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Estimating Trends in Tree-Ring Data

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Two methods from econometrics are introduced to estimate growth trends in time series of ring widths or basal-area increments. First, a trend model is described with a stochastic level and slope. The second model combines a doubly differenced trend and an ARMA model additively. Both models are put into a state-space form and are estimated using the discrete Kalman filter. Unknown noise variances, which control the flexibility of the trends, can be estimated by maximum-likelihood optimization or chosen by hand. It is concluded that the trend plus AR (1) model in combination with ML estimation performs very well. This model is attractive, because the ML-estimation procedure enables an objective choice for unknown parameters. Examples are given of two special features: the prediction of future growth, and the weighing of missing or unreliable data. Finally, both models are compared with spline interpolation and are validated by means of simulated time series. For. Sci. 36(1):87-100.

Keywords: ARIMA models; Kalman filter; air pollution; dendroclimatology; growth curves; maximum likelihood

Document Type: Journal Article

Affiliations: Applied Mathematician, Mathematics Consulting Department, Eindhoven University, P.O. Box 513, 5600 MB Eindhoven, The Netherlands

Publication date: 1990-03-01

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  • Forest Science is a peer-reviewed journal publishing fundamental and applied research that explores all aspects of natural and social sciences as they apply to the function and management of the forested ecosystems of the world. Topics include silviculture, forest management, biometrics, economics, entomology & pathology, fire & fuels management, forest ecology, genetics & tree improvement, geospatial technologies, harvesting & utilization, landscape ecology, operations research, forest policy, physiology, recreation, social sciences, soils & hydrology, and wildlife management.
    Forest Science is published bimonthly in February, April, June, August, October, and December.

    2015 Impact Factor: 1.702
    Ranking: 16 of 66 in forestry

    Average time from submission to first decision: 62.5 days*
    June 1, 2016 to Feb. 28, 2017

    Also published by SAF:
    Journal of Forestry
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