ARMA Models for Mortality Forecast

Robust Estimation for Arma Models

This paper introduces a new class of robust estimates for ARMA models. They are M-estimates, but the residuals are computed so the effect of one outlier is limited to the period where it occurs. These estimates are closely related to those based on a robust filter, but they have two important advantages: they are consistent and the asymptotic theory is tractable. We perform a Monte Carlo where ...

R-estimation for Arma Models

This paper is devoted to the R-estimation problem for the parameter of a stationary ARMA model. The asymptotic uniform linearity of a suitable vector of rank statistics leads to the asymptotic normality of √ n-consistent R-estimates resulting from the minimization of the norm of this vector. By using a discretized √ n-consistent preliminary estimate, we construct a new class of one-step R-estim...

Lecture 2 : ARMA Models ∗ 1 ARMA Process

As we have remarked, dependence is very common in time series observations. To model this time series dependence, we start with univariate ARMA models. To motivate the model, basically we can track two lines of thinking. First, for a series xt, we can model that the level of its current observations depends on the level of its lagged observations. For example, if we observe a high GDP realizati...

Kernel smoothed prediction intervals for ARMA models

Asymptotic results for spatial causal ARMA models

The paper establishes a functional central limit theorem for the empirical distribution function of a stationary, causal, ARMA process given by Xs,t = i≥0 j≥0 a i,j ξ s−i,t−j , (s, t) ∈ Z 2 , where the ξ i,j are independent and identically distributed, zero mean innovations. By judicious choice of σ−fields and element enumeration, one dimensional martingale arguments are employed to establish t...