27,600 research outputs found

    Randomized opinion dynamics over networks: influence estimation from partial observations

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    In this paper, we propose a technique for the estimation of the influence matrix in a sparse social network, in which nn 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

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    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

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    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

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    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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