The Stochastics of Threshold Accepting: Analysis of an Application to the Uniform Design Problem

Threshold Accepting (TA) is a powerful optimization heuristic from the class of stochastic local search algorithms. It has been applied successfully to different optimization problems in statistics and econometrics, including the uniform design problem. Using the latter application as example, the stochastic properties of a TA implementation are analyzed. We provide a formal framework for the analysis of optimization heuristics like TA, which can be used to estimate lower bounds and to derive convergence results. It is also helpful for tuning real applications. Based on this framework, empirical results are presented for the uniform design problem. In particular, for two problem instances, the rate of convergence of the algorithm is estimated to be of the order of a power of -0.3 to -0.7 of the number of iterations. --Heuristic optimization,Threshold Accepting,Stochastic analysis of heuristics

Heuristic model selection for leading indicators in Russia and Germany

Business tendency survey indicators are widely recognized as a key instrument for business cycle forecasting. Their leading indicator property is assessed with regard to forecasting industrial production in Russia and Germany. For this purpose, vector autoregressive (VAR) models are specified and estimated to construct forecasts. As the potential number of lags included is large, we compare full–specified VAR models with subset models obtained using a Genetic Algorithm enabling ’holes’ in multivariate lag structures. The problem is complicated by the fact that a structural break and seasonal variation of indicators have to be taken into account. The models allow for a comparison of the dynamic adjustment and the forecasting performance of the leading indicators for both countries revealing marked differences between Russia and Germany.Leading indicators, business cycle forecasts, VAR, model selection, genetic algorithms

The convergence of optimization based estimators : theory and application to a GARCH-model

The convergence of estimators, e.g. maximum likelihood estimators, for increasing sample size is well understood in many cases. However, even when the rate of convergence of the estimator is known, practical application is hampered by the fact, that the estimator cannot always be obtained at tenable computational cost. This paper combines the analysis of convergence of the estimator itself with the analysis of the convergence of stochastic optimization algorithms, e.g. threshold accepting, to the theoretical estimator. We discuss the joint convergence of estimator and algorithm in a formal framework. An application to a GARCH-model demonstrates the approach in practice by estimating actual rates of convergence through a large scale simulation study. Despite of the additional stochastic component introduced by the use of an optimization heuristic, the overall quality of the estimates turns out to be superior compared to conventional approaches. --GARCH,Threshold Accepting,Optimization Heuristics,Convergence

The Economics of Crime: Investigating the Drugs-Crime Channel

The rising trends both in drug addiction and crime rates are of major public concern in Germany. Surprisingly, the economic theory of crime seems to ignore the drugs-crime nexus, whereas the criminological literature considers illicit drug use a main reason of criminal activities. This paper provides an econometric assessment of the drugs-crime channel within a Becker-Ehrlich model of crime supply. We analyse three different channels from drug abuse to crime: system-related, economic-related and pharmacological effects. Estimation with panel data from the German states allows us to take into account further factors that might influence both drug abuse and crime. The results indicate that drug offences have a significant impact, in particular on property crimes. We attribute this to a strong economic-related channel of drug abuse on crime.

Indirect Estimation of the Parameters of Agent Based Models of Financial Markets

Agent based models take into account limited rational behaviour of individuals acting on financial markets. Explicit simulation of this behaviour and the resulting interac-tion of individuals provide a description of aggregate financial market time series. Al-though the outcomes of such simulations often exhibit similarities with real financial market time series, methods for explicit validation are required. This paper proposes validation using simulation based indirect estimation. It uses typical characteristic moments of financial market data to assess the similarity of simulation outcomes. Fur-thermore, the parameters of the agent based models can be estimated by maximizing this similarity. The paper presents details of this estimation approach and first results for the US–$/DM exchange rate.Agent Based Models; Indirect Estimation; Validation

Least Median of Squares Estimation by Optimization Heuristics with an Application to the CAPM and Multi Factor Models

For estimating the parameters of models for financial market data, the use of robust techniques is of particular interest. Conditional forecasts, based on the capital asset pricing model, and a factor model are considered. It is proposed to consider least median of squares estimators as one possible alternative to ordinary least squares. Given the complexity of the objective function for the least median of squares estimator, the estimates are obtained by means of optimization heuristics. The performance of two heuristics is compared, namely differential evolution and threshold accepting. It is shown that these methods are well suited to obtain least median of squares estimators for real world problems. Furthermore, it is analyzed to what extent parameter estimates and conditional forecasts differ between the two estimators. The empirical analysis considers daily and monthly data on some stocks from the Dow Jones Industrial Average Index (DJIA).LMS, CAPM, Multi Factor Model, Differential Evolution, Threshold Accepting

Threshold Accepting for Credit Risk Assessment and Validation

According to the latest Basel framework of Banking Supervision, financial institutions should internally assign their borrowers into a number of homogeneous groups. Each group is assigned a probability of default which distinguishes it from other groups. This study aims at determining the optimal number and size of groups that allow for statistical ex post validation of the efficiency of the credit risk assignment system. Our credit risk assignment approach is based on Threshold Accepting, a local search optimization technique, which has recently performed reliably in credit risk clustering especially when considering several realistic constraints. Using a relatively large real-world retail credit portfolio, we propose a new technique to validate ex post the precision of the grading system.credit risk assignment, Threshold Accepting, statistical validation

Hedonic regression for digital cameras in Germany

Standard measures of consumer price inflation are based on a bundle of representative goods. It is well known that this approach might overstate inflation for new products and products with fast increasing quality. For this reason, hedonic adjustment methods have been proposed and introduced in official statistics for some products like personal computers. In this contribution, we consider the application of a hedonic regression to digital cameras, which have been introduced in the product bundle of the German consumer price index in 2003 – so far without hedonic quality adjustment. We present first results on hedonic price measurement for digital cameras in Germany for the time period 1999 to 2004. The results are based on data sampled from public interest journals and advertisements. --Hedonic regression,hedonic price index,quality adjustment

The Stochastics of Threshold Accepting: Analysis of an Application to the Uniform Design Problem

Threshold Accepting (TA) is a powerful optimization heuristic from the class of stochastic local search algorithms. It has been applied successfully to different optimization problems in statistics and econometrics, including the uniform design problem. Using the latter application as example, the stochastic properties of a TA implementation are analyzed. We provide a formal framework for the analysis of optimization heuristics like TA, which can be used to estimate lower bounds and to derive convergence results. It is also helpful for tuning real applications. Based on this framework, empirical results are presented for the uniform design problem. In particular, for two problem instances, the rate of convergence of the algorithm is estimated to be of the order of a power of -0.3 to -0.7 of the number of iterations