Analysis of ecological time series with ARMA(p,q) models
Analysis of ecological time series with ARMA(p,q) models
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DOI：
10.1890/09-0442.1
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发表时间：
2010-03-01
期刊：
影响因子：
4.8
通讯作者：
Ziebarth, Nicolas L.
中科院分区：
文献类型：
--
作者：
Ives, Anthony R.;Abbott, Karen C.;Ziebarth, Nicolas L.
自回归滑动平均（阿尔马）模型是研究生态时间序列数据动态特性的有效统计工具。在这里，我们说明了应用阿尔马（p，q）模型的效用和挑战，其中p是模型的自回归分量的维数，q是移动平均分量的维数。我们专注于参数估计和模型选择，比较最大似然（ML）和限制最大似然（REML）参数估计。对于p = 1的阿尔马（p，q）模型，REML估计比ML估计性能更好（偏差更小）（如前所述），而对于p > 1的模型，估计量的性能因多模态似然函数而变得复杂。由此产生的困难估计导致我们的建议，似然函数进行常规调查时，应用阿尔马（p，q）模型。为了帮助这项调查，我们提供了ML和REML似然函数的MATLAB和R代码。我们进一步探讨了测量误差的后果，展示了它是如何显式和隐式地纳入估计。除了参数估计，我们还研究了模型选择，以确定正确的模型维度（p和q）。最后，我们估计的特征回报率的随机过程，其平稳分布，一个数量，描述了人口动态的一个关键属性，并调查偏差，结果从估计和模型选择。虽然拟合阿尔马模型的生态时间序列具有复杂的动态挑战，这些挑战可以克服，使阿尔马一个有用的和广泛适用的方法。
Autoregressive moving average (ARMA) models are useful statistical tools to examine the dynamical characteristics of ecological time-series data. Here, we illustrate the utility and challenges of applying ARMA(p,q) models, where p is the dimension of the autoregressive component of the model, and q is the dimension of the moving average component. We focus on parameter estimation and model selection, comparing both maximum likelihood (ML) and restricted maximum likelihood (REML) parameter estimation. While REML estimation performs better (has less bias) than ML estimation for ARMA(p,q) models with p = 1 (as has been found previously), for models with p > 1 the performance of the estimators is complicated by multimodal likelihood functions. The resulting difficulties in estimation lead to our recommendation that likelihood functions be routinely investigated when applying ARMA(p,q) models. To aid this investigation, we provide MATLAB and R code for the ML and REML likelihood functions. We further explore the consequences of measurement error, showing how it can be explicitly and implicitly incorporated into estimation. In addition to parameter estimation, we also examine model selection for identifying the correct model dimensions (p and q). Finally, we estimate the characteristic return rate of the stochastic process to its stationary distribution, a quantity that describes a key property of population dynamics, and investigate bias that results from both estimation and model selection. While fitting ARMA models to ecological time series with complex dynamics has challenges, these challenges can be surmounted, making ARMA a useful and broadly applicable approach.