Continuous-time state-space methods for delta-O-18 and delta-C-13
Abstract: Time series analysis of delta-O-18 and delta-C-13 measurements from benthic foraminifera for purposes of paleoclimatology is challenging. The time series reach back tens of millions of years, they are relatively sparse in the early record and relatively dense in the later, the time stamps of the observations are not evenly spaced, and there are instances of multiple different observations at the same time stamp. The time series appear non-stationary over most of the historical record with clearly visible temporary trends of varying directions. In this paper, we propose a continuous-time state-space framework to analyze the time series. State space models are uniquely suited for this purpose, since they can accommodate all the challenging features mentioned above. We specify univariate models and joint bivariate models for the two time series of delta-O-18 and delta-C-13. The models are estimated using maximum likelihood by way of the Kalman filter recursions. The suite of models we consider has an interpretation as an application of the Butterworth filter. We propose model specifications that take the origin of the data from different studies into account and that allow for a partition of the total period into sub-periods reflecting different climate states. The models can be used, for example, to impute evenly time-stamped values by way of Kalman filtering. They can also be used, in future work, to analyze the relation to proxies for CO2 concentrations.
- Bagchi, S. and S. K. Mitra (1996). The nonuniform discrete Fourier transform and its applications in filter design. I. 1-D. IEEE Transactions on Circuits and Systems II: Analog and Digital Signal Processing 43(6), 422–433.
- Bell, W. (1984). Signal extraction for nonstationary time series. The Annals of Statistics 12(2), 646–664.
- Doornik, J. (2021). An Introduction to OxMetrics 9. Timberlake Consultants.
- Durbin, J. and S. J. Koopman (2012). Time Series Analysis by State Space Methods (2 ed.). Oxford University Press.
- Gómez, V. (1999). Three equivalent methods for filtering finite nonstationary time series. Journal of Business & Economic Statistics 17(1), 109–116.
- Gómez, V. (2001). The use of butterworth filters for trend and cycle estimation in economic time series. Journal of Business & Economic Statistics 19(3), 365–373.
- Harvey, A. and S. J. Koopman (2000). Signal extraction and the formulation of unobserved components models. The Econometrics Journal 3(1), 84–107.
- Harvey, A. and S. J. Koopman (2009). Unobserved components models in economics and finance. IEEE Control Systems Magazine 29(6), 71–81.
- Harvey, A. C. (1989). Forecasting, Structural Time Series Models and the Kalman Filter. Cambridge: Cambridge University Press.
- Harvey, A. C. and T. M. Trimbur (2003). General model-based filters for extracting cycles and trends in economic time series. Review of Economics and Statistics 85(2), 244–255.
- Helske, J. (2017). KFAS: Exponential family state space models in R. Journal of Statistical Software 78, 1–38.
- Helske, J. (2019). Package “KFAS”: Kalman filter and smoother for exponential family state-space models. Technical report, CRAN repository, version 1.3.4.
- Karatzas, I. and S. E. Shreve (1991). Brownian Motion and Stochastic Calculus (second ed.). Springer.
- Turner, S. K. (2014). Pliocene switch in orbital-scale carbon cycle/climate dynamics. Paleoceanography 29(12), 1256–1266.
- An astronomically dated record of earth’s climate and its predictability over the last 66 million years. Science 369(6509), 1383–1387.
- Whittle, P. (1983). Prediction and Regulation by Linear Least-Square Methods (second ed.). University of Minnesota Press.
- Trends, rhythms, and aberrations in global climate 65 ma to present. Science 292(5517), 686–693.
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