
on Econometric Time Series 
By:  Riccardo DiCecio; Michael T. Owyang 
Abstract:  Since Galí [1999], longrun restricted VARs have become the standard for identifying the effects of technology shocks. In a recent paper, Francis et al. [2008] proposed an alternative to identify technology as the shock that maximizes the forecasterror variance share of labor productivity at long horizons. In this paper, we propose a variant of the Max Share identification, which focuses on maximizing the variance share of labor productivity in the frequency domain. We consider the responses to technology shocks identified from various frequency bands. Two distinct technology shocks emerge. An expansionary shock increases productivity, output, and hours at businesscycle frequencies. The technology shock that maximizes productivity in the medium and long runs instead has clear contractionary effects on hours, while increasing output and productivity. 
Keywords:  Business cycles ; Technology  Economic aspects ; Productivity 
Date:  2010 
URL:  http://d.repec.org/n?u=RePEc:fip:fedlwp:2010025&r=ets 
By:  Gareth W. Peters; Balakrishnan B. Kannan; Ben Lasscock; Chris Mellen; Simon Godsill 
Abstract:  We consider a statistical model for pairs of traded assets, based on a Cointegrated Vector Auto Regression (CVAR) Model. We extend standard CVAR models to incorporate estimation of model parameters in the presence of price series level shifts which are not accurately modeled in the standard Gaussian error correction model (ECM) framework. This involves developing a novel matrix variate Bayesian CVAR mixture model comprised of Gaussian errors intraday and Alphastable errors interday in the ECM framework. To achieve this we derive a novel conjugate posterior model for the Scaled Mixtures of Normals (SMiN CVAR) representation of Alphastable interday innovations. These results are generalized to asymmetric models for the innovation noise at interday boundaries allowing for skewed Alphastable models. Our proposed model and sampling methodology is general, incorporating the current literature on Gaussian models as a special subclass and also allowing for price series level shifts either at random estimated time points or known a priori time points. We focus analysis on regularly observed nonGaussian level shifts that can have significant effect on estimation performance in statistical models failing to account for such level shifts, such as at the close and open of markets. We compare the estimation accuracy of our model and estimation approach to standard frequentist and Bayesian procedures for CVAR models when nonGaussian price series level shifts are present in the individual series, such as interday boundaries. We fit a bivariate Alphastable model to the interday jumps and model the effect of such jumps on estimation of matrixvariate CVAR model parameters using the likelihood based Johansen procedure and a Bayesian estimation. We illustrate our model and the corresponding estimation procedures we develop on both synthetic and actual data. 
Date:  2010–08 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:1008.0149&r=ets 
By:  Peter Imkeller; Anthony Reveillac; Anja Richter 
Abstract:  In this paper we consider a class of BSDEs with drivers of quadratic growth, on a stochastic basis generated by continuous local martingales. We first derive the Markov property of a forwardbackward system (FBSDE) if the generating martingale is a strong Markov process. Then we establish the differentiability of a FBSDE with respect to the initial value of its forward component. This enables us to obtain the main result of this article, namely a representation formula for the control component of its solution. The latter is relevant in the context of securitization of random liabilities arising from exogenous risk, which are optimally hedged by investment in a given financial market with respect to exponential preferences. In a purely stochastic formulation, the control process of the backward component of the FBSDE steers the system into the random liability, and describes its optimal derivative hedge by investment in the capital market the dynamics of which is given by the forward component. The representation formula of the main result describes this delta hedge in terms of the derivative of the BSDE's solution process on the one hand, and the correlation structure of the internal uncertainty captured by the forward process and the external uncertainty responsible for the market incompleteness on the other hand. The formula extends the scope of validity of the results obtained by several authors in the Brownian setting. It is designed to extend a genuinely stochastic representation of the optimal replication in cross hedging insurance derivatives from the classical BlackScholes model to incomplete markets on general stochastic bases. In this setting, Malliavin's calculus which is required in the Brownian framework is replaced by new tools based on techniques related to a calculus of quadratic covariations of basis martingales. 
Date:  2009–07 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:0907.0941&r=ets 