Sufficiently informative measurements for stability of approximate conditional mean estimates

This paper establishes sufficient conditions to bound the error in perturbed conditional mean estimates derived from a perturbed model (only the scalar case is shown in this paper but a similar result is expected to hold for the vector case). The results established here extend recent stability results on approximating information state filter recursions to stability results on the approximate conditional mean estimates. The presented filter stability results provide bounds for a wide variety of model error situations.

Conditional mean functions of non-linear models of US output

We compare a number of models of post War US output growth in terms of the degree and pattern of non-linearity they impart to the conditional mean, where we condition on either the previous period's growth rate, or the previous two periods' growth rates. The conditional means are estimated non-parametrically using a nearest-neighbour technique on data simulated from the models. In this way, we condense the complex, dynamic, responses that may be present in to graphical displays of the implied conditional mean.

Conditional Moments in Asset Pricing

A better understanding of stock price changes is important in guiding many economic activities. Since prices often do not change without good reasons, searching for related explanatory variables has involved many enthusiasts. This book seeks answers from prices per se by relating price changes to their conditional moments. This is based on the belief that prices are the products of a complex psychological and economic process and their conditional moments derive ultimately from these psychological and economic shocks. Utilizing information about conditional moments hence makes it an attractive alternative to using other selective financial variables in explaining price changes. The first paper examines the relation between the conditional mean and the conditional variance using information about moments in three types of conditional distributions; it finds that the significance of the estimated mean and variance ratio can be affected by the assumed distributions and the time variations in skewness. The second paper decomposes the conditional industry volatility into a concurrent market component and an industry specific component; it finds that market volatility is on average responsible for a rather small share of total industry volatility — 6 to 9 percent in UK and 2 to 3 percent in Germany. The third paper looks at the heteroskedasticity in stock returns through an ARCH process supplemented with a set of conditioning information variables; it finds that the heteroskedasticity in stock returns allows for several forms of heteroskedasticity that include deterministic changes in variances due to seasonal factors, random adjustments in variances due to market and macro factors, and ARCH processes with past information. The fourth paper examines the role of higher moments — especially skewness and kurtosis — in determining the expected returns; it finds that total skewness and total kurtosis are more relevant non-beta risk measures and that they are costly to be diversified due either to the possible eliminations of their desirable parts or to the unsustainability of diversification strategies based on them.

Short-Horizon Asymmetric Mean-Reversion and Overreactions: Evidence from the Nordic Stock Markets

This paper examines the asymmetric behavior of conditional mean and variance. Short-horizon mean-reversion behavior in mean is modeled with an asymmetric nonlinear autoregressive model, and the variance is modeled with an Exponential GARCH in Mean model. The results of the empirical investigation of the Nordic stock markets indicates that negative returns revert faster to positive returns when positive returns generally persist longer. Asymmetry in both mean and variance can be seen on all included markets and are fairly similar. Volatility rises following negative returns more than following positive returns which is an indication of overreactions. Negative returns lead to increased variance and positive returns leads even to decreased variance.

Assessment of conditional moment closure models of turbulent autoignition using DNS data

A systematic assessment of the submodels of conditional moment closure (CMC) formalism for the autoignition problem is carried out using direct numerical simulation (DNS) data. An initially non-premixed, n-heptane/air system, subjected to a three-dimensional, homogeneous, isotropic, and decaying turbulence, is considered. Two kinetic schemes, (1) a one-step and (2) a reduced four-step reaction mechanism, are considered for chemistry An alternative formulation is developed for closure of the mean chemical source term , based on the condition that the instantaneous fluctuation of excess temperature is small. With this model, it is shown that the CMC equations describe the autoignition process all the way up to near the equilibrium limit. The effect of second-order terms (namely, conditional variance of temperature excess sigma(2) and conditional correlations of species q(ij)) in modeling is examined. Comparison with DNS data shows that sigma(2) has little effect on the predicted conditional mean temperature evolution, if the average conditional scalar dissipation rate is properly modeled. Using DNS data, a correction factor is introduced in the modeling of nonlinear terms to include the effect of species fluctuations. Computations including such a correction factor show that the species conditional correlations q(ij) have little effect on model predictions with a one-step reaction, but those q(ij) involving intermediate species are found to be crucial when four-step reduced kinetics is considered. The "most reactive mixture fraction" is found to vary with time when a four-step kinetics is considered. First-order CMC results are found to be qualitatively wrong if the conditional mean scalar dissipation rate is not modeled properly. The autoignition delay time predicted by the CMC model compares excellently with DNS results and shows a trend similar to experimental data over a range of initial temperatures.

Conditional Moment Closure for Turbulent Premixed Flames

The conditional moment closure (CMC) method has been successfully applied to various non-premixed combustion systems in the past, but its application to premixed flames is not fully tested and validated. The main difficulty is associated with the modeling of conditional scalar dissipation rate of the conditioning scalar, the progress variable. A simple algebraic model for the conditional dissipation rate is validated using DNS results of a V-flame. This model along with the standard k- turbulence modeling is used in computations of stoichiometric pilot stabilized Bunsen flames using the RANS-CMC method. A first-order closure is used for the conditional mean reaction rate. The computed non reacting and reacting scalars are in reasonable agreement with the experimental measurements and are consistent with earlier computations using flamelets and transported PDF methods. Sensitivity to chemical kinetic mechanism is also assessed. The results suggest that the CMC may be applied across the regimes of premixed combustion.

Conditional Moment Closure for Turbulent Premixed Flames

The conditional moment closure (CMC) method has been successfully applied to various non-premixed combustion systems in the past, but its application to premixed flames is not fully tested and validated. The main difficulty is associated with the modeling of conditional scalar dissipation rate of the conditioning scalar, the progress variable. A simple algebraic model for the conditional dissipation rate is validated using DNS results of a V-flame. This model along with the standard k- turbulence modeling is used in computations of stoichiometric pilot stabilized Bunsen flames using the RANS-CMC method. A first-order closure is used for the conditional mean reaction rate. The computed non reacting and reacting scalars are in reasonable agreement with the experimental measurements and are consistent with earlier computations using flamelets and transported PDF methods. Sensitivity to chemical kinetic mechanism is also assessed. The results suggest that the CMC may be applied across the regimes of premixed combustion.

Computations of turbulent lean premixed combustion using conditional moment closure

Conditional Moment Closure (CMC) is a suitable method for predicting scalars such as carbon monoxide with slow chemical time scales in turbulent combustion. Although this method has been successfully applied to non-premixed combustion, its application to lean premixed combustion is rare. In this study the CMC method is used to compute piloted lean premixed combustion in a distributed combustion regime. The conditional scalar dissipation rate of the conditioning scalar, the progress variable, is closed using an algebraic model and turbulence is modelled using the standard k-e{open} model. The conditional mean reaction rate is closed using a first order CMC closure with the GRI-3.0 chemical mechanism to represent the chemical kinetics of methane oxidation. The PDF of the progress variable is obtained using a presumed shape with the Beta function. The computed results are compared with the experimental measurements and earlier computations using the transported PDF approach. The results show reasonable agreement with the experimental measurements and are consistent with the transported PDF computations. When the compounded effects of shear-turbulence and flame are strong, second order closures may be required for the CMC. © 2013 Copyright Taylor and Francis Group, LLC.

Prediction in dynamic models with time-dependent conditional variances

This paper considers forecasting the conditional mean and variance from a single-equation dynamic model with autocorrelated disturbances following an ARMA process, and innovations with time-dependent conditional heteroskedasticity as represented by a linear GARCH process. Expressions for the minimum MSE predictor and the conditional MSE are presented. We also derive the formula for all the theoretical moments of the prediction error distribution from a general dynamic model with GARCH(1, 1) innovations. These results are then used in the construction of ex ante prediction confidence intervals by means of the Cornish-Fisher asymptotic expansion. An empirical example relating to the uncertainty of the expected depreciation of foreign exchange rates illustrates the usefulness of the results. © 1992.

Conditional labour supply, quantile functions in Brazil

The estimation of labor supply elasticities has been an important issue m the economic literature. Yet all works have estimated conditional mean labor supply functions only. The objective of this paper is to obtain more information on labor supply, by estimating the conditional quantile labor supply function. vI/e use a sample of prime age urban males employees in Brazil. Two stage estimators are used as the net wage and virtual income are found to be endogenous to the model. Contrary to previous works using conditional mean estimators, it is found that labor supply elasticities vary significantly and asymmetrically across hours of work. vVhile the income and wage elasticities at the standard work week are zero, for those working longer hours the elasticities are negative.

Estimating conditional volatility with neural networks

It is well known that one of the obstacles to effective forecasting of exchange rates is heteroscedasticity (non-stationary conditional variance). The autoregressive conditional heteroscedastic (ARCH) model and its variants have been used to estimate a time dependent variance for many financial time series. However, such models are essentially linear in form and we can ask whether a non-linear model for variance can improve results just as non-linear models (such as neural networks) for the mean have done. In this paper we consider two neural network models for variance estimation. Mixture Density Networks (Bishop 1994, Nix and Weigend 1994) combine a Multi-Layer Perceptron (MLP) and a mixture model to estimate the conditional data density. They are trained using a maximum likelihood approach. However, it is known that maximum likelihood estimates are biased and lead to a systematic under-estimate of variance. More recently, a Bayesian approach to parameter estimation has been developed (Bishop and Qazaz 1996) that shows promise in removing the maximum likelihood bias. However, up to now, this model has not been used for time series prediction. Here we compare these algorithms with two other models to provide benchmark results: a linear model (from the ARIMA family), and a conventional neural network trained with a sum-of-squares error function (which estimates the conditional mean of the time series with a constant variance noise model). This comparison is carried out on daily exchange rate data for five currencies.

Conditional volatility and firm size:an empirical analysis of UK equity portfolios

The techniques and insights from two distinct areas of financial economic modelling are combined to provide evidence of the influence of firm size on the volatility of stock portfolio returns. Portfolio returns are characterized by positive serial correlation induced by the varying levels of non-synchronous trading among the component stocks. This serial correlation is greatest for portfolios of small firms. The conditional volatility of stock returns has been shown to be well represented by the GARCH family of statistical processes. Using a GARCH model of the variance of capitalization-based portfolio returns, conditioned on the autocorrelation structure in the conditional mean, striking differences related to firm size are uncovered.

Relative entropy rate based multiple hidden Markov Model Approximation

This paper proposes a novel relative entropy rate (RER) based approach for multiple HMM (MHMM) approximation of a class of discrete-time uncertain processes. Under different uncertainty assumptions, the model design problem is posed either as a min-max optimisation problem or stochastic minimisation problem on the RER between joint laws describing the state and output processes (rather than the more usual RER between output processes). A suitable filter is proposed for which performance results are established which bound conditional mean estimation performance and show that estimation performance improves as the RER is reduced. These filter consistency and convergence bounds are the first results characterising multiple HMM approximation performance and suggest that joint RER concepts provide a useful model selection criteria. The proposed model design process and MHMM filter are demonstrated on an important image processing dim-target detection problem.

Experimental investigation of a turbulent reacting plume

An experimental investigation has been made of a round, non-buoyant plume of nitric oxide, NO, in a turbulent grid flow of ozone, 03, using the Turbulent Smog Chamber at the University of Sydney. The measurements have been made at a resolution not previously reported in the literature. The reaction is conducted at non-equilibrium so there is significant interaction between turbulent mixing and chemical reaction. The plume has been characterized by a set of constant initial reactant concentration measurements consisting of radial profiles at various axial locations. Whole plume behaviour can thus be characterized and parameters are selected for a second set of fixed physical location measurements where the effects of varying the initial reactant concentrations are investigated. Careful experiment design and specially developed chemilurninescent analysers, which measure fluctuating concentrations of reactive scalars, ensure that spatial and temporal resolutions are adequate to measure the quantities of interest. Conserved scalar theory is used to define a conserved scalar from the measured reactive scalars and to define frozen, equilibrium and reaction dominated cases for the reactive scalars. Reactive scalar means and the mean reaction rate are bounded by frozen and equilibrium limits but this is not always the case for the reactant variances and covariances. The plume reactant statistics are closer to the equilibrium limit than those for the ambient reactant. The covariance term in the mean reaction rate is found to be negative and significant for all measurements made. The Toor closure was found to overestimate the mean reaction rate by 15 to 65%. Gradient model turbulent diffusivities had significant scatter and were not observed to be affected by reaction. The ratio of turbulent diffusivities for the conserved scalar mean and that for the r.m.s. was found to be approximately 1. Estimates of the ratio of the dissipation timescales of around 2 were found downstream. Estimates of the correlation coefficient between the conserved scalar and its dissipation (parallel to the mean flow) were found to be between 0.25 and the significant value of 0.5. Scalar dissipations for non-reactive and reactive scalars were found to be significantly different. Conditional statistics are found to be a useful way of investigating the reactive behaviour of the plume, effectively decoupling the interaction of chemical reaction and turbulent mixing. It is found that conditional reactive scalar means lack significant transverse dependence as has previously been found theoretically by Klimenko (1995). It is also found that conditional variance around the conditional reactive scalar means is relatively small, simplifying the closure for the conditional reaction rate. These properties are important for the Conditional Moment Closure (CMC) model for turbulent reacting flows recently proposed by Klimenko (1990) and Bilger (1993). Preliminary CMC model calculations are carried out for this flow using a simple model for the conditional scalar dissipation. Model predictions and measured conditional reactive scalar means compare favorably. The reaction dominated limit is found to indicate the maximum reactedness of a reactive scalar and is a limiting case of the CMC model. Conventional (unconditional) reactive scalar means obtained from the preliminary CMC predictions using the conserved scalar p.d.f. compare favorably with those found from experiment except where measuring position is relatively far upstream of the stoichiometric distance. Recommendations include applying a full CMC model to the flow and investigations both of the less significant terms in the conditional mean species equation and the small variation of the conditional mean with radius. Forms for the p.d.f.s, in addition to those found from experiments, could be useful for extending the CMC model to reactive flows in the atmosphere.

Forecasting time-varying value-at-risk

In this thesis we are interested in financial risk and the instrument we want to use is Value-at-Risk (VaR). VaR is the maximum loss over a given period of time at a given confidence level. Many definitions of VaR exist and some will be introduced throughout this thesis. There two main ways to measure risk and VaR: through volatility and through percentiles. Large volatility in financial returns implies greater probability of large losses, but also larger probability of large profits. Percentiles describe tail behaviour. The estimation of VaR is a complex task. It is important to know the main characteristics of financial data to choose the best model. The existing literature is very wide, maybe controversial, but helpful in drawing a picture of the problem. It is commonly recognised that financial data are characterised by heavy tails, time-varying volatility, asymmetric response to bad and good news, and skewness. Ignoring any of these features can lead to underestimating VaR with a possible ultimate consequence being the default of the protagonist (firm, bank or investor). In recent years, skewness has attracted special attention. An open problem is the detection and modelling of time-varying skewness. Is skewness constant or there is some significant variability which in turn can affect the estimation of VaR? This thesis aims to answer this question and to open the way to a new approach to model simultaneously time-varying volatility (conditional variance) and skewness. The new tools are modifications of the Generalised Lambda Distributions (GLDs). They are four-parameter distributions, which allow the first four moments to be modelled nearly independently: in particular we are interested in what we will call para-moments, i.e., mean, variance, skewness and kurtosis. The GLDs will be used in two different ways. Firstly, semi-parametrically, we consider a moving window to estimate the parameters and calculate the percentiles of the GLDs. Secondly, parametrically, we attempt to extend the GLDs to include time-varying dependence in the parameters. We used the local linear regression to estimate semi-parametrically conditional mean and conditional variance. The method is not efficient enough to capture all the dependence structure in the three indices —ASX 200, S&P 500 and FT 30—, however it provides an idea of the DGP underlying the process and helps choosing a good technique to model the data. We find that GLDs suggest that moments up to the fourth order do not always exist, there existence appears to vary over time. This is a very important finding, considering that past papers (see for example Bali et al., 2008; Hashmi and Tay, 2007; Lanne and Pentti, 2007) modelled time-varying skewness, implicitly assuming the existence of the third moment. However, the GLDs suggest that mean, variance, skewness and in general the conditional distribution vary over time, as already suggested by the existing literature. The GLDs give good results in estimating VaR on three real indices, ASX 200, S&P 500 and FT 30, with results very similar to the results provided by historical simulation.