Trimmed portmanteau test for linear processes with infinite variance

Moving Average Processes with Infinite Variance

The sample autocorrelation function (acf) of a stationary process has played a central statistical role in traditional time series analysis, where the assumption is made that the marginal distribution has a second moment. Now, the classical methods based on acf are not applicable in heavy tailed modeling. Using the codifference function as dependence measure for such processes be shown it be as...

Portmanteau Tests for Arma Models with Infinite Variance

Autoregressive and moving-average (ARMA) models with stable Paretian errors is one of the most studied models for time series with infinite variance. Estimation methods for these models have been studied by many researchers but the problem of diagnostic checking fitted models has not been addressed. In this paper, we develop portmanteau tests for checking randomness of a time series with infini...

Nonparametric density estimation for linear processes with infinite variance

We consider nonparametric estimation of marginal density functions of linear processes by using kernel density estimators. We assume that the innovation processes are i.i.d. and have infinite-variance. We present the asymptotic distributions of the kernel density estimators with the order of bandwidths fixed as h = cn−1/5, where n is the sample size. The asymptotic distributions depend on both ...

Linear Prediction of Arma Processes with Infinite Variance

In order to predict unobserved values of a linear process with infinite variance, we introduce a linear predictor which minimizes the dispersion (suitably defined) of the error distribution. When the linear process is driven by symmetric stable white noise this predictor minimizes the scale parameter of the error distribution. In the more general case when the driving white noise process has re...

Online Appendix for Portmanteau Tests for ARMA Models with Infinite Variance