6 research outputs found
Estimation of AR and ARMA models by stochastic complexity
In this paper the stochastic complexity criterion is applied to estimation of
the order in AR and ARMA models. The power of the criterion for short strings
is illustrated by simulations. It requires an integral of the square root of
Fisher information, which is done by Monte Carlo technique. The stochastic
complexity, which is the negative logarithm of the Normalized Maximum
Likelihood universal density function, is given. Also, exact asymptotic
formulas for the Fisher information matrix are derived.Comment: Published at http://dx.doi.org/10.1214/074921706000000941 in the IMS
Lecture Notes Monograph Series
(http://www.imstat.org/publications/lecnotes.htm) by the Institute of
Mathematical Statistics (http://www.imstat.org
Time-varying effective EEG source connectivity: the optimization of model parameters*
Adaptive estimation methods based on general Kalman filter are powerful tools to investigate brain networks dynamics given the non-stationary nature of neural signals. These methods rely on two parameters, the model order p and adaptation constant c, which determine the resolution and smoothness of the time-varying multivariate autoregressive estimates. A sub-optimal filtering may present consistent biases in the frequency domain and temporal distortions, leading to fallacious interpretations. Thus, the performance of these methods heavily depends on the accurate choice of these two parameters in the filter design. In this work, we sought to define an objective criterion for the optimal choice of these parameters. Since residual- and information-based criteria are not guaranteed to reach an absolute minimum, we propose to study the partial derivatives of these functions to guide the choice of p and c. To validate the performance of our method, we used a dataset of human visual evoked potentials during face perception where the generation and propagation of information in the brain is well understood and a set of simulated data where the ground truth is available
Finite Sample FPE and AIC Criteria for Autoregressive Model Order Selection Using Same-Realization Predictions
A new theoretical approximation for expectation of the prediction error is derived using the same-realization predictions. This approximation is derived for the case that the Least-Squares-Forward (LSF) method (the covariance method) is used for estimating the parameters of the autoregressive (AR) model. This result is used for obtaining modified versions of the AR order selection criteria FPE and AIC in the finite sample case. The performance of these modified criteria is compared with other same-realization AR order selection criteria using simulated data. The results of this comparison show that the proposed criteria have better performance
ACCUMULATED PREDICTION ERRORS, INFORMATION CRITERIA AND OPTIMAL FORECASTING FOR AUTOREGRESSIVE TIME SERIES
The predictive capability of a modification of Rissanen's accumulated prediction error (APE) criterion, APE,is investigated in infinite-order autoregressive (AR()) models. Instead of accumulating squares of sequential prediction errors from the beginning, APE is obtained by summing these squared errors from stage , where is the sample size and $0Accumulated prediction errors, Asymptotic equivalence, Asymptotic efficiency, Information criterion, Order selection, Optimal forecasting