In this correspondence, we prove that if X is a random variable with P(X=0)=0 and E|X|=∞, then there exists a continuous function G on (0,∞) with 0G(x)↑∞ and xG(x)↑∞ as 0x↑∞ such that E(|X|/G(|X|))=∞. An application of this result pertaining to the Kolmogorov strong law of...

We investigate the asymptotic behavior of the least squares estimator of the unknown parameters of random coefficient bifurcating autoregressive processes. Under suitable assumptions on inherited and environmental effects, we establish the almost sure convergence of our estimates. In addition,...

<Para ID="Par1">We study the asymptotic behavior of the weighted least squares estimators of the unknown parameters of bifurcating integer-valued autoregressive processes. Under suitable assumptions on the immigration, we establish the almost sure convergence of our estimators, together with a quadratic strong...</para>

A functional ARMA-GARCH model for predicting the value-at-risk of the EURUSD exchange rate is introduced. The model implements the yield curve differentials between EUR and the US as exogenous factors. Functional principal component analysis allows us to use the information of basically the...

Economic data are often generated by stochastic processes that take place in continuous time, though observations may occur only at discrete times. For example, electricity and gas consumption take place in continuous time. Data generated by a continuous time stochastic process are called...

Economic data are often generated by stochastic processes that take place in continuous time, though observations may occur only at discrete times. For example, electricity and gas consumption take place in continuous time. Data generated by a continuous time stochastic process are called...

Abstract A powerful tool for the analysis of nonrandomized observational studies has been the potential outcomes model. Utilization of this framework allows analysts to estimate average treatment effects. This article considers the situation in which high-dimensional covariates are present and...

Abstract We consider the problem of maximizing the utility of consumption and terminal wealth in a geometric Ornstein–Uhlenbeck market. We calculate the optimal consumption and wealth processes for power, logarithmic and exponential utility as well as their behavior depending e.g. on...

The objective of this dissertation is to develop a suitable statistical methodologyfor functional data analysis. Modern advanced technology allows researchers to collectsamples as functional which means the ideal unit of samples is a curve. We considereach functional observation as the resulting...

Semi-parametric and nonparametric modeling and inference have been widely studied duringthe last two decades. In this manuscript, we do statistical inference based on semi-parametricand nonparametric models in several different scenarios.Firstly, we develop a semi-parametric additivity test for...