A time-series autoregressive moving average (ARMA) approach was used to develop stochastic models of tree crown profiles for five conifer species of the Sierran mixed conifer habitat type. Models consisted of three components: (1) a polynomial trend; (2) an ARMA model; and (3) random error. A Bayesian information criterion was used to evaluate alternative models. It was found that 70% of the cr...

Long intermediate AR models are used in Durbin's algorithms for ARMA estimation. The order of that long AR model is infinite in the asymptotical theory, but very high AR orders are known to give inaccurate ARMA models in practice. A theoretical derivation is given for two different finite AR orders, as a function of the sample size. The first is the AR order optimal for prediction with a purely...

For a given time series observation sequence, we can estimate the parameters of the AutoRegression Moving Average (ARMA) model, thereby representing a potentially long time series by a limited dimensional vector. In many applications, these parameter vectors will be separable into different groups, due to the different underlying mechanisms that generate differing time series. We can then use c...

Discrete time-varying autoregressive moving average (ARMA) models are used to describe realistic earthquake ground motion time histories. Both amplitude and frequency nonstationarities are incorporated in the model. An iterative Kalman filtering scheme is introduced to identify the time-varying parameters of an ARMA model from an actual earthquake record. Several model verification tests are pe...

This paper investigates the issue on how to effectively model time series with a new algorithm given by a Multilayer Feedforward Neural Network (MLFNN) and an Autoregressive Moving Average (ARMA). The static nonlinear part is modeled by MLFNN, and the linear part is modeled by an ARMA model. The algorithm is developed for estimating the weights of the MLFNN and the parameters of ARMA model. To ...

This paper investigates the asymptotic theory for a vector autoregressive moving average–generalized autoregressive conditional heteroskedasticity ~ARMAGARCH! model+ The conditions for the strict stationarity, the ergodicity, and the higher order moments of the model are established+ Consistency of the quasimaximum-likelihood estimator ~QMLE! is proved under only the second-order moment conditi...

There is a great demand for statist ical modeling of phenomena tha t evolve in bo th space and time. Practical examples are those in Haslett and Raf tery (1989), Handcock and Wallis (1994), Cressie and Huang (1999), Brix and Diggle (2001), Stroud et al. (2001), De Iaco et al. (2002), Gneit ing (2002), and Hartfield and Gunst (2003), to mention but a few. Two commonly used tools to describe the ...

This paper presents a unified framework of stationary ARMA processes for discrete-valued time series based on Pegram’s [Pegram, G.G.S., 1980. An autoregressive model for multilag markov chains. J. Appl. Probab. 17, 350–362] mixing operator. Such a stochastic operator appears to be more flexible than the currently popular thinning operator to construct Box and Jenkins’ type stationary ARMAproces...

Using a perturbation matrix, we introduced a hyperplane used to define a generalized null-spectrum, based on both the signal and noise subspaces, while the MUSIC and Min-Norm null-spectra are defined based only on the noise subspace. With the generalized nullspectrum, we derived the upper and lower bounds of a class of the generalized null-spectrum, called the maximum and minimum null-spectra, ...