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...

Autoregressive (AR) modeling is widely used in signal processing. The coefficients of an AR model can be easily obtained with a least mean square (LMS) prediction error filter. However, it is known that this filter gives a biased solution when the input signal is corrupted by white Gaussian noise. Treichler suggested the -LMS algorithm to remedy this problem and proved that the mean weight vect...

We propese an exact maximum likelihood (ML) approach for hidden Markov modeling of speech signals using models with mixtures of Gaussian autoregressive (AR) output probability distributions. This approach differs from the commonly used approach in two aspects. First, the parameters of the AR models are calculated using the exact, rather than the asymptotic, form of the likelihood function. Seco...

In this paper a nonparametric neural network (NN) technique for prediction of future values of a signal based on its past history is presented. This approach bypasses modeling, identification, and parameter estimation phases that are required by conventional parametric techniques. A multi-layer feed forward NN is employed. It develops an internal model of the signal through a training operation...

We present particle-based algorithms for sequential filtering and parameter learning in state-space autoregressive (AR) models with structured priors. Non-conjugate priors are specified on the AR coefficients at the system level by imposing uniform or truncated normal priors on the moduli and wavelengths of the reciprocal roots of the AR characteristic polynomial. Sequential Monte Carlo algorit...

In this paper, novel techniques in increasing the accuracy and speed of convergence of a Feed forward Back propagation Artificial Neural Network (FFBPNN) with polynomial activation function reported in literature is presented. These technique was subsequently used to determine the coefficients of Autoregressive Moving Average (ARMA) and Autoregressive (AR) system. The results obtained by introd...

We present a family of spatio-temporal models which are geared to provide time-forward predictions in environmental applications where data is spatially sparse but temporally rich. That is measurements are made at few spatial locations (stations), but at many regular time intervals. When predictions in the time direction is the purpose of the analysis, then spatial-stationarity assumptions whic...

In vector autoregressive modeling, the order selected with the Akaike Information Criterion tends to be too high. This effect is called overfit. Finite sample effects are an important cause of overfit. By incorporating finite sample effects, an order selection criterion for vector AR models can be found with an optimal trade-off of underfit and overfit. The finite sample formulae in this paper ...

In this brief, a novel algorithm is presented for the efficient two-dimensional (2-D) symmetric noncausal finite impulse response (FIR) filtering and autoregressive (AR) modeling. Symmetric filter masks of general boundaries are allowed. The proposed algorithm offers the greatest maneuverability in the 2-D index space in a computationally efficient way. This flexibility can be taken advantage o...

The present study investigates linear and volatile (nonlinear) correlations of firstorder autoregressive process with uncorrelated AR (1) and long-range correlated CAR (1) Gaussian innovations as a function of the process parameter (θ). In the light of recent findings [1], we discuss the choice of CAR (1) in modeling daily temperature records. We demonstrate that while CAR (1) is able to captur...