1 Corresponding and presenting author: Y. K. Wong, Tel: (852) 2766-6140, Fax: (852) 2330-1544, Email: [email protected] Abstract The needs of accuracy of machines are strictly increasing for the manufacturing processes. It is costly to use high precision machine to achieve the goal. Therefore, if the forecasting of errors can be obtained from the gathered past error values, it allows the co...

A linear Markov system can be represented by an autoregressive and moving average (ARMA) model in discrete time domain. It can be used to identify some system model and its associated parameters. Recently, the ARMA model has been extended to an ARMA-LiNGAM model which is a canonical form to represent the system. It is expected to provide more detailed information of the model structure and the ...

The paper investigates the relation between the parameters of an autoregressive moving average (ARMA) model and its equivalent moving average (EMA) model. On the basis of this relation, a new method is proposed for determining the ARMA model parameters from the coefficients of a finite-order EMA model. This method is a three-step approach: in the first step, a simple recursion relating the EMA ...

In the 2011 SAS® Global Forum, two weighted portmanteau tests were introduced for goodness-of-fit of an Autoregressive-Moving Average (ARMA) time series process. This result is summarized and extended for use as a diagnostic tool in detecting nonlinear and variance-changing processes such as the Generalized Autoregressive Conditional Heteroscedasticity process. The efficacy of the weighting sch...

In a recent publication Stadnitski (2012) presented an overview of methods to estimate fractal scaling in time series, outlined as an accessible tutorial1. The publication was set-up as a comparison between monofractal and ARFIMA methods, and promotes ARFIMA to distinguish between spurious and genuine 1/f noise, shedding light on “the problem that the log–log power spectrum of short-memory ARMA...

The generalized Langevin equation is useful for modeling a wide range of physical processes. Unfortunately its parameters, especially the memory function, are difficult to determine for nontrivial processes. We establish relations between a time-discrete generalized Langevin model and discrete multivariate autoregressive (AR) or autoregressive moving average models (ARMA). This allows a wide ra...

In the theory of stochastic differential equations, it is commonly assumed that the forcing function is a Wiener process. Such a process has an infinite bandwidth in the frequency domain. In practice, however, all stochastic processes have a limited bandwidth. A theory of band-limited linear stochastic processes is described that reflects this reality, and it is shown how the corresponding ARMA...

BACKGROUND Gene clustering of periodic transcriptional profiles provides an opportunity to shed light on a variety of biological processes, but this technique relies critically upon the robust modeling of longitudinal covariance structure over time. METHODOLOGY We propose a statistical method for functional clustering of periodic gene expression by modeling the covariance matrix of serial mea...