When we were fitting ARMA models to the data, we first looked at the sample autocovariance or autocorrelation function and we then tried to find the ARMA model whose theoretical acf matched with the sample acf. Now the sample autocovariance function is a nonparametric estimate of the theoretical autocovariance function of the process. In other words, we first estimated γ(h) nonparametrically by...

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 sel...

To solve the problem in which the conventional ARMA modeling methods for gyro random noise require a large number of samples and converge slowly, an ARMA modeling method using a robust Kalman filtering is developed. The ARMA model parameters are employed as state arguments. Unknown time-varying estimators of observation noise are used to achieve the estimated mean and variance of the observatio...

The well-known prediction-error-based maximum likelihood (PEML) method can only handle minimum phase ARMA models. This likelihood (BFML) method, which can handle nonminimum phase and noncausal ARMA models. The BFML method is identical to the PEML method in the case of a minimum phase ARMA model, and it turns out that the BFML method incorporates a noncausal ARMA filter with poles outside the un...

In this paper, the short-term load forecast by use of autoregressive moving average (ARMA) model including non-Gaussian process considerations is proposed. In the proposed method, the concept of cumulant and bispectrum are embedded into the ARMA model in order to facilitate Gaussian and non-Gaussian process. With embodiment of a Gaussianity verification procedure, the forecasted model is identi...

Autoregressive moving average (ARMA) models are a fundamental tool in time series analysis that offer intuitive modeling capability and efficient predictors. Unfortunately, the lack of globally optimal parameter estimation strategies for these models remains a problem: application studies often adopt the simpler autoregressive model that can be easily estimated by maximizing (a posteriori) like...

A feasibility study of using of Dynamic Bayesian Networks in combination with ARMA modeling in exchange rate prediction is presented. A new algorithm (ARMA-DBN) is constructed and applied to the exchange rate forecast of RMB. Results show that the improved dynamic Bayesian forecast algorithm has better performance than the standard ARMA model.

An approach to handling colored observation noise in large least-squares (LS) problems is presented. The handling of colored noise is reduced to the problem of solving a Toeplitz system of linear equations. The colored noise is represented as an auto regressive moving-average (ARMA) process. Stability and invertability of the ARMA model allows the solution of the Toeplitz system to be reduced t...

The renewable energies prediction and particularly global radiation forecasting is a challenge studied by a growing number of research teams. This paper proposes an original technique to model the insolation time series based on combining Artificial Neural Network (ANN) and Auto-Regressive and Moving Average (ARMA) model. While ANN by its non-linear nature is effective to predict cloudy days, A...

Since the empirical characteristic function (ECF) is the Fourier transform of the empirical distribution function, it retains all the information in the sample but can overcome difficulties arising from the likelihood. This paper discusses an estimation method via the ECF for strictly stationary processes. Under some regularity conditions, the resulting estimators are shown to be consistent and...