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Estimation of a time series model from unequally spaced data

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  • Robinson, P. M.

Abstract

A process generated by a stochastic differential equation driven by pure noise is sampled at irregular intervals. A model for the sampled sequence is deduced. We describe a maximum likelihood procedure for estimating the parameters and establish the strong consistency and asymptotic normality of the estimates. The use of the model in prediction is considered. Simplifications in the case of periodic sampling are explored.

Suggested Citation

  • Robinson, P. M., 1977. "Estimation of a time series model from unequally spaced data," Stochastic Processes and their Applications, Elsevier, vol. 6(1), pages 9-24, November.
    • Handle: RePEc:eee:spapps:v:6:y:1977:i:1:p:9-24
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    Citations

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    Cited by:

    1. Peter M Robinson, 2009. "Correlation Testing in Time Series, SpatialandCross-Sectional Data," STICERD - Econometrics Paper Series 530, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    2. Philip Hans Franses, 2021. "Estimating persistence for irregularly spaced historical data," Quality & Quantity: International Journal of Methodology, Springer, vol. 55(6), pages 2177-2187, December.
    3. Robinson, Peter, 2008. "Correlation testing in time series, spatial and cross-sectional data," LSE Research Online Documents on Economics 25470, London School of Economics and Political Science, LSE Library.
    4. Robinson, Peter, 2019. "Spatial long memory," LSE Research Online Documents on Economics 102182, London School of Economics and Political Science, LSE Library.
    5. Vilar, José A. & Vilar, Juan M., 2000. "Finite sample performance of density estimators from unequally spaced data," Statistics & Probability Letters, Elsevier, vol. 50(1), pages 63-73, October.
    6. Massimiliano Marcellino & Oscar Jorda, "undated". "Stochastic Processes Subject to Time-Scale Transformations: An Application to High-Frequency FX Data," Working Papers 164, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
    7. Peter Robinson, 2007. "Correlation testing in time series, spatial and cross-sectional data," CeMMAP working papers CWP01/07, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    8. Yacine Ait--Sahalia & Per A. Mykland, 2003. "The Effects of Random and Discrete Sampling when Estimating Continuous--Time Diffusions," Econometrica, Econometric Society, vol. 71(2), pages 483-549, March.
    9. repec:cep:stiecm:/2013/568 is not listed on IDEAS
    10. Peter Robinson, 2007. "On Discrete Sampling Of Time-Varyingcontinuous-Time Systems," STICERD - Econometrics Paper Series 520, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    11. Delgado, Miguel A. & Robinson, Peter M., 2015. "Non-nested testing of spatial correlation," Journal of Econometrics, Elsevier, vol. 187(1), pages 385-401.
    12. Massimiliano Marcellino & Oscar Jorda, "undated". "Stochastic Processes Subject to Time-Scale Transformations: An Application to High-Frequency FX Data," Working Papers 164, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
    13. Robinson, P.M., 2008. "Correlation testing in time series, spatial and cross-sectional data," Journal of Econometrics, Elsevier, vol. 147(1), pages 5-16, November.
    14. Josué M. Polanco-Martínez, 2014. "Estimación espectral de datos ambientales no equiespaciados vía el periodograma suavizado de Lomb-Scargle. Una breve revisión," Analítika, Analítika - Revista de Análisis Estadístico/Journal of Statistical Analysis, vol. 8(2), pages 7-23, Diciembre.
    15. Robinson, P.M., 2011. "Asymptotic theory for nonparametric regression with spatial data," Journal of Econometrics, Elsevier, vol. 165(1), pages 5-19.
    16. Robinson, Peter, 2007. "On discrete sampling of time-varying continuous-time systems," LSE Research Online Documents on Economics 6795, London School of Economics and Political Science, LSE Library.
    17. P. Thomson, 1992. "Signal estimation using stochastic velocity models and irregular arrays," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 44(1), pages 13-25, March.

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