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Prediction of time series by statistical learning: general losses and fast rates

Pierre Alquier, Xiaoyin Li, Olivier Wintenberger (2013)

Dependence Modeling

We establish rates of convergences in statistical learning for time series forecasting. Using the PAC-Bayesian approach, slow rates of convergence √ d/n for the Gibbs estimator under the absolute loss were given in a previous work [7], where n is the sample size and d the dimension of the set of predictors. Under the same weak dependence conditions, we extend this result to any convex Lipschitz loss function. We also identify a condition on the parameter space that ensures similar rates for the...

Prediction problems related to a first-order autoregressive process in the presence of outliers

Sugata Sen Roy, Sourav Chakraborty (2006)

Applicationes Mathematicae

Outliers in a time series often cause problems in fitting a suitable model to the data. Hence predictions based on such models are liable to be erroneous. In this paper we consider a stable first-order autoregressive process and suggest two methods of substituting an outlier by imputed values and then predicting on the basis of it. The asymptotic properties of both the process parameter estimators and the predictors are also studied.

Probabilistic properties of a Markov-switching periodic G A R C H process

Billel Aliat, Fayçal Hamdi (2019)

Kybernetika

In this paper, we propose an extension of a periodic G A R C H ( P G A R C H ) model to a Markov-switching periodic G A R C H ( M S - P G A R C H ), and provide some probabilistic properties of this class of models. In particular, we address the question of strictly periodically...

QMLE of periodic bilinear models and of PARMA models with periodic bilinear innovations

Abdelouahab Bibi, Ahmed Ghezal (2018)

Kybernetika

This paper develops an asymptotic inference theory for bilinear B L time series models with periodic coefficients P B L for short . For this purpose, we establish firstly a necessary and sufficient conditions for such models to have a unique stationary and ergodic solutions (in periodic sense). Secondly, we examine the consistency and the asymptotic normality of the quasi-maximum likelihood estimator Q M L E under very mild moment condition for the innovation errors. As a result, it is shown that whenever the model is...

Ramanujan-Fourier series and the conjecture D of Hardy and Littlewood

H. Gopalakrishna Gadiyar, Ramanathan Padma (2014)

Czechoslovak Mathematical Journal

We give a heuristic proof of a conjecture of Hardy and Littlewood concerning the density of prime pairs to which twin primes and Sophie Germain primes are special cases. The method uses the Ramanujan-Fourier series for a modified von Mangoldt function and the Wiener-Khintchine theorem for arithmetical functions. The failing of the heuristic proof is due to the lack of justification of interchange of certain limits. Experimental evidence using computer calculations is provided for the plausibility...

Rate of convergence for a class of RCA estimators

Pavel Vaněček (2006)

Kybernetika

This work deals with Random Coefficient Autoregressive models where the error process is a martingale difference sequence. A class of estimators of unknown parameter is employed. This class was originally proposed by Schick and it covers both least squares estimator and maximum likelihood estimator for instance. Asymptotic behavior of such estimators is explored, especially the rate of convergence to normal distribution is established.

Regime-switching models of time series with cubic spline transition function in geodetic application

Tomáš Bognár, Jozef Komorník, Magda Komorníková (2004)

Kybernetika

A new class of Smooth Transition Autoregressive models, based on cubic spline type transition functions, has been introduced and subjected to comparison with models based on the traditional logistic transition functions. A very high degree of similarity between the two model classes has been demonstrated. The new class of models can be slightly preferable because of its more simple formal and geometrical structure that may enable users more convenient manipulation in statistical inference procedures....

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