthlisberger R, Fleitmann D, Mangini A, Wolff EW (2009) Climate spectrum estimation in the presence of timescale errors. Nonlinear Processes in Geophysics 16(1): 43–56. Mudelsee M, Scholz D, Röthlisberger R, Fleitmann D, Mangini A, Wolff EW (2009) Climate spectrum estimation in the presence of timescale errors. Nonlinear Processes in Geophysics 16(1): 43–56.
go back to reference Mudelsee M, Schulz M (1997) The Mid-Pleistocene Climate Transition: Onset of 100 ka cycle lags ice volume build-up by 280 ka. Earth and Planetary Science Letters 151(1–2): 117–123. Mudelsee M, Schulz M (1997) The Mid-Pleistocene Climate Transition: Onset of 100 ka cycle lags ice volume build-up by 280 ka. Earth and Planetary Science Letters 151(1–2): 117–123.
go back to reference Muller RA, MacDonald GJ (1995) Glacial cycles and orbital inclination. Nature 377(6545): 107–108. Muller RA, MacDonald GJ (1995) Glacial cycles and orbital inclination. Nature 377(6545): 107–108.
go back to reference Muller RA, MacDonald GJ (1997a) Glacial cycles and astronomical forcing. Science 277(5323): 215–218. Muller RA, MacDonald GJ (1997a) Glacial cycles and astronomical forcing. Science 277(5323): 215–218.
go back to reference Muller RA, MacDonald GJ (1997b) Simultaneous presence of orbital inclination and eccentricity in proxy climate records from Ocean Drilling Program Site 806. Geology 25(1): 3–6. Muller RA, MacDonald GJ (1997b) Simultaneous presence of orbital inclination and eccentricity in proxy climate records from Ocean Drilling Program Site 806. Geology 25(1): 3–6.
go back to reference Muller RA, MacDonald GJ (2000) Ice Ages and Astronomical Causes: Data, spectral analysis and mechanisms. Springer, London, 318 pp. Muller RA, MacDonald GJ (2000) Ice Ages and Astronomical Causes: Data, spectral analysis and mechanisms. Springer, London, 318 pp.
go back to reference Mullis CT, Scharf LL (1991) Quadratic estimators of the power spectrum. In: Haykin S (Ed) Advances in Spectrum Analysis and Array Processing, volume 1. Prentice-Hall, Englewood Cliffs, NJ, pp 1–57. Mullis CT, Scharf LL (1991) Quadratic estimators of the power spectrum. In: Haykin S (Ed) Advances in Spectrum Analysis and Array Processing, volume 1. Prentice-Hall, Englewood Cliffs, NJ, pp 1–57.
go back to reference Munk W, Hasselmann K (1964) Super-resolution of tides. In: Yoshida K (Ed) Studies on Oceanography: A Collection of Papers dedicated to Koji Hidaka. University of Washington Press, Seattle, WA, pp 339–344. Munk W, Hasselmann K (1964) Super-resolution of tides. In: Yoshida K (Ed) Studies on Oceanography: A Collection of Papers dedicated to Koji Hidaka. University of Washington Press, Seattle, WA, pp 339–344.
go back to reference Münnich KO, östlund HG, de Vries H (1958) Carbon-14 activity during the past 5,000 years. Nature 182(4647): 1432–1433. Münnich KO, östlund HG, de Vries H (1958) Carbon-14 activity during the past 5,000 years. Nature 182(4647): 1432–1433.
go back to reference Neff U, Burns SJ, Mangini A, Mudelsee M, Fleitmann D, Matter A (2001) Strong coherence between solar variability and the monsoon in Oman between 9 and 6 kyr ago. Nature 411(6835): 290–293. Neff U, Burns SJ, Mangini A, Mudelsee M, Fleitmann D, Matter A (2001) Strong coherence between solar variability and the monsoon in Oman between 9 and 6 kyr ago. Nature 411(6835): 290–293.
go back to reference Niggemann S, Mangini A, Mudelsee M, Richter DK, Wurth G (2003) Sub-Milankovitch climatic cycles in Holocene stalagmites from Sauerland, Germany. Earth and Planetary Science Letters 216(4): 539–547. Niggemann S, Mangini A, Mudelsee M, Richter DK, Wurth G (2003) Sub-Milankovitch climatic cycles in Holocene stalagmites from Sauerland, Germany. Earth and Planetary Science Letters 216(4): 539–547.
go back to reference Nordgaard A (1992) Resampling stochastic processes using a bootstrap approach. In: Jöckel K-H, Rothe G, Sendler W (Eds) Bootstrapping and Related Techniques. Springer, Berlin, pp 181–185. Nordgaard A (1992) Resampling stochastic processes using a bootstrap approach. In: Jöckel K-H, Rothe G, Sendler W (Eds) Bootstrapping and Related Techniques. Springer, Berlin, pp 181–185.
go back to reference Nuttall AH (1981) Some windows with very good sidelobe behavior. IEEE Transactions on Acoustics, Speech, and Signal Processing 29(1): 84–91. Nuttall AH (1981) Some windows with very good sidelobe behavior. IEEE Transactions on Acoustics, Speech, and Signal Processing 29(1): 84–91.
go back to reference Oh H-S, Nychka D, Brown T, Charbonneau P (2004) Period analysis of variable stars by robust smoothing. Applied Statistics 53(1): 15–30. Oh H-S, Nychka D, Brown T, Charbonneau P (2004) Period analysis of variable stars by robust smoothing. Applied Statistics 53(1): 15–30.
go back to reference Paparoditis E (2002) Frequency domain bootstrap for time series. In: Dehling H, Mikosch T, Sørensen M (Eds) Empirical Process Techniques for Dependent Data. Birkhäuser, Boston, pp 365–381. Paparoditis E (2002) Frequency domain bootstrap for time series. In: Dehling H, Mikosch T, Sørensen M (Eds) Empirical Process Techniques for Dependent Data. Birkhäuser, Boston, pp 365–381.
go back to reference Pardo-Igúzquiza E, Chica-Olmo M, Rodríguez-Tovar FJ (1994) CYSTRATI: A computer program for spectral analysis of stratigraphic successions. Computers and Geosciences 20(4): 511–584. Pardo-Igúzquiza E, Chica-Olmo M, Rodríguez-Tovar FJ (1994) CYSTRATI: A computer program for spectral analysis of stratigraphic successions. Computers and Geosciences 20(4): 511–584.
go back to reference Park J (1992) Envelope estimation for quasi-periodic geophysical signals in noise: A multitaper approach. In: Walden AT, Guttorp P (Eds) Statistics in the Environmental & Earth Sciences. Edward Arnold, London, pp 189–219. Park J (1992) Envelope estimation for quasi-periodic geophysical signals in noise: A multitaper approach. In: Walden AT, Guttorp P (Eds) Statistics in the Environmental & Earth Sciences. Edward Arnold, London, pp 189–219.
go back to reference Percival DB, Walden AT (1993) Spectral Analysis for Physical Applications: Multitaper and Conventional Univariate Techniques. Cambridge University Press, Cambridge, 583 pp. Percival DB, Walden AT (1993) Spectral Analysis for Physical Applications: Multitaper and Conventional Univariate Techniques. Cambridge University Press, Cambridge, 583 pp.
go back to reference Pisias NG, Mix AC (1988) Aliasing of the geologic record and the search for long-period Milankovitch cycles. Paleoceanography 3(5): 613–619. Pisias NG, Mix AC (1988) Aliasing of the geologic record and the search for long-period Milankovitch cycles. Paleoceanography 3(5): 613–619.
go back to reference Pittock AB (1978) A critical look at long-term Sun–weather relationships. Reviews of Geophysics and Space Physics 16(3): 400–420. Pittock AB (1978) A critical look at long-term Sun–weather relationships. Reviews of Geophysics and Space Physics 16(3): 400–420.
go back to reference Politis DN, Romano JP (1992b) A general resampling scheme for triangular arrays of α-mixing random variables with application to the problem of spectral density estimation. The Annals of Statistics 20(4): 1985–2007. Politis DN, Romano JP (1992b) A general resampling scheme for triangular arrays of α-mixing random variables with application to the problem of spectral density estimation. The Annals of Statistics 20(4): 1985–2007.
go back to reference Politis DN, Romano JP, Lai T-L (1992) Bootstrap confidence bands for spectra and cross-spectra. IEEE Transactions on Signal Processing 40(5): 1206–1215. Politis DN, Romano JP, Lai T-L (1992) Bootstrap confidence bands for spectra and cross-spectra. IEEE Transactions on Signal Processing 40(5): 1206–1215.
go back to reference Press WH, Teukolsky SA, Vetterling WT, Flannery BP (1992) Numerical Recipes in Fortran 77: The Art of Scientific Computing. Second edition. Cambridge University Press, Cambridge, 933 pp. Press WH, Teukolsky SA, Vetterling WT, Flannery BP (1992) Numerical Recipes in Fortran 77: The Art of Scientific Computing. Second edition. Cambridge University Press, Cambridge, 933 pp.
go back to reference Priestley MB (1962a) The analysis of stationary processes with mixed spectra–-I. Journal of the Royal Statistical Society, Series B 24(1): 215–233. Priestley MB (1962a) The analysis of stationary processes with mixed spectra–-I. Journal of the Royal Statistical Society, Series B 24(1): 215–233.
go back to reference Priestley MB (1981) Spectral Analysis and Time Series. Academic Press, London, 890 pp. Priestley MB (1981) Spectral Analysis and Time Series. Academic Press, London, 890 pp.
go back to reference Priestley MB (1988) Non-linear and Non-stationary Time Series Analysis. Academic Press, London, 237 pp. Priestley MB (1988) Non-linear and Non-stationary Time Series Analysis. Academic Press, London, 237 pp.
go back to reference Priestley MB (1996) Wavelets and time-dependent spectral analysis. Journal of Time Series Analysis 17(1): 85–103. Priestley MB (1996) Wavelets and time-dependent spectral analysis. Journal of Time Series Analysis 17(1): 85–103.
go back to reference Priestley MB (1997) Detection of periodicities. In: Subba Rao T, Priestley MB, Lessi O (Eds) Applications of Time Series Analysis in Astronomy and Meteorology. Chapman and Hall, London, pp 65–88. Priestley MB (1997) Detection of periodicities. In: Subba Rao T, Priestley MB, Lessi O (Eds) Applications of Time Series Analysis in Astronomy and Meteorology. Chapman and Hall, London, pp 65–88.
go back to reference Prieto GA, Parker RL, Vernon III FL (2009) A Fortran 90 library for multitaper spectrum analysis. Computers and Geosciences 35(8): 1701–1710. Prieto GA, Parker RL, Vernon III FL (2009) A Fortran 90 library for multitaper spectrum analysis. Computers and Geosciences 35(8): 1701–1710.
go back to reference Prieto GA, Thomson DJ, Vernon FL, Shearer PM, Parker RL (2007) Confidence intervals for earthquake source parameters. Geophysical Journal International 168(3): 1227–1234. Prieto GA, Thomson DJ, Vernon FL, Shearer PM, Parker RL (2007) Confidence intervals for earthquake source parameters. Geophysical Journal International 168(3): 1227–1234.
go back to reference Prokopenko AA, Hinnov LA, Williams DF, Kuzmin MI (2006) Orbital forcing of continental climate during the Pleistocene: A complete astronomically tuned climatic record from Lake Baikal, SE Siberia. Quaternary Science Reviews 25(23–24): 3431–3457. Prokopenko AA, Hinnov LA, Williams DF, Kuzmin MI (2006) Orbital forcing of continental climate during the Pleistocene: A complete astronomically tuned climatic record from Lake Baikal, SE Siberia. Quaternary Science Reviews 25(23–24): 3431–3457.
go back to reference Quinn BG (1989) Estimating the number of terms in a sinusoidal regression. Journal of Time Series Analysis 10(1): 71–75. Quinn BG (1989) Estimating the number of terms in a sinusoidal regression. Journal of Time Series Analysis 10(1): 71–75.
go back to reference Quinn BG, Hannan EJ (2001) The Estimation and Tracking of Frequency. Cambridge University Press, Cambridge, 266 pp. Quinn BG, Hannan EJ (2001) The Estimation and Tracking of Frequency. Cambridge University Press, Cambridge, 266 pp.
go back to reference Raymo ME (1997) The timing of major climate terminations. Paleoceanography 12(4): 577–585. Raymo ME (1997) The timing of major climate terminations. Paleoceanography 12(4): 577–585.
go back to reference Raymo ME, Huybers P (2008) Unlocking the mysteries of the ice ages. Nature 451(7176): 284–285. Raymo ME, Huybers P (2008) Unlocking the mysteries of the ice ages. Nature 451(7176): 284–285.
go back to reference Rimbu N, Lohmann G, Lorenz SJ, Kim JH, Schneider RR (2004) Holocene climate variability as derived from alkenone sea surface temperature and coupled ocean–atmosphere model experiments. Climate Dynamics 23(2): 215–227. Rimbu N, Lohmann G, Lorenz SJ, Kim JH, Schneider RR (2004) Holocene climate variability as derived from alkenone sea surface temperature and coupled ocean–atmosphere model experiments. Climate Dynamics 23(2): 215–227.
go back to reference Rind D (2002) The Sun’s role in climate variations. Science 296(5568): 673–677. Rind D (2002) The Sun’s role in climate variations. Science 296(5568): 673–677.
go back to reference Roberts DH, Lehár J, Dreher JW (1987) Time series analysis with CLEAN. I. Derivation of a spectrum. The Astronomical Journal 93(4): 968–989. Roberts DH, Lehár J, Dreher JW (1987) Time series analysis with CLEAN. I. Derivation of a spectrum. The Astronomical Journal 93(4): 968–989.
go back to reference Rodó X, Baert E, Comín FA (1997) Variations in seasonal rainfall in southern Europe during the present century: Relationships with the North Atlantic Oscillation and the El Niño–{S}outhern Oscillation. Climate Dynamics 13(4): 275–284. Rodó X, Baert E, Comín FA (1997) Variations in seasonal rainfall in southern Europe during the present century: Relationships with the North Atlantic Oscillation and the El Niño–{S}outhern Oscillation. Climate Dynamics 13(4): 275–284.
go back to reference Rohling EJ, Pälike H (2005) Centennial-scale climate cooling with a sudden cold event around 8,200 years ago. Nature 434(7036): 975–979. Rohling EJ, Pälike H (2005) Centennial-scale climate cooling with a sudden cold event around 8,200 years ago. Nature 434(7036): 975–979.
go back to reference Rutherford S, D’Hondt S (2000) Early onset and tropical forcing of 100,000-year Pleistocene glacial cycles. Nature 408(6808): 72–75. Rutherford S, D’Hondt S (2000) Early onset and tropical forcing of 100,000-year Pleistocene glacial cycles. Nature 408(6808): 72–75.
go back to reference Saltzman B, Verbitsky MY (1993) Multiple instabilities and modes of glacial rhythmicity in the Plio–Pleistocene: A general theory of late Cenozoic climatic change. Climate Dynamics 9(1): 1–15. Saltzman B, Verbitsky MY (1993) Multiple instabilities and modes of glacial rhythmicity in the Plio–Pleistocene: A general theory of late Cenozoic climatic change. Climate Dynamics 9(1): 1–15.
go back to reference Scargle JD (1982) Studies in astronomical time series analysis. II. Statistical aspects of spectral analysis of unevenly spaced data. The Astrophysical Journal 263(2): 835–853. Scargle JD (1982) Studies in astronomical time series analysis. II. Statistical aspects of spectral analysis of unevenly spaced data. The Astrophysical Journal 263(2): 835–853.
go back to reference Scargle JD (1989) Studies in astronomical time series analysis. III. Fourier transforms, autocorrelation functions, and cross-correlation functions of unevenly spaced data. The Astrophysical Journal 343(2): 874–887. Scargle JD (1989) Studies in astronomical time series analysis. III. Fourier transforms, autocorrelation functions, and cross-correlation functions of unevenly spaced data. The Astrophysical Journal 343(2): 874–887.
go back to reference Scargle JD (1997) Wavelet methods in astronomical time series analysis. In: Subba Rao T, Priestley MB, Lessi O (Eds) Applications of Time Series Analysis in Astronomy and Meteorology. Chapman and Hall, London, pp 226–248. Scargle JD (1997) Wavelet methods in astronomical time series analysis. In: Subba Rao T, Priestley MB, Lessi O (Eds) Applications of Time Series Analysis in Astronomy and Meteorology. Chapman and Hall, London, pp 226–248.
go back to reference Schulz M (1996) SPECTRUM und ENVELOPE: Computerprogramme zur Spektralanalyse nicht äquidistanter paläoklimatischer Zeitreihen. Sonderforschungsbereich 313, University of Kiel, Kiel, 131 pp. [Report No. 65] Schulz M (1996) SPECTRUM und ENVELOPE: Computerprogramme zur Spektralanalyse nicht äquidistanter paläoklimatischer Zeitreihen. Sonderforschungsbereich 313, University of Kiel, Kiel, 131 pp. [Report No. 65]
go back to reference Schulz M (2002) On the 1470-year pacing of Dansgaard–Oeschger warm events. Paleoceanography 17(2): 1014. [doi:10.1029/2000PA000571] Schulz M (2002) On the 1470-year pacing of Dansgaard–Oeschger warm events. Paleoceanography 17(2): 1014. [doi:10.1029/2000PA000571]
go back to reference Schulz M, Berger WH, Sarnthein M, Grootes PM (1999) Amplitude variations of 1470-year climate oscillations during the last 100,000 years linked to fluctuations of continental ice mass. Geophysical Research Letters 26(22): 3385–3388. Schulz M, Berger WH, Sarnthein M, Grootes PM (1999) Amplitude variations of 1470-year climate oscillations during the last 100,000 years linked to fluctuations of continental ice mass. Geophysical Research Letters 26(22): 3385–3388.
go back to reference Schulz M, Mudelsee M (2002) REDFIT: Estimating red-noise spectra directly from unevenly spaced paleoclimatic time series. Computers and Geosciences 28(3): 421–426. Schulz M, Mudelsee M (2002) REDFIT: Estimating red-noise spectra directly from unevenly spaced paleoclimatic time series. Computers and Geosciences 28(3): 421–426.
go back to reference Schulz M, Stattegger K (1997) SPECTRUM: Spectral analysis of unevenly spaced paleoclimatic time series. Computers and Geosciences 23(9): 929–945. Schulz M, Stattegger K (1997) SPECTRUM: Spectral analysis of unevenly spaced paleoclimatic time series. Computers and Geosciences 23(9): 929–945.
go back to reference Schuster A (1898) On the investigation of hidden periodicities with application to a supposed 26 day period of meteorological phenomena. Terrestrial Magnetism 3(1): 13–41. Schuster A (1898) On the investigation of hidden periodicities with application to a supposed 26 day period of meteorological phenomena. Terrestrial Magnetism 3(1): 13–41.
go back to reference Schuster A (1906) On the periodicities of sunspots. Philosophical Transactions of the Royal Society of London, Series A 206: 69–100. Schuster A (1906) On the periodicities of sunspots. Philosophical Transactions of the Royal Society of London, Series A 206: 69–100.
go back to reference Schwarzacher W (1964) An application of statistical time-series analysis of a limestone–shale sequence. Journal of Geology 72(2): 195–213. Schwarzacher W (1964) An application of statistical time-series analysis of a limestone–shale sequence. Journal of Geology 72(2): 195–213.
go back to reference Schwarzacher W (1975) Sedimentation Models and Quantitative Stratigraphy. Elsevier, Amsterdam, 382 pp. Schwarzacher W (1975) Sedimentation Models and Quantitative Stratigraphy. Elsevier, Amsterdam, 382 pp.
go back to reference Schwarzacher W (1991) Milankovitch cycles and the measurement of time. In: Einsele G, Ricken W, Seilacher A (Eds) Cycles and Events in Stratigraphy. Springer, Berlin, pp 855–863. Schwarzacher W (1991) Milankovitch cycles and the measurement of time. In: Einsele G, Ricken W, Seilacher A (Eds) Cycles and Events in Stratigraphy. Springer, Berlin, pp 855–863.
go back to reference Schwarzacher W (1993) Cyclostratigraphy and the Milankovitch Theory. Elsevier, Amsterdam, 225 pp. Schwarzacher W (1993) Cyclostratigraphy and the Milankovitch Theory. Elsevier, Amsterdam, 225 pp.
go back to reference Schwarzacher W (1994) Searching for long cycles in short sections. Mathematical Geology 26(7): 759–768. Schwarzacher W (1994) Searching for long cycles in short sections. Mathematical Geology 26(7): 759–768.
go back to reference Shapiro HS, Silverman RA (1960) Alias-free sampling of random noise. Journal of the Society for Industrial and Applied Mathematics 8(2): 225–248. Shapiro HS, Silverman RA (1960) Alias-free sampling of random noise. Journal of the Society for Industrial and Applied Mathematics 8(2): 225–248.
go back to reference Siegel AF (1980) Testing for periodicity in a time series. Journal of the American Statistical Association 75(370): 345–348. Siegel AF (1980) Testing for periodicity in a time series. Journal of the American Statistical Association 75(370): 345–348.
go back to reference Silverman BW (1999) Wavelets in statistics: Beyond the standard assumptions. Philosophical Transactions of the Royal Society of London, Series A 357(1760): 2459–2473. Silverman BW (1999) Wavelets in statistics: Beyond the standard assumptions. Philosophical Transactions of the Royal Society of London, Series A 357(1760): 2459–2473.
go back to reference Slepian D (1978) Prolate spheroidal wave functions, Fourier analysis, and uncertainty–-V: The discrete case. Bell System Technical Journal 57(5): 1371–1430. Slepian D (1978) Prolate spheroidal wave functions, Fourier analysis, and uncertainty–-V: The discrete case. Bell System Technical Journal 57(5): 1371–1430.
go back to reference Solanki SK, Usoskin IG, Kromer B, Schüssler M, Beer J (2004) Unusual activity of the Sun during recent decades compared to the previous 11,000 years. Nature 431(7012): 1084–1087. Solanki SK, Usoskin IG, Kromer B, Schüssler M, Beer J (2004) Unusual activity of the Sun during recent decades compared to the previous 11,000 years. Nature 431(7012): 1084–1087.
go back to reference Stine RA (1997) Nonlinear time series. In: Kotz S, Read CB, Banks DL (Eds) Encyclopedia of statistical sciences, volume U1. Wiley, New York, pp 430–437. Stine RA (1997) Nonlinear time series. In: Kotz S, Read CB, Banks DL (Eds) Encyclopedia of statistical sciences, volume U1. Wiley, New York, pp 430–437.
go back to reference Stuiver M, Braziunas TF (1993) Sun, ocean, climate and atmospheric 14CO2: An evaluation of causal and spectral relationships. The Holocene 3(4): 289–305. Stuiver M, Braziunas TF (1993) Sun, ocean, climate and atmospheric 14CO2: An evaluation of causal and spectral relationships. The Holocene 3(4): 289–305.
go back to reference Subba Rao T, Gabr MM (1984) An Introduction to Bispectral Analysis and Bilinear Time Series Models. Springer, New York, 280 pp. Subba Rao T, Gabr MM (1984) An Introduction to Bispectral Analysis and Bilinear Time Series Models. Springer, New York, 280 pp.
go back to reference Suess HE (1965) Secular variations of the cosmic-ray-produced carbon 14 in the atmosphere and their interpretations. Journal of Geophysical Research 70(23): 5937–5952. Suess HE (1965) Secular variations of the cosmic-ray-produced carbon 14 in the atmosphere and their interpretations. Journal of Geophysical Research 70(23): 5937–5952.
go back to reference Sweldens W, Schröder P (2000) Building your own wavelets at home. In: Klees R, Haagmans R (Eds) Wavelets in the Geosciences. Springer, Berlin, pp 72–130. Sweldens W, Schröder P (2000) Building your own wavelets at home. In: Klees R, Haagmans R (Eds) Wavelets in the Geosciences. Springer, Berlin, pp 72–130.
go back to reference Theiler J, Eubank S, Longtin A, Galdrikian B, Farmer JD (1992) Testing for nonlinearity in time series: The method of surrogate data. Physica D 58(1–4): 77–94. Theiler J, Eubank S, Longtin A, Galdrikian B, Farmer JD (1992) Testing for nonlinearity in time series: The method of surrogate data. Physica D 58(1–4): 77–94.
go back to reference Thomson DJ (1982) Spectrum estimation and harmonic analysis. Proceedings of the IEEE 70(9): 1055–1096. Thomson DJ (1982) Spectrum estimation and harmonic analysis. Proceedings of the IEEE 70(9): 1055–1096.
go back to reference Thomson DJ (1990a) Quadratic-inverse spectrum estimates: Applications to palaeoclimatology. Philosophical Transactions of the Royal Society of London, Series A 332(1627): 539–597. Thomson DJ (1990a) Quadratic-inverse spectrum estimates: Applications to palaeoclimatology. Philosophical Transactions of the Royal Society of London, Series A 332(1627): 539–597.
go back to reference Thomson DJ (1990b) Time series analysis of Holocene climate data. Philosophical Transactions of the Royal Society of London, Series A 330(1615): 601–616. Thomson DJ (1990b) Time series analysis of Holocene climate data. Philosophical Transactions of the Royal Society of London, Series A 330(1615): 601–616.
go back to reference Thomson DJ (1997) Dependence of global temperatures on atmospheric CO2 and solar irradiance. Proceedings of the National Academy of Sciences of the United States of America 94(16): 8370–8377. Thomson DJ (1997) Dependence of global temperatures on atmospheric CO2 and solar irradiance. Proceedings of the National Academy of Sciences of the United States of America 94(16): 8370–8377.
go back to reference Thomson DJ, Chave AD (1991) Jackknifed error estimates for spectra, coherences, and transfer functions. In: Haykin S (Ed) Advances in Spectrum Analysis and Array Processing, volume 1. Prentice-Hall, Englewood Cliffs, NJ, pp 58–113. Thomson DJ, Chave AD (1991) Jackknifed error estimates for spectra, coherences, and transfer functions. In: Haykin S (Ed) Advances in Spectrum Analysis and Array Processing, volume 1. Prentice-Hall, Englewood Cliffs, NJ, pp 58–113.
go back to reference Thomson PJ, Robinson PM (1996) Estimation of second-order properties from jittered time series. Annals of the Institute of Statistical Mathematics 48(1): 29–48. Thomson PJ, Robinson PM (1996) Estimation of second-order properties from jittered time series. Annals of the Institute of Statistical Mathematics 48(1): 29–48.
go back to reference Urban FE, Cole JE, Overpeck JT (2000) Influence of mean climate change on climate variability from a 155-year tropical Pacific coral record. Nature 407(6807): 989–993. Urban FE, Cole JE, Overpeck JT (2000) Influence of mean climate change on climate variability from a 155-year tropical Pacific coral record. Nature 407(6807): 989–993.
go back to reference VanDongen HPA, Olofsen E, VanHartevelt JH, Kruyt EW (1997) Periodogram analysis of unequally spaced data: The Lomb method. Leiden University, Leiden, 66 pp. [ISBN 9080385115] VanDongen HPA, Olofsen E, VanHartevelt JH, Kruyt EW (1997) Periodogram analysis of unequally spaced data: The Lomb method. Leiden University, Leiden, 66 pp. [ISBN 9080385115]
go back to reference Van Dongen HPA, Olofsen E, VanHartevelt JH, Kruyt EW (1999) A procedure of multiple period searching in unequally spaced time-series with the Lomb–Scargle method. Biological Rhythm Research 30(2): 149–177. Van Dongen HPA, Olofsen E, VanHartevelt JH, Kruyt EW (1999) A procedure of multiple period searching in unequally spaced time-series with the Lomb–Scargle method. Biological Rhythm Research 30(2): 149–177.
go back to reference Vidakovic B (1999) Statistical Modeling by Wavelets. Wiley, New York, 382 pp. Vidakovic B (1999) Statistical Modeling by Wavelets. Wiley, New York, 382 pp.
go back to reference Walden AT (1992) Asymptotic percentage points for Siegel’s test statistic for compound periodicities. Biometrika 79(2): 438–440. Walden AT (1992) Asymptotic percentage points for Siegel’s test statistic for compound periodicities. Biometrika 79(2): 438–440.
go back to reference Walker GT (1914) Correlation in seasonal variations of weather, III. On the criterion for the reality of relationships or periodicities. Memoirs of the Indian Meteorological Department 21(9): 13–15. Walker GT (1914) Correlation in seasonal variations of weather, III. On the criterion for the reality of relationships or periodicities. Memoirs of the Indian Meteorological Department 21(9): 13–15.
go back to reference Wanner H, Beer J, Bütikofer J, Crowley TJ, Cubasch U, Flückiger J, Goosse H, Grosjean M, Joos F, Kaplan JO, Küttel M, Müller SA, Prentice IC, Solomina O, Stocker TF, Tarasov P, Wagner M, Widmann M (2008) Mid- to late Holocene climate change: An overview. Quaternary Science Reviews 27(19–20): 1791–1828. Wanner H, Beer J, Bütikofer J, Crowley TJ, Cubasch U, Flückiger J, Goosse H, Grosjean M, Joos F, Kaplan JO, Küttel M, Müller SA, Prentice IC, Solomina O, Stocker TF, Tarasov P, Wagner M, Widmann M (2008) Mid- to late Holocene climate change: An overview. Quaternary Science Reviews 27(19–20): 1791–1828.
go back to reference Weedon GP (2003) Time-Series Analysis and Cyclostratigraphy. Cambridge University Press, Cambridge, 259 pp. Weedon GP (2003) Time-Series Analysis and Cyclostratigraphy. Cambridge University Press, Cambridge, 259 pp.
go back to reference Welch PD (1967) The use of Fast Fourier Transform for the estimation of power spectra: A method based on time averaging over short, modified periodograms. IEEE Transactions on Audio and Electroacoustics 15(2): 70–73. Welch PD (1967) The use of Fast Fourier Transform for the estimation of power spectra: A method based on time averaging over short, modified periodograms. IEEE Transactions on Audio and Electroacoustics 15(2): 70–73.
go back to reference Whittle P (1952) The simultaneous estimation of a time series harmonic components and covariance structure. Trabajos de Estadística 3(1–2): 43–57. Whittle P (1952) The simultaneous estimation of a time series harmonic components and covariance structure. Trabajos de Estadística 3(1–2): 43–57.
go back to reference Willson RC, Hudson HS (1988) Solar luminosity variations in solar cycle 21. Nature 332(6167): 810–812. Willson RC, Hudson HS (1988) Solar luminosity variations in solar cycle 21. Nature 332(6167): 810–812.
go back to reference Witt A, Schumann AY (2005) Holocene climate variability on millennial scales recorded in Greenland ice cores. Nonlinear Processes in Geophysics 12(3): 345–352. Witt A, Schumann AY (2005) Holocene climate variability on millennial scales recorded in Greenland ice cores. Nonlinear Processes in Geophysics 12(3): 345–352.
go back to reference Woods TN, Lean J (2007) Anticipating the next decade of Sun–Earth system variations. Eos, Transactions of the American Geophysical Union 88(44): 457–458. Woods TN, Lean J (2007) Anticipating the next decade of Sun–Earth system variations. Eos, Transactions of the American Geophysical Union 88(44): 457–458.
go back to reference Wunsch C (2000) On sharp spectral lines in the climate record and the millennial peak. Paleoceanography 15(4): 417–424. Wunsch C (2000) On sharp spectral lines in the climate record and the millennial peak. Paleoceanography 15(4): 417–424.
go back to reference Wunsch C (2001) Reply. Paleoceanography 16(5): 548. Wunsch C (2001) Reply. Paleoceanography 16(5): 548.
go back to reference Wunsch C, Gunn DE (2003) A densely sampled core and climate variable aliasing. Geo-Marine Letters 23(1): 64–71. Wunsch C, Gunn DE (2003) A densely sampled core and climate variable aliasing. Geo-Marine Letters 23(1): 64–71.
go back to reference Zalasiewicz J, Williams M, Smith A, Barry TL, Coe AL, Brown PR, Brenchley P, Cantrill D, Gale A, Gibbard P, Gregory FJ, Hounslow MW, Kerr AC, Pearson P, Knox R, Powell J, Waters C, Marshall J, Oates M, Rawson P, Stone P (2008) Are we now living in the Anthropocene? GSA Today 18(2): 4–8. Zalasiewicz J, Williams M, Smith A, Barry TL, Coe AL, Brown PR, Brenchley P, Cantrill D, Gale A, Gibbard P, Gregory FJ, Hounslow MW, Kerr AC, Pearson P, Knox R, Powell J, Waters C, Marshall J, Oates M, Rawson P, Stone P (2008) Are we now living in the Anthropocene? GSA Today 18(2): 4–8.
go back to reference Kodera K (2004) Solar influence on the Indian Ocean monsoon through dynamical processes. Geophysical Research Letters 31(24): L24209. [doi:10.1029/2004GL020928] Kodera K (2004) Solar influence on the Indian Ocean monsoon through dynamical processes. Geophysical Research Letters 31(24): L24209. [doi:10.1029/2004GL020928]
go back to reference Brillinger DR (2002) John W. Tukey’s work on time series and spectrum analysis. The Annals of Statistics 30(6): 1595–1618. Brillinger DR (2002) John W. Tukey’s work on time series and spectrum analysis. The Annals of Statistics 30(6): 1595–1618.
go back to reference Rahmstorf S (2003) Timing of abrupt climate change: A precise clock. Geophysical Research Letters 30(10): 1510. [doi:10.1029/2003GL017115] Rahmstorf S (2003) Timing of abrupt climate change: A precise clock. Geophysical Research Letters 30(10): 1510. [doi:10.1029/2003GL017115]
go back to reference McMillan DG, Constable CG, Parker RL (2002) Limitations on stratigraphic analyses due to incomplete age control and their relevance to sedimentary paleomagnetism. Earth and Planetary Science Letters 201(3–4): 509–523. McMillan DG, Constable CG, Parker RL (2002) Limitations on stratigraphic analyses due to incomplete age control and their relevance to sedimentary paleomagnetism. Earth and Planetary Science Letters 201(3–4): 509–523.
go back to reference Schulz M, Paul A (2002) Holocene climate variability on centennial-to-millennial time scales: 1. Climate records from the North-Atlantic realm. In: Wefer G, Berger W, Behre K-E, Jansen E (Eds) Climate Development and History of the North Atlantic Realm. Springer, Berlin, pp 41–54. Schulz M, Paul A (2002) Holocene climate variability on centennial-to-millennial time scales: 1. Climate records from the North-Atlantic realm. In: Wefer G, Berger W, Behre K-E, Jansen E (Eds) Climate Development and History of the North Atlantic Realm. Springer, Berlin, pp 41–54.
go back to reference Trauth MH (2007) MATLAB ® Recipes for Earth Sciences. Second edition. Springer, Berlin, 288 pp. Trauth MH (2007) MATLAB ® Recipes for Earth Sciences. Second edition. Springer, Berlin, 288 pp.
Metadata
Title
Spectral Analysis
Author
Dr. Manfred Mudelsee
Copyright Year
2010
Publisher
Springer Netherlands
DOI
https://doi.org/10.1007/978-90-481-9482-7_5