1,753 research outputs found
Forecasting Time Series with VARMA Recursions on Graphs
Graph-based techniques emerged as a choice to deal with the dimensionality
issues in modeling multivariate time series. However, there is yet no complete
understanding of how the underlying structure could be exploited to ease this
task. This work provides contributions in this direction by considering the
forecasting of a process evolving over a graph. We make use of the
(approximate) time-vertex stationarity assumption, i.e., timevarying graph
signals whose first and second order statistical moments are invariant over
time and correlated to a known graph topology. The latter is combined with VAR
and VARMA models to tackle the dimensionality issues present in predicting the
temporal evolution of multivariate time series. We find out that by projecting
the data to the graph spectral domain: (i) the multivariate model estimation
reduces to that of fitting a number of uncorrelated univariate ARMA models and
(ii) an optimal low-rank data representation can be exploited so as to further
reduce the estimation costs. In the case that the multivariate process can be
observed at a subset of nodes, the proposed models extend naturally to Kalman
filtering on graphs allowing for optimal tracking. Numerical experiments with
both synthetic and real data validate the proposed approach and highlight its
benefits over state-of-the-art alternatives.Comment: submitted to the IEEE Transactions on Signal Processin
A globally convergent matricial algorithm for multivariate spectral estimation
In this paper, we first describe a matricial Newton-type algorithm designed
to solve the multivariable spectrum approximation problem. We then prove its
global convergence. Finally, we apply this approximation procedure to
multivariate spectral estimation, and test its effectiveness through
simulation. Simulation shows that, in the case of short observation records,
this method may provide a valid alternative to standard multivariable
identification techniques such as MATLAB's PEM and MATLAB's N4SID
Vector Autoregresive Moving Average Identification for Macroeconomic Modeling: Algorithms and Theory
This paper develops a new methodology for identifying the structure of VARMA time series models. The analysis proceeds by examining the echelon canonical form and presents a fully automatic data driven approach to model specification using a new technique to determine the Kronecker invariants. A novel feature of the inferential procedures developed here is that they work in terms of a canonical scalar ARMAX representation in which the exogenous regressors are given by predetermined contemporaneous and lagged values of other variables in the VARMA system. This feature facilitates the construction of algorithms which, from the perspective of macroeconomic modeling, are efficacious in that they do not use AR approximations at any stage. Algorithms that are applicable to both asymptotically stationary and unit-root, partially nonstationary (cointegrated) time series models are presented. A sequence of lemmas and theorems show that the algorithms are based on calculations that yield strongly consistent estimates.Keywords: Algorithms, asymptotically stationary and cointegrated time series, echelon
The State Space Models Toolbox for MATLAB
State Space Models (SSM) is a MATLAB toolbox for time series analysis by state space methods. The software features fully interactive construction and combination of models, with support for univariate and multivariate models, complex time-varying (dy- namic) models, non-Gaussian models, and various standard models such as ARIMA and structural time-series models. The software includes standard functions for Kalman fil- tering and smoothing, simulation smoothing, likelihood evaluation, parameter estimation, signal extraction and forecasting, with incorporation of exact initialization for filters and smoothers, and support for missing observations and multiple time series input with com- mon analysis structure. The software also includes implementations of TRAMO model selection and Hillmer-Tiao decomposition for ARIMA models. The software will provide a general toolbox for time series analysis on the MATLAB platform, allowing users to take advantage of its readily available graph plotting and general matrix computation capabilities.
Using Subspace Methods for Estimating ARMA Models for Multivariate Time Series with Conditionally Heteroskedastic Innovations
This paper deals with the estimation of linear dynamic models of the ARMA type for the conditional mean for time series with conditionally heteroskedastic innovation process widely used in modelling financial time series. Estimation is performed using subspace methods which are known to have computational advantages as compared to prediction error methods based on criterion minimization. These advantages are especially strong for high dimensional time series. The subspace methods are shown to provide consistent estimators. Moreover asymptotic equivalence to prediction error estimators in terms of the asymptotic variance is proved. Also order estimation techniques are proposed and analyzed. The estimators are not efficient as they do not model the conditional variance. Nevertheless, they can be used to obtain consistent estimators of the innovations. In a second step these estimated residuals can be used in order to levitate the problem of specifying the variance model in particular in the multi-output case. This is demonstrated in an ARCH setting, where it is proved that the estimated innovations can be used in place of the true innovations for testing in a linear least squares context in order to specify the structure of the ARCH model without changing the asymptotic distribution.Multivariate models, conditional heteroskedasticity, ARMA systems, subspace methods
A new family of high-resolution multivariate spectral estimators
In this paper, we extend the Beta divergence family to multivariate power
spectral densities. Similarly to the scalar case, we show that it smoothly
connects the multivariate Kullback-Leibler divergence with the multivariate
Itakura-Saito distance. We successively study a spectrum approximation problem,
based on the Beta divergence family, which is related to a multivariate
extension of the THREE spectral estimation technique. It is then possible to
characterize a family of solutions to the problem. An upper bound on the
complexity of these solutions will also be provided. Simulations suggest that
the most suitable solution of this family depends on the specific features
required from the estimation problem
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