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A practical software package for estimating the periodicities in time series by least-squares spectral analysis

Yıl 2024, , 191 - 198, 28.07.2024
https://doi.org/10.26833/ijeg.1366950

Öz

The researchers investigate some phenomena by continuously observing physical variables, i.e., time series. Nowadays, the Least-Squares Spectral Analysis (LSSA) technique has been preferred for the analysis of time series to conduct more reliable analysis. This technique uses the least-squares principle to estimate the hidden periodicities in the time series. Based on the previous investigations, LSSA gives more reasonable results in the experimental time series that have disturbing effects such as the datum shifts, linear trend, unequally spaced data and etc. The LSSA method is a unique method that can overcome these problems without pre-processing the original series. However, a practical and user-friendly software package in C programming language is not available for scientific purposes to implement the LSSA method. In this paper, we review the computational scheme of the LSSA method, then a software (LSSASOFT) package in the C programming language is developed in the view of the simplicity of the method and compatibility of all types of data. Finally, LSSASOFT is applied in two sample studies for the determining hidden periods in the synthetic data and sea level observations. Consequently, the numerical results indicate that LSSASOFT is a useful tool that can efficiently predicting hidden periodicity for the experimental time series that have disturbing effects.

Teşekkür

The author cordially thanks to eng. Habibe Saraçoğlu for assistance with typesetting the manuscript and fruitful discussions during the compilation of the manuscript. The author is grateful to General Directorate of Mapping for providing the sea level data.

Kaynakça

  • Zeray Öztürk, E., & Abbak, R. A. (2020). PHCSOFT: A Software package for computing physical height changes from GRACE based global geopotential models. Earth Science Informatics, 13(4), 1499-1505. https://doi.org/10.1007/s12145-020-00490-5
  • Zeray Öztürk, E., Godah, W., & Abbak, R. A. (2020). Estimation of physical height changes from GRACE satellite mission data and WGHM over Turkey. Acta Geodaetica et Geophysica, 55(2), 301-317. https://doi.org/10.1007/s40328-020-00294-5
  • Beşel, C., & Kayıkçı, E. T. (2020). Investigation of Black Sea mean sea level variability by singular spectrum analysis. International Journal of Engineering and Geosciences, 5(1), 33-41. https://doi.org/10.26833/ijeg.580510
  • Erol, S. (2011). Time-frequency analyses of tide-gauge sensor data. Sensors, 11(4), 3939-3961. https://doi.org/10.3390/s110403939
  • Abbasi, M. (1999). Comparison of Fourier, least-squares and wavelet spectral analysis methods, tested on Persian Gulf tidal data. [Master's Thesis, KN Toosi University of Technology].
  • Craymer, M. R. (1998). The least squares spectrum, its inverse transform and autocorrelation function: theory and some applications in geodesy. [Doctoral Dissertation, University of Toronto].
  • Abbak, R. A., & Yerci, M. (2012). En küçük karelerle spektral analiz ve fourier tekniğinin karşılaştırılması. Selcuk University Journal of Engineering Sciences, 11(1), 32-47.
  • Ghaderpour, E., Ince, E. S., & Pagiatakis, S. D. (2018). Least-squares cross-wavelet analysis and its applications in geophysical time series. Journal of Geodesy, 92(10), 1223-1236. https://doi.org/10.1007/s00190-018-1156-9
  • Vaníček, P. (1969). Approximate spectral analysis by least-squares fit: Successive spectral analysis. Astrophysics and Space Science, 4, 387-391. https://doi.org/10.1007/BF00651344
  • Vaníček, P. (1971). Further development and properties of the spectral analysis by least-squares. Astrophysics and Space Science, 12, 10-33. https://doi.org/10.1007/BF00656134
  • Taylor, J., & Hamilton, S. (1972). Some tests of the Vaníček method of spectral analysis. Astrophysics and Space Science, 17, 357-367. https://doi.org/10.1007/BF00642907
  • Wells, D. E., Vaníček, P., & Pagiatakis, S. D. (1985). Least squares spectral analysis revisited. Technical Report 84, Geodesy and Geomatics Engineering, University of New Brunswick, Canada.
  • Espy, P. J., & Witt, G. (1996). Observation of a quasi 16‐day oscillation in the polar summer mesospheric temperature. Geophysical Research Letters, 23(10), 1071-1074. https://doi.org/10.1029/96GL01068
  • Mantegazza, L. (1997). High azimuthal number pulsation modes in fast rotating delta Scuti stars: the case of HD 101158= V837 Cen. Astronomy and Astrophysics, 323, 844-852.
  • Abd El-Gelil, M., Pagiatakis, S., & El-Rabbany, A. (2010). Normal mode detection and splitting after Sumatra–Andaman earthquake. Journal of Geodynamics, 50(2), 49-56. https://doi.org/10.1016/j.jog.2010.02.003
  • Abbasi, M., & Mashhadizadeh Maleki, S. (2017). Iranian surface air temperature periodicities and correlations with the North Atlantic and Indian Ocean Sea surface temperature variations. Meteorological Applications, 24(2), 268-275. https://doi.org/10.1002/met.1625
  • Ghaderpour, E., Liao, W., & Lamoureux, M. P. (2018). Antileakage least-squares spectral analysis for seismic data regularization and random noise attenuation. Geophysics, 83(3), V157-V170. https://doi.org/10.1190/geo2017-0284.1
  • Omerbashich, M. (2003). Earth-Model Discrimination Method. [Doctoral Dissertation, University of New Brunswick].
  • Amerian, Y., & Voosoghi, B. (2011). Least squares spectral analysis for detection of systematic behaviour of digital level compensator. Journal of Geodetic Science, 1(1), 35-40. https://doi.org/10.2478/v10156-010-0005-4
  • Vanicek, P. & Krakiwsky, E. (1987). Geodesy: The Concepts, 2. Elsevier Science Publishers B.V.
  • Pagiatakis, S. D. (1999). Stochastic significance of peaks in the least-squares spectrum. Journal of Geodesy, 73, 67-78. https://doi.org/10.1007/s001900050220
  • Abd El-Gelil, M., Pagiatakis, S., & El-Rabbany, A. (2008). Frequency-dependent atmospheric pressure admittance of superconducting gravimeter records using least squares response method. Physics of the Earth and Planetary Interiors, 170(1-2), 24-33. https://doi.org/10.1016/j.pepi.2008.06.031
  • Ainscow, B., Blackman, D., Kerrigde, J., Pugh, D., & Shaw, S. (1985). Manual on sea level measurement and interpretation, I.
  • Abbak, R. A. (2005). Deniz düzeyi gözlemlerinin en küçük kareler yöntemiyle spektral analizi. [Master’s Thesis, Selcuk University].
  • Maul, G. A., & Yanaway, A. (1978). Deep sea tides determination from GEOS-3. Collected Reprints, 78.
  • Stewart, R. H. (2004). Introduction to physical oceanography. Texas A&M University, USA.
  • Abbak, R. A. (2023). Least-Squares Spectral Analysis of Hourly Tide Gauge Data–A Case Study: LSSA of Hourly Tide-Gauge Data. Advanced Geomatics, 3(1), 23-27.
  • İl, H. T. A., Abbak, R. A., Bildirici, İ. Ö., & Demir, S. (2018). SRTM1 ve ASTER sayısal yükseklik modellerinin gravimetrik jeoit belirlemeye katkısı. Geomatik, 3(3), 203-212. https://doi.org/10.29128/geomatik.402331
  • Demir, S., Abbak, R. A., & İl, H. T. A. (2018). Global yerpotansiyel modellerin gravimetrik jeoit belirlemeye katkısı. Geomatik, 3(3), 213-224. https://doi.org/10.29128/geomatik.403776
  • Ghaderpour, E., & Pagiatakis, S. D. (2017). Least-squares wavelet analysis of unequally spaced and non-stationary time series and its applications. Mathematical Geosciences, 49, 819-844. https://doi.org/10.1007/s11004-017-9691-0
Yıl 2024, , 191 - 198, 28.07.2024
https://doi.org/10.26833/ijeg.1366950

Öz

Kaynakça

  • Zeray Öztürk, E., & Abbak, R. A. (2020). PHCSOFT: A Software package for computing physical height changes from GRACE based global geopotential models. Earth Science Informatics, 13(4), 1499-1505. https://doi.org/10.1007/s12145-020-00490-5
  • Zeray Öztürk, E., Godah, W., & Abbak, R. A. (2020). Estimation of physical height changes from GRACE satellite mission data and WGHM over Turkey. Acta Geodaetica et Geophysica, 55(2), 301-317. https://doi.org/10.1007/s40328-020-00294-5
  • Beşel, C., & Kayıkçı, E. T. (2020). Investigation of Black Sea mean sea level variability by singular spectrum analysis. International Journal of Engineering and Geosciences, 5(1), 33-41. https://doi.org/10.26833/ijeg.580510
  • Erol, S. (2011). Time-frequency analyses of tide-gauge sensor data. Sensors, 11(4), 3939-3961. https://doi.org/10.3390/s110403939
  • Abbasi, M. (1999). Comparison of Fourier, least-squares and wavelet spectral analysis methods, tested on Persian Gulf tidal data. [Master's Thesis, KN Toosi University of Technology].
  • Craymer, M. R. (1998). The least squares spectrum, its inverse transform and autocorrelation function: theory and some applications in geodesy. [Doctoral Dissertation, University of Toronto].
  • Abbak, R. A., & Yerci, M. (2012). En küçük karelerle spektral analiz ve fourier tekniğinin karşılaştırılması. Selcuk University Journal of Engineering Sciences, 11(1), 32-47.
  • Ghaderpour, E., Ince, E. S., & Pagiatakis, S. D. (2018). Least-squares cross-wavelet analysis and its applications in geophysical time series. Journal of Geodesy, 92(10), 1223-1236. https://doi.org/10.1007/s00190-018-1156-9
  • Vaníček, P. (1969). Approximate spectral analysis by least-squares fit: Successive spectral analysis. Astrophysics and Space Science, 4, 387-391. https://doi.org/10.1007/BF00651344
  • Vaníček, P. (1971). Further development and properties of the spectral analysis by least-squares. Astrophysics and Space Science, 12, 10-33. https://doi.org/10.1007/BF00656134
  • Taylor, J., & Hamilton, S. (1972). Some tests of the Vaníček method of spectral analysis. Astrophysics and Space Science, 17, 357-367. https://doi.org/10.1007/BF00642907
  • Wells, D. E., Vaníček, P., & Pagiatakis, S. D. (1985). Least squares spectral analysis revisited. Technical Report 84, Geodesy and Geomatics Engineering, University of New Brunswick, Canada.
  • Espy, P. J., & Witt, G. (1996). Observation of a quasi 16‐day oscillation in the polar summer mesospheric temperature. Geophysical Research Letters, 23(10), 1071-1074. https://doi.org/10.1029/96GL01068
  • Mantegazza, L. (1997). High azimuthal number pulsation modes in fast rotating delta Scuti stars: the case of HD 101158= V837 Cen. Astronomy and Astrophysics, 323, 844-852.
  • Abd El-Gelil, M., Pagiatakis, S., & El-Rabbany, A. (2010). Normal mode detection and splitting after Sumatra–Andaman earthquake. Journal of Geodynamics, 50(2), 49-56. https://doi.org/10.1016/j.jog.2010.02.003
  • Abbasi, M., & Mashhadizadeh Maleki, S. (2017). Iranian surface air temperature periodicities and correlations with the North Atlantic and Indian Ocean Sea surface temperature variations. Meteorological Applications, 24(2), 268-275. https://doi.org/10.1002/met.1625
  • Ghaderpour, E., Liao, W., & Lamoureux, M. P. (2018). Antileakage least-squares spectral analysis for seismic data regularization and random noise attenuation. Geophysics, 83(3), V157-V170. https://doi.org/10.1190/geo2017-0284.1
  • Omerbashich, M. (2003). Earth-Model Discrimination Method. [Doctoral Dissertation, University of New Brunswick].
  • Amerian, Y., & Voosoghi, B. (2011). Least squares spectral analysis for detection of systematic behaviour of digital level compensator. Journal of Geodetic Science, 1(1), 35-40. https://doi.org/10.2478/v10156-010-0005-4
  • Vanicek, P. & Krakiwsky, E. (1987). Geodesy: The Concepts, 2. Elsevier Science Publishers B.V.
  • Pagiatakis, S. D. (1999). Stochastic significance of peaks in the least-squares spectrum. Journal of Geodesy, 73, 67-78. https://doi.org/10.1007/s001900050220
  • Abd El-Gelil, M., Pagiatakis, S., & El-Rabbany, A. (2008). Frequency-dependent atmospheric pressure admittance of superconducting gravimeter records using least squares response method. Physics of the Earth and Planetary Interiors, 170(1-2), 24-33. https://doi.org/10.1016/j.pepi.2008.06.031
  • Ainscow, B., Blackman, D., Kerrigde, J., Pugh, D., & Shaw, S. (1985). Manual on sea level measurement and interpretation, I.
  • Abbak, R. A. (2005). Deniz düzeyi gözlemlerinin en küçük kareler yöntemiyle spektral analizi. [Master’s Thesis, Selcuk University].
  • Maul, G. A., & Yanaway, A. (1978). Deep sea tides determination from GEOS-3. Collected Reprints, 78.
  • Stewart, R. H. (2004). Introduction to physical oceanography. Texas A&M University, USA.
  • Abbak, R. A. (2023). Least-Squares Spectral Analysis of Hourly Tide Gauge Data–A Case Study: LSSA of Hourly Tide-Gauge Data. Advanced Geomatics, 3(1), 23-27.
  • İl, H. T. A., Abbak, R. A., Bildirici, İ. Ö., & Demir, S. (2018). SRTM1 ve ASTER sayısal yükseklik modellerinin gravimetrik jeoit belirlemeye katkısı. Geomatik, 3(3), 203-212. https://doi.org/10.29128/geomatik.402331
  • Demir, S., Abbak, R. A., & İl, H. T. A. (2018). Global yerpotansiyel modellerin gravimetrik jeoit belirlemeye katkısı. Geomatik, 3(3), 213-224. https://doi.org/10.29128/geomatik.403776
  • Ghaderpour, E., & Pagiatakis, S. D. (2017). Least-squares wavelet analysis of unequally spaced and non-stationary time series and its applications. Mathematical Geosciences, 49, 819-844. https://doi.org/10.1007/s11004-017-9691-0
Toplam 30 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Jeomatik Mühendisliği (Diğer)
Bölüm Articles
Yazarlar

Ramazan Alpay Abbak 0000-0002-6944-5329

Erken Görünüm Tarihi 23 Temmuz 2024
Yayımlanma Tarihi 28 Temmuz 2024
Yayımlandığı Sayı Yıl 2024

Kaynak Göster

APA Abbak, R. A. (2024). A practical software package for estimating the periodicities in time series by least-squares spectral analysis. International Journal of Engineering and Geosciences, 9(2), 191-198. https://doi.org/10.26833/ijeg.1366950
AMA Abbak RA. A practical software package for estimating the periodicities in time series by least-squares spectral analysis. IJEG. Temmuz 2024;9(2):191-198. doi:10.26833/ijeg.1366950
Chicago Abbak, Ramazan Alpay. “A Practical Software Package for Estimating the Periodicities in Time Series by Least-Squares Spectral Analysis”. International Journal of Engineering and Geosciences 9, sy. 2 (Temmuz 2024): 191-98. https://doi.org/10.26833/ijeg.1366950.
EndNote Abbak RA (01 Temmuz 2024) A practical software package for estimating the periodicities in time series by least-squares spectral analysis. International Journal of Engineering and Geosciences 9 2 191–198.
IEEE R. A. Abbak, “A practical software package for estimating the periodicities in time series by least-squares spectral analysis”, IJEG, c. 9, sy. 2, ss. 191–198, 2024, doi: 10.26833/ijeg.1366950.
ISNAD Abbak, Ramazan Alpay. “A Practical Software Package for Estimating the Periodicities in Time Series by Least-Squares Spectral Analysis”. International Journal of Engineering and Geosciences 9/2 (Temmuz 2024), 191-198. https://doi.org/10.26833/ijeg.1366950.
JAMA Abbak RA. A practical software package for estimating the periodicities in time series by least-squares spectral analysis. IJEG. 2024;9:191–198.
MLA Abbak, Ramazan Alpay. “A Practical Software Package for Estimating the Periodicities in Time Series by Least-Squares Spectral Analysis”. International Journal of Engineering and Geosciences, c. 9, sy. 2, 2024, ss. 191-8, doi:10.26833/ijeg.1366950.
Vancouver Abbak RA. A practical software package for estimating the periodicities in time series by least-squares spectral analysis. IJEG. 2024;9(2):191-8.