27,600 research outputs found
Randomized opinion dynamics over networks: influence estimation from partial observations
In this paper, we propose a technique for the estimation of the influence
matrix in a sparse social network, in which individual communicate in a
gossip way. At each step, a random subset of the social actors is active and
interacts with randomly chosen neighbors. The opinions evolve according to a
Friedkin and Johnsen mechanism, in which the individuals updates their belief
to a convex combination of their current belief, the belief of the agents they
interact with, and their initial belief, or prejudice. Leveraging recent
results of estimation of vector autoregressive processes, we reconstruct the
social network topology and the strength of the interconnections starting from
\textit{partial observations} of the interactions, thus removing one of the
main drawbacks of finite horizon techniques. The effectiveness of the proposed
method is shown on randomly generation networks
Model selection criteria and quadratic discrimination in ARMA and SETAR time series models
We show that analyzing model selection in ARMA time series models as a quadratic discrimination problem provides a unifying approach for deriving model selection criteria. Also this approach suggest a different definition of expected likelihood that the one proposed by Akaike. This approach leads to including a correction term in the criteria which does not modify their large sample performance but can produce significant improvement in the performance of the criteria in small samples. Thus we propose a family of criteria which generalizes the commonly used model selection criteria. These ideas can be extended to self exciting autoregressive models (SETAR) and we generalize the proposed approach for these non linear time series models. A Monte-Carlo study shows that this family improves the finite sample performance of criteria such as AIC, corrected AIC and BIC, for ARMA models, and AIC, corrected AIC, BIC and some cross-validation criteria for SETAR models. In particular, for small and medium sample size the frequency of selecting the true model improves for the consistent criteria and the root mean square error of prediction improves for the efficient criteria. These results are obtained for both linear ARMA models and SETAR models in which we assume that the threshold and the parameters are unknown
Aggregation and long memory: recent developments
It is well-known that the aggregated time series might have very different
properties from those of the individual series, in particular, long memory. At
the present time, aggregation has become one of the main tools for modelling of
long memory processes. We review recent work on contemporaneous aggregation of
random-coefficient AR(1) and related models, with particular focus on various
long memory properties of the aggregated process
Bootstrap tests for unit root AR(1) models
In this paper, we propose bootstrap tests for unit roots in first-order autoregressive models. We provide the bootstrap functional limit theory needed to prove the asymptotic validity of these tests both for independent and autoregressive errors; in this case, the usual corrections due to innovations dependence can be avoided. We also present a power empirical study comparing these tests with existing alternative methods
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