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.
ABSTRACT
PUBLICATION RECORD
- Publication year
1990
- Venue
Forestry sciences
- Publication date
1990-03-01
- Fields of study
Mathematics, Economics, Environmental Science
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- External record
- Source metadata
Semantic Scholar
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EXTRACTION MAP
CLAIMS
CONCEPTS
- arma model
A time-series component used to represent autocorrelated residual variation with autoregressive and moving-average terms.
Aliases: autoregressive moving-average model, ARMA
- discrete kalman filter
A recursive estimation algorithm used here for linear Gaussian state-space models.
Aliases: Kalman filter
- doubly differenced trend
A trend component formed by differencing the series twice before combining it with another model component.
Aliases: double-differenced trend
- maximum-likelihood optimization
A parameter-fitting procedure that selects values by maximizing the likelihood of the observed data.
Aliases: maximum likelihood estimation, ML estimation
- noise variances
Variance parameters of the disturbance terms that determine how flexible the trend component is.
Aliases: unknown noise variances
- simulated time series
Artificially generated time series used to check how the models behave under known conditions.
Aliases: simulated series, simulation data
- spline interpolation
A smooth interpolation baseline used to fit and compare growth trend curves.
Aliases: spline
- state-space form
A representation that writes the latent trend dynamics and observations as linked state and measurement equations.
Aliases: state space form, SSM form
- trend model with a stochastic level and slope
A trend specification in which the latent level and slope evolve stochastically over time.
Aliases: stochastic level-and-slope model, level-slope trend model
- trend plus ar(1) model
A combined model that pairs a trend component with first-order autoregressive residual structure.
Aliases: trend-plus-AR(1) model, trend plus AR1 model
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