{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,6]],"date-time":"2026-04-06T10:18:05Z","timestamp":1775470685421,"version":"3.50.1"},"reference-count":48,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2011,7,2]],"date-time":"2011-07-02T00:00:00Z","timestamp":1309564800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Stat Comput"],"published-print":{"date-parts":[[2012,7]]},"DOI":"10.1007\/s11222-011-9256-x","type":"journal-article","created":{"date-parts":[[2011,7,1]],"date-time":"2011-07-01T14:58:07Z","timestamp":1309532287000},"page":"877-895","source":"Crossref","is-referenced-by-count":26,"title":["Spectral estimation for locally stationary time series with missing observations"],"prefix":"10.1007","volume":"22","author":[{"given":"Marina I.","family":"Knight","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Matthew A.","family":"Nunes","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Guy P.","family":"Nason","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2011,7,2]]},"reference":[{"key":"9256_CR1","doi-asserted-by":"crossref","first-page":"2362","DOI":"10.1175\/1520-0469(1978)035<2362:LTVODI>2.0.CO;2","volume":"35","author":"A.L. Berger","year":"1978","unstructured":"Berger, A.L.: Long-term variations of daily insolation and quaternary climatic changes. J. Atmos. Sci. 35, 2362\u20132367 (1978)","journal-title":"J. Atmos. Sci."},{"issue":"6","key":"9256_CR2","doi-asserted-by":"crossref","first-page":"1289","DOI":"10.1109\/TIM.2002.808031","volume":"51","author":"R. Bos","year":"2002","unstructured":"Bos, R., de Waele, S., Broersen, P.M.T.: Autoregressive spectral estimation by application of the Burg algorithm to irregularly sampled data. IEEE Trans. Instrum. Meas. 51(6), 1289\u20131294 (2002)","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"9256_CR3","volume-title":"Time Series: Theory and Methods","author":"P.J. Brockwell","year":"2009","unstructured":"Brockwell, P.J., Davis, R.A.: Time Series: Theory and Methods, 2nd edn. Springer, Berlin (2009)","edition":"2"},{"issue":"6","key":"9256_CR4","doi-asserted-by":"crossref","first-page":"754","DOI":"10.1016\/j.dsp.2006.01.001","volume":"16","author":"P.M.T. Broersen","year":"2006","unstructured":"Broersen, P.M.T.: Automatic spectral analysis with missing data. Digit. Signal Process. 16(6), 754\u2013766 (2006)","journal-title":"Digit. Signal Process."},{"issue":"1","key":"9256_CR5","volume":"19","author":"P.M.T. Broersen","year":"2008","unstructured":"Broersen, P.M.T.: Time series models for spectral analysis of irregular data far beyond the mean data rate. Meas. Sci. Technol. 19(1), 015103 (2008). http:\/\/stacks.iop.org\/0957-0233\/19\/i=1\/a=015103","journal-title":"Meas. Sci. Technol."},{"issue":"9","key":"9256_CR6","doi-asserted-by":"crossref","first-page":"1495","DOI":"10.1016\/j.automatica.2004.04.011","volume":"40","author":"P.M.T. Broersen","year":"2004","unstructured":"Broersen, P.M.T., de Waele, S., Bos, R.: Autoregressive spectral analysis when observations are missing. Automatica 40(9), 1495\u20131504 (2004)","journal-title":"Automatica"},{"issue":"15","key":"9256_CR7","doi-asserted-by":"crossref","first-page":"625","DOI":"10.1098\/rsif.2007.0212","volume":"4","author":"B. Cazelles","year":"2007","unstructured":"Cazelles, B., Chavez, M., Magny, G.C., Gu\u00e9gan, J., Hales, S.: Time-dependent spectral analysis of epidemiological time-series with wavelets. J. R. Soc. Interface 4(15), 625\u2013636 (2007)","journal-title":"J. R. Soc. Interface"},{"key":"9256_CR8","volume-title":"The Analysis of Time Series: An Introduction","author":"C. Chatfield","year":"2004","unstructured":"Chatfield, C.: The Analysis of Time Series: An Introduction. Chapman & Hall\/CRC Press, London\/Boca Raton (2004)"},{"issue":"4","key":"9256_CR9","doi-asserted-by":"crossref","first-page":"736","DOI":"10.1214\/aos\/1176343545","volume":"4","author":"W. Clinger","year":"1976","unstructured":"Clinger, W., Van Ness, J.W.: On unequally spaced time points in time series. Ann. Stat. 4(4), 736\u2013745 (1976)","journal-title":"Ann. Stat."},{"issue":"9","key":"9256_CR10","doi-asserted-by":"crossref","first-page":"988","DOI":"10.1109\/TBME.2002.802015","volume":"49","author":"S.D. Cranstoun","year":"2002","unstructured":"Cranstoun, S.D., Ombao, H.C., von Sachs, R., Guo, W., Litt, B.: Time-frequency spectral estimation of multichannel EEG using the Auto-SLEX method. IEEE Trans. Biomed. Eng. 49(9), 988\u2013996 (2002)","journal-title":"IEEE Trans. Biomed. Eng."},{"issue":"7218","key":"9256_CR11","doi-asserted-by":"crossref","first-page":"47","DOI":"10.1038\/456047a","volume":"456","author":"M. Crucifix","year":"2008","unstructured":"Crucifix, M.: Global change: climate\u2019s astronomical sensors. Nature 456(7218), 47\u201348 (2008)","journal-title":"Nature"},{"issue":"1","key":"9256_CR12","first-page":"11","volume":"174","author":"M. Crucifix","year":"2009","unstructured":"Crucifix, M., Rougier, J.: On the use of simple dynamical systems for climate predictions. Euro Phys. J. 174(1), 11\u201331 (2009)","journal-title":"Euro Phys. J."},{"key":"9256_CR13","series-title":"Space Sciences Series of ISSI","doi-asserted-by":"crossref","first-page":"213","DOI":"10.1007\/978-0-387-48341-2_17","volume-title":"Solar Variability and Planetary Climates","author":"M. Crucifix","year":"2007","unstructured":"Crucifix, M., Loutre, M.F., Berger, A.: The climate response to the astronomical forcing. In: Calisesi, Y., Bonnet, R.M., Gray, L., Langen, J., Lockwood, M. (eds.) Solar Variability and Planetary Climates. Space Sciences Series of ISSI, vol. 23, pp. 213\u2013226. Springer, New York (2007)"},{"issue":"1","key":"9256_CR14","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1214\/aos\/1034276620","volume":"25","author":"R. Dahlhaus","year":"1997","unstructured":"Dahlhaus, R.: Fitting time series models to nonstationary processes. Ann. Stat. 25(1), 1\u201337 (1997)","journal-title":"Ann. Stat."},{"issue":"3","key":"9256_CR15","doi-asserted-by":"crossref","first-page":"1075","DOI":"10.1214\/009053606000000227","volume":"34","author":"R. Dahlhaus","year":"2006","unstructured":"Dahlhaus, R., Subba Rao, S.: Statistical inference for time-varying ARCH processes. Ann. Stat. 34(3), 1075\u20131114 (2006)","journal-title":"Ann. Stat."},{"issue":"2","key":"9256_CR16","doi-asserted-by":"crossref","first-page":"389","DOI":"10.3150\/07-BEJ5009","volume":"13","author":"R. Dahlhaus","year":"2007","unstructured":"Dahlhaus, R., Subba Rao, S.: A recursive online algorithm for the estimation of time-varying ARCH parameters. Bernoulli 13(2), 389\u2013422 (2007)","journal-title":"Bernoulli"},{"issue":"20","key":"9256_CR17","doi-asserted-by":"crossref","first-page":"7030","DOI":"10.1021\/es0700247","volume":"41","author":"S. Dilmaghani","year":"2007","unstructured":"Dilmaghani, S., Henry, I.C., Soonthornnonda, P., Christensen, E.R., Henry, R.C.: Harmonic analysis of environmental time series with missing data or irregular sample spacing. Environ. Sci. Technol. 41(20), 7030\u20137038 (2007)","journal-title":"Environ. Sci. Technol."},{"issue":"1","key":"9256_CR18","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1111\/1468-0262.00091","volume":"68","author":"R.F. Engle","year":"2000","unstructured":"Engle, R.F.: The econometrics of ultra-high-frequency data. Econometrica 68(1), 1\u201322 (2000)","journal-title":"Econometrica"},{"key":"9256_CR19","unstructured":"Fry\u017alewicz, P.: Wavelet techniques for time series and Poisson data. Ph.D. thesis, University of Bristol, UK (2003)"},{"key":"9256_CR20","doi-asserted-by":"crossref","first-page":"611","DOI":"10.1111\/j.1467-9868.2006.00558.x","volume":"68","author":"P. Fry\u017alewicz","year":"2006","unstructured":"Fry\u017alewicz, P., Nason, G.P.: Haar-Fisz estimation of evolutionary wavelet spectra. J. R. Stat. Soc. B 68, 611\u2013634 (2006)","journal-title":"J. R. Stat. Soc. B"},{"issue":"3","key":"9256_CR21","doi-asserted-by":"crossref","first-page":"687","DOI":"10.1093\/biomet\/93.3.687","volume":"93","author":"P. Fry\u017alewicz","year":"2006","unstructured":"Fry\u017alewicz, P., Sapatinas, T., Rao, S.: A Haar-Fisz technique for locally stationary volatility estimation. Biometrika 93(3), 687 (2006)","journal-title":"Biometrika"},{"issue":"4","key":"9256_CR22","doi-asserted-by":"crossref","first-page":"2115","DOI":"10.1214\/aos\/1176325774","volume":"22","author":"P. Hall","year":"1994","unstructured":"Hall, P., Fisher, N.I., Hoffmann, B.: On the nonparametric estimation of covariance functions. Ann. Stat. 22(4), 2115\u20132134 (1994)","journal-title":"Ann. Stat."},{"key":"9256_CR23","series-title":"SPIE","doi-asserted-by":"crossref","first-page":"87","DOI":"10.1117\/12.449738","volume-title":"Wavelet Applications in Signal and Image Processing IX","author":"M. Jansen","year":"2001","unstructured":"Jansen, M., Nason, G.P., Silverman, B.W.: Scattered data smoothing by empirical Bayesian shrinkage of second generation wavelet coefficients. In: Unser, M., Aldroubi, A. (eds.) Wavelet Applications in Signal and Image Processing IX. SPIE, vol. 4478, pp. 87\u201397 (2001)"},{"key":"9256_CR24","unstructured":"Jansen, M., Nason, G.P., Silverman, B.W.: Multidimensional nonparametric regression using lifting. Tech. Rep. 04:17, Statistics Group, Department of Mathematics, University of Bristol, UK (2004)"},{"issue":"1","key":"9256_CR25","doi-asserted-by":"crossref","first-page":"97","DOI":"10.1111\/j.1467-9868.2008.00672.x","volume":"71","author":"M. Jansen","year":"2009","unstructured":"Jansen, M., Nason, G.P., Silverman, B.W.: Multiscale methods for data on graphs and irregular multidimensional situations. J. R. Stat. B 71(1), 97\u2013125 (2009)","journal-title":"J. R. Stat. B"},{"issue":"2","key":"9256_CR26","doi-asserted-by":"crossref","first-page":"455","DOI":"10.1214\/aoms\/1177704572","volume":"33","author":"R.H. Jones","year":"1962","unstructured":"Jones, R.H.: Spectral analysis with regularly missed observations. Ann. Math. Stat. 33(2), 455\u2013461 (1962)","journal-title":"Ann. Math. Stat."},{"key":"9256_CR27","doi-asserted-by":"crossref","first-page":"115","DOI":"10.1137\/050623863","volume":"5","author":"M.I. Knight","year":"2006","unstructured":"Knight, M.I., Nason, G.P.: Improving prediction of hydrophobic segments along a transmembrane protein sequence using adaptive multiscale lifting. SIAM J. Multiscale Model. Simul. 5, 115\u2013129 (2006)","journal-title":"SIAM J. Multiscale Model. Simul."},{"issue":"1","key":"9256_CR28","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s11222-008-9062-2","volume":"19","author":"M.I. Knight","year":"2009","unstructured":"Knight, M.I., Nason, G.P.: A nondecimated lifting transform. Stat. Comput. 19(1), 1\u201316 (2009)","journal-title":"Stat. Comput."},{"key":"9256_CR29","doi-asserted-by":"crossref","unstructured":"Knight, M.I., Nunes, M.A.: nlt: a nondecimated lifting scheme algorithm. R package version 2.1-1 (2010)","DOI":"10.1007\/s11222-008-9062-2"},{"issue":"7193","key":"9256_CR30","doi-asserted-by":"crossref","first-page":"379","DOI":"10.1038\/nature06949","volume":"453","author":"D. L\u00fcthi","year":"2008","unstructured":"L\u00fcthi, D., Le Floch, M., Bereiter, B., Blunier, T., Barnola, J.M., Siegenthaler, U., Raynaud, D., Jouzel, J., Fischer, H., Kawamura, K., et al.: High-resolution carbon dioxide concentration record 650,000\u2013800,000 years before present. Nature 453(7193), 379\u2013382 (2008)","journal-title":"Nature"},{"issue":"1","key":"9256_CR31","doi-asserted-by":"crossref","first-page":"378","DOI":"10.1162\/003465304323023886","volume":"86","author":"T. Mikosch","year":"2004","unstructured":"Mikosch, T., Starica, C.: Nonstationarities in financial time series, the long-range dependence, and the IGARCH effects. Rev. Econ. Stat. 86(1), 378\u2013390 (2004)","journal-title":"Rev. Econ. Stat."},{"issue":"5","key":"9256_CR32","doi-asserted-by":"crossref","first-page":"943","DOI":"10.1007\/s10463-008-0195-z","volume":"62","author":"D. Mondal","year":"2010","unstructured":"Mondal, D., Percival, D.B.: Wavelet variance analysis for gappy time series. Ann. Inst. Stat. Math. 62(5), 943\u2013966 (2010)","journal-title":"Ann. Inst. Stat. Math."},{"key":"9256_CR33","doi-asserted-by":"crossref","DOI":"10.1007\/978-0-387-75961-6","volume-title":"Wavelet Methods in Statistics with R","author":"G.P. Nason","year":"2008","unstructured":"Nason, G.P.: Wavelet Methods in Statistics with R. Springer, Berlin (2008)"},{"issue":"1760","key":"9256_CR34","doi-asserted-by":"crossref","first-page":"2511","DOI":"10.1098\/rsta.1999.0445","volume":"357","author":"G.P. Nason","year":"1999","unstructured":"Nason, G.P., Von Sachs, R.: Wavelets in time-series analysis. Philos. Trans. R. Soc. Lond. A 357(1760), 2511\u20132526 (1999)","journal-title":"Philos. Trans. R. Soc. Lond. A"},{"issue":"2","key":"9256_CR35","doi-asserted-by":"crossref","first-page":"271","DOI":"10.1111\/1467-9868.00231","volume":"62","author":"G.P. Nason","year":"2000","unstructured":"Nason, G.P., Von Sachs, R., Kroisandt, G.: Wavelet processes and adaptive estimation of the evolutionary wavelet spectrum. J. R. Stat. Soc. B 62(2), 271\u2013292 (2000)","journal-title":"J. R. Stat. Soc. B"},{"issue":"2","key":"9256_CR36","first-page":"199","volume":"63","author":"G.P. Nason","year":"2001","unstructured":"Nason, G.P., Sapatinas, T., Sawczenko, A.: Wavelet packet modelling of infant sleep state using heart rate data. Sankhy\u0101 B 63(2), 199\u2013217 (2001)","journal-title":"Sankhy\u0101 B"},{"key":"9256_CR37","unstructured":"Nason, G.P., Kovac, A., Maechler, M.: Wavethresh: Software to perform wavelet statistics and transforms. R package version 4.2-1 (2008)"},{"key":"9256_CR38","unstructured":"Nunes, M.A., Knight, M.I.: Adlift: an adaptive lifting scheme algorithm. R package version 1.2-3"},{"issue":"2","key":"9256_CR39","doi-asserted-by":"crossref","first-page":"143","DOI":"10.1007\/s11222-006-6560-y","volume":"16","author":"M.A. Nunes","year":"2006","unstructured":"Nunes, M.A., Knight, M.I., Nason, G.P.: Adaptive lifting for nonparametric regression. Stat. Comput. 16(2), 143\u2013159 (2006)","journal-title":"Stat. Comput."},{"issue":"1","key":"9256_CR40","doi-asserted-by":"crossref","first-page":"171","DOI":"10.1023\/A:1016130108440","volume":"54","author":"H. Ombao","year":"2002","unstructured":"Ombao, H., Raz, J., Von Sachs, R., Guo, W.: The SLEX model of a non-stationary random process. Ann. Inst. Stat. Math. 54(1), 171\u2013200 (2002)","journal-title":"Ann. Inst. Stat. Math."},{"key":"9256_CR41","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511841040","volume-title":"Wavelet Methods for Time Series Analysis","author":"D.B. Percival","year":"2000","unstructured":"Percival, D.B., Walden, A.T.: Wavelet Methods for Time Series Analysis. Cambridge University Press, Cambridge (2000)"},{"key":"9256_CR42","volume-title":"Spectral Analysis and Time Series","author":"M.B. Priestley","year":"1981","unstructured":"Priestley, M.B.: Spectral Analysis and Time Series. Academic Press, San Diego (1981)"},{"key":"9256_CR43","unstructured":"Sanderson, J.: Wavelet methods for time series with bivariate observations and irregular sampling grids. Ph.D. thesis, University of Bristol, UK (2010)"},{"issue":"6","key":"9256_CR44","doi-asserted-by":"crossref","first-page":"712","DOI":"10.1016\/j.dsp.2006.08.012","volume":"16","author":"P. Stoica","year":"2006","unstructured":"Stoica, P., Sandgren, N.: Spectral analysis of irregularly-sampled data: Paralleling the regularly-sampled data approaches. Digit. Signal Process. 16(6), 712\u2013734 (2006)","journal-title":"Digit. Signal Process."},{"key":"9256_CR45","series-title":"Proc. SPIE","doi-asserted-by":"crossref","first-page":"68","DOI":"10.1117\/12.217619","volume-title":"Wavelet Applications in Signal and Image Processing III","author":"W. Sweldens","year":"1995","unstructured":"Sweldens, W.: The lifting scheme: a new philosophy in biorthogonal wavelet construction. In: Laine, A., Unser, M. (eds.) Wavelet Applications in Signal and Image Processing III. Proc. SPIE, vol. 2569, pp. 68\u201379 (1995)"},{"key":"9256_CR46","doi-asserted-by":"crossref","first-page":"1879","DOI":"10.1214\/07-AOS524","volume":"36","author":"S. Bellegem Van","year":"2008","unstructured":"Van Bellegem, S., Von Sachs, R.: Locally adaptive estimation of evolutionary wavelet spectra. Ann. Stat. 36, 1879\u20131924 (2008)","journal-title":"Ann. Stat."},{"issue":"3","key":"9256_CR47","doi-asserted-by":"crossref","first-page":"345","DOI":"10.5194\/npg-12-345-2005","volume":"12","author":"A. Witt","year":"2005","unstructured":"Witt, A., Schumann, A.Y.: Holocene climate variability on millennial scales recorded in Greenland ice cores. Nonlinear Process. Geophys. 12(3), 345\u2013352 (2005)","journal-title":"Nonlinear Process. Geophys."},{"issue":"04","key":"9256_CR48","doi-asserted-by":"crossref","first-page":"487","DOI":"10.1017\/S0954102005002919","volume":"17","author":"E.W. Wolff","year":"2005","unstructured":"Wolff, E.W.: Understanding the past-climate history from Antarctica. Antarct. Sci. 17(04), 487\u2013495 (2005)","journal-title":"Antarct. Sci."}],"container-title":["Statistics and Computing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11222-011-9256-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11222-011-9256-x\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11222-011-9256-x","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,6,12]],"date-time":"2019-06-12T16:39:17Z","timestamp":1560357557000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11222-011-9256-x"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,7,2]]},"references-count":48,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2012,7]]}},"alternative-id":["9256"],"URL":"https:\/\/doi.org\/10.1007\/s11222-011-9256-x","relation":{},"ISSN":["0960-3174","1573-1375"],"issn-type":[{"value":"0960-3174","type":"print"},{"value":"1573-1375","type":"electronic"}],"subject":[],"published":{"date-parts":[[2011,7,2]]}}}