44,784 research outputs found
On recursive estimation for time varying autoregressive processes
This paper focuses on recursive estimation of time varying autoregressive
processes in a nonparametric setting. The stability of the model is revisited
and uniform results are provided when the time-varying autoregressive
parameters belong to appropriate smoothness classes. An adequate normalization
for the correction term used in the recursive estimation procedure allows for
very mild assumptions on the innovations distributions. The rate of convergence
of the pointwise estimates is shown to be minimax in -Lipschitz classes
for . For , this property no longer holds. This
can be seen by using an asymptotic expansion of the estimation error. A bias
reduction method is then proposed for recovering the minimax rate.Comment: Published at http://dx.doi.org/10.1214/009053605000000624 in the
Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Mathematical Statistics (http://www.imstat.org
A General Framework for Observation Driven Time-Varying Parameter Models
We propose a new class of observation driven time series models that we refer to as Generalized Autoregressive Score (GAS) models. The driving mechanism of the GAS model is the scaled likelihood score. This provides a unified and consistent framework for introducing time-varying parameters in a wide class of non-linear models. The GAS model encompasses other well-known models such as the generalized autoregressive conditional heteroskedasticity, autoregressive conditional duration, autoregressive conditional intensity and single source of error models. In addition, the GAS specification gives rise to a wide range of new observation driven models. Examples include non-linear regression models with time-varying parameters, observation driven analogues of unobserved components time series models, multivariate point process models with time-varying parameters and pooling restrictions, new models for time-varying copula functions and models for time-varying higher order moments. We study the properties of GAS models and provide several non-trivial examples of their application.dynamic models, time-varying parameters, non-linearity, exponential family, marked point processes, copulas
Dynamic Spatial Autoregressive Models with Autoregressive and Heteroskedastic Disturbances
We propose a new class of models specifically tailored for spatio-temporal
data analysis. To this end, we generalize the spatial autoregressive model with
autoregressive and heteroskedastic disturbances, i.e. SARAR(1,1), by exploiting
the recent advancements in Score Driven (SD) models typically used in time
series econometrics. In particular, we allow for time-varying spatial
autoregressive coefficients as well as time-varying regressor coefficients and
cross-sectional standard deviations. We report an extensive Monte Carlo
simulation study in order to investigate the finite sample properties of the
Maximum Likelihood estimator for the new class of models as well as its
flexibility in explaining several dynamic spatial dependence processes. The new
proposed class of models are found to be economically preferred by rational
investors through an application in portfolio optimization.Comment: 33 pages, 5 figure
Aggregation of predictors for nonstationary sub-linear processes and online adaptive forecasting of time varying autoregressive processes
In this work, we study the problem of aggregating a finite number of
predictors for nonstationary sub-linear processes. We provide oracle
inequalities relying essentially on three ingredients: (1) a uniform bound of
the norm of the time varying sub-linear coefficients, (2) a Lipschitz
assumption on the predictors and (3) moment conditions on the noise appearing
in the linear representation. Two kinds of aggregations are considered giving
rise to different moment conditions on the noise and more or less sharp oracle
inequalities. We apply this approach for deriving an adaptive predictor for
locally stationary time varying autoregressive (TVAR) processes. It is obtained
by aggregating a finite number of well chosen predictors, each of them enjoying
an optimal minimax convergence rate under specific smoothness conditions on the
TVAR coefficients. We show that the obtained aggregated predictor achieves a
minimax rate while adapting to the unknown smoothness. To prove this result, a
lower bound is established for the minimax rate of the prediction risk for the
TVAR process. Numerical experiments complete this study. An important feature
of this approach is that the aggregated predictor can be computed recursively
and is thus applicable in an online prediction context.Comment: Published at http://dx.doi.org/10.1214/15-AOS1345 in the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Time-varying model identification for time-frequency feature extraction from EEG data
A novel modelling scheme that can be used to estimate and track time-varying properties of nonstationary signals is investigated. This scheme is based on a class of time-varying AutoRegressive with an eXogenous input (ARX) models where the associated time-varying parameters are represented by multi-wavelet basis functions. The orthogonal least square (OLS) algorithm is then applied to refine the model parameter estimates of the time-varying ARX model. The main features of the multi-wavelet approach is that it enables smooth trends to be tracked but also to capture sharp changes in the time-varying process parameters. Simulation studies and applications to real EEG data show that the proposed algorithm can provide important transient information on the inherent dynamics of nonstationary processes
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