Detection of multiplicative noise in stationary random processes using second- and higher order statistics

This paper addresses the problem of detecting the presence of colored multiplicative noise, when the information process can be modeled as a parametric ARMA process. For the case of zero-mean multiplicative noise, a cumulant based suboptimal detector is studied. This detector tests the nullity of a specific cumulant slice. A second detector is developed when the multiplicative noise is nonzero mean. This detector consists of filtering the data by an estimated AR filter. Cumulants of the residual data are then shown to be well suited to the detection problem. Theoretical expressions for the asymptotic probability of detection are given. Simulation-derived finite-sample ROC curves are shown for different sets of model parameters

Bibliographic Review on Distributed Kalman Filtering

In recent years, a compelling need has arisen to understand the effects of distributed information structures on estimation and filtering. In this paper, a bibliographical review on distributed Kalman filtering (DKF) is provided.\ud The paper contains a classification of different approaches and methods involved to DKF. The applications of DKF are also discussed and explained separately. A comparison of different approaches is briefly carried out. Focuses on the contemporary research are also addressed with emphasis on the practical applications of the techniques. An exhaustive list of publications, linked directly or indirectly to DKF in the open literature, is compiled to provide an overall picture of different developing aspects of this area

Combining long memory and level shifts in modeling and forecasting the volatility of asset returns

We propose a parametric state space model of asset return volatility with an accompanying estimation and forecasting framework that allows for ARFIMA dynamics, random level shifts and measurement errors. The Kalman filter is used to construct the state-augmented likelihood function and subsequently to generate forecasts, which are mean- and path-corrected. We apply our model to eight daily volatility series constructed from both high-frequency and daily returns. Full sample parameter estimates reveal that random level shifts are present in all series. Genuine long memory is present in high-frequency measures of volatility whereas there is little remaining dynamics in the volatility measures constructed using daily returns. From extensive forecast evaluations, we find that our ARFIMA model with random level shifts consistently belongs to the 10% Model Confidence Set across a variety of forecast horizons, asset classes, and volatility measures. The gains in forecast accuracy can be very pronounced, especially at longer horizons

Combining long memory and level shifts in modeling and forecasting the volatility of asset returns

We propose a parametric state space model of asset return volatility with an accompanying estimation and forecasting framework that allows for ARFIMA dynamics, random level shifts and measurement errors. The Kalman filter is used to construct the state-augmented likelihood function and subsequently to generate forecasts, which are mean and path-corrected. We apply our model to eight daily volatility series constructed from both high-frequency and daily returns. Full sample parameter estimates reveal that random level shifts are present in all series. Genuine long memory is present in most high-frequency measures of volatility, whereas there is little remaining dynamics in the volatility measures constructed using daily returns. From extensive forecast evaluations, we find that our ARFIMA model with random level shifts consistently belongs to the 10% Model Confidence Set across a variety of forecast horizons, asset classes and volatility measures. The gains in forecast accuracy can be very pronounced, especially at longer horizons