State Estimation with Sets of Densities considering Stochastic and Systematic Errors

In practical applications, state estimation requires the consideration of stochastic and systematic errors. If both error types are present, an exact probabilistic description of the state estimate is not possible, so that common Bayesian estimators have to be questioned. This paper introduces a theoretical concept, which allows for incorporating unknown but bounded errors into a Bayesian inference scheme by utilizing sets of densities. In order to derive a tractable estimator, the Kalman filter is applied to ellipsoidal sets of means, which are used to bound additive systematic errors. Also, an extension to nonlinear system and observation models with ellipsoidal error bounds is presented. The derived estimator is motivated by means of two example applications

Pricing stock options under stochastic volatility and interest rates with efficient method of moments estimation

While the stochastic volatility (SV) generalization has been shown to improve the explanatory power over the Black-Scholes model, empirical implications of SV models on option pricing have not yet been adequately tested. The purpose of this paper is to first estimate a multivariate SV model using the efficient method of moments (EMM) technique from observations of underlying state variables and then investigate the respective effect of stochastic interest rates, systematic volatility and idiosyncratic volatility on option prices. We compute option prices using reprojected underlying historical volatilities and implied stochastic volatility risk to gauge each model’s performance through direct comparison with observed market option prices. Our major empirical findings are summarized as follows. First, while theory predicts that the short-term interest rates are strongly related to the systematic volatility of the consumption process, our estimation results suggest that the short-term interest rate fails to be a good proxy of the systematic volatility factor; Second, while allowing for stochastic volatility can reduce the pricing errors and allowing for asymmetric volatility or leverage effect does help to explain the skewness of the volatility smile, allowing for stochastic interest rates has minimal impact on option prices in our case; Third, similar to Melino and Turnbull (1990), our empirical findings strongly suggest the existence of a non-zero risk premium for stochastic volatility of stock returns. Based on implied volatility risk, the SV models can largely reduce the option pricing errors, suggesting the importance of incorporating the information in the options market in pricing options; Finally, both the model diagnostics and option pricing errors in our study suggest that the Gaussian SV model is not sufficient in modeling short-term kurtosis of asset returns, a SV model with fatter-tailed noise or jump component may have better explanatory power.

Robust scaling in fusion science: case study for the L-H power threshold

In regression analysis for deriving scaling laws in the context of fusion studies, standard regression methods are usually applied, of which ordinary least squares (OLS) is the most popular. However, concerns have been raised with respect to several assumptions underlying OLS in its application to fusion data. More sophisticated statistical techniques are available, but they are not widely used in the fusion community and, moreover, the predictions by scaling laws may vary significantly depending on the particular regression technique. Therefore we have developed a new regression method, which we call geodesic least squares regression (GLS), that is robust in the presence of significant uncertainty on both the data and the regression model. The method is based on probabilistic modeling of all variables involved in the scaling expression, using adequate probability distributions and a natural similarity measure between them (geodesic distance). In this work we revisit the scaling law for the power threshold for the L-to-H transition in tokamaks, using data from the multi-machine ITPA databases. Depending on model assumptions, OLS can yield different predictions of the power threshold for ITER. In contrast, GLS regression delivers consistent results. Consequently, given the ubiquity and importance of scaling laws and parametric dependence studies in fusion research, GLS regression is proposed as a robust and easily implemented alternative to classic regression techniques

Estimating Fiscal Multipliers: News From A Non-linear World

open4siCaggiano acknowledges the financial support received by the Visiting Research Scholar programme offered by the University of MelbourneWe estimate non-linear VARs to assess to what extent fiscal spending multipliers are countercyclical in the US. We deal with the issue of non-fundamentalness due to fiscal foresight by appealing to sums of revisions of expectations of fiscal expenditures. This measure of anticipated fiscal shocks is shown to carry valuable information about future dynamics of public spending. Results based on generalised impulse responses suggest that fiscal spending multipliers in recessions are greater than one, but not statistically larger than those in expansions. However, non-linearities arise when focusing on 'extreme' events, that is, deep recessions versus strong expansionary periods.openCaggiano, Giovanni; Castelnuovo, Efrem; Colombo, Valentina; Nodari, GabrielaCaggiano, Giovanni; Castelnuovo, Efrem; Colombo, Valentina; Nodari, Gabriel

Spatial snow water equivalent estimation for mountainous areas using wireless-sensor networks and remote-sensing products

We developed an approach to estimate snow water equivalent (SWE) through interpolation of spatially representative point measurements using a k-nearest neighbors (k-NN) algorithm and historical spatial SWE data. It accurately reproduced measured SWE, using different data sources for training and evaluation. In the central-Sierra American River basin, we used a k-NN algorithm to interpolate data from continuous snow-depth measurements in 10 sensor clusters by fusing them with 14 years of daily 500-m resolution SWE-reconstruction maps. Accurate SWE estimation over the melt season shows the potential for providing daily, near real-time distributed snowmelt estimates. Further south, in the Merced-Tuolumne basins, we evaluated the potential of k-NN approach to improve real-time SWE estimates. Lacking dense ground-measurement networks, we simulated k-NN interpolation of sensor data using selected pixels of a bi-weekly Lidar-derived snow water equivalent product. k-NN extrapolations underestimate the Lidar-derived SWE, with a maximum bias of −10 cm at elevations below 3000 m and +15 cm above 3000 m. This bias was reduced by using a Gaussian-process regression model to spatially distribute residuals. Using as few as 10 scenes of Lidar-derived SWE from 2014 as training data in the k-NN to estimate the 2016 spatial SWE, both RMSEs and MAEs were reduced from around 20–25 cm to 10–15 cm comparing to using SWE reconstructions as training data. We found that the spatial accuracy of the historical data is more important for learning the spatial distribution of SWE than the number of historical scenes available. Blending continuous spatially representative ground-based sensors with a historical library of SWE reconstructions over the same basin can provide real-time spatial SWE maps that accurately represents Lidar-measured snow depth; and the estimates can be improved by using historical Lidar scans instead of SWE reconstructions