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Estimation of a Regression Function on a Point Process and its Application to Financial Ruin Risk Forecast

Dia, Galaye, Kone, Abdoulaye (2009)

Serdica Mathematical Journal

2000 Mathematics Subject Classification: Primary 60G55; secondary 60G25.We estimate a regression function on a point process by the Tukey regressogram method in a general setting and we give an application in the case of a Risk Process. We show among other things that, in classical Poisson model with parameter r, if W is the amount of the claim with finite espectation E(W) = m, Sn (resp. Rn) the accumulated interval waiting time for successive claims (resp. the aggregate claims amount) up to the...

Estimation of variances in a heteroscedastic RCA(1) model

Hana Janečková (2002)

Kybernetika

The paper concerns with a heteroscedastic random coefficient autoregressive model (RCA) of the form X t = b t X t - 1 + Y t . Two different procedures for estimating σ t 2 = E Y t 2 , σ b 2 = E b t 2 or σ B 2 = E ( b t - E b t ) 2 , respectively, are described under the special seasonal behaviour of σ t 2 . For both types of estimators strong consistency and asymptotic normality are proved.

Exponential smoothing and resampling techniques in time series prediction

Maria Manuela Neves, Clara Cordeiro (2010)

Discussiones Mathematicae Probability and Statistics

Time series analysis deals with records that are collected over time. The objectives of time series analysis depend on the applications, but one of the main goals is to predict future values of the series. These values depend, usually in a stochastic manner, on the observations available at present. Such dependence has to be considered when predicting the future from its past, taking into account trend, seasonality and other features of the data. Some of the most successful forecasting methods are...

Exponential smoothing based on L-estimation

Přemysl Bejda, Tomáš Cipra (2015)

Kybernetika

Robust methods similar to exponential smoothing are suggested in this paper. First previous results for exponential smoothing in L 1 are generalized using the regression quantiles, including a generalization to more parameters. Then a method based on the classical sign test is introduced that should deal not only with outliers but also with level shifts, including a detection of change points. Properties of various approaches are investigated by means of a simulation study. A real data example is...

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