The finite sample properties of the state space methods applied to long memory time series are analyzed through Monte Carlo simulations. The state space setup allows to introduce a novel modeling approach in the long memory framework, which directly tackles measurement errors and random level...

This paper estimates the stock market and its price dynamics in terms of the multifractional Brownian motion. In our analysis, we use the financial dataset of the Dow Jones Industrial Average (DJI) time series from March 2009 to June 2015. First, we briefly introduce the definitions and...

In this paper, we prove the validity of an Edgeworth expansion to the distribution of the Whittle maximum likelihood estimator for stationary long-memory Gaussian models with unknown parameter theta in Theta subset R^{d_theta) . The error of the (s-2)-order expansion is shown to be...

The aim of these notes is to revisit sequential Monte Carlo (SMC) sampling. SMC sampling is a powerful simulation tool for solving non-linear and/or non-Gaussian state space models. We illustrate this with several examples.

In recent years state space models, particularly the linear Gaussian version, have become the standard framework for analyzing macro-economic and financial data. However, many heoretically motivated models imply non-linear or non-Gaussian specifications – or both. Existing methods for...