Prof. Dr. Wolfgang Schmid

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Forschungsschwerpunkte

Statistics in Finance

In finance, a portfolio is a collection of investments held by an institution or a private individual. In building up an investment portfolio a financial institution will typically conduct its own investment analysis, whilst a private individual may make use of the services of a financial advisor or a financial institution which offers portfolio management services. Holding a portfolio is part of an investment and risk-limiting strategy called diversification. By owning several assets, certain types of risk (in particular specific risk) can be reduced. The assets in the portfolio could include stocks, bonds, options, warrants, gold certificates, real estate, futures contracts, production facilities, or any other item that is expected to retain its value. Portfolio management involves deciding what assets to include in the portfolio, given the goals of the portfolio owner and changing economic conditions. Selection involves deciding what assets to purchase, how many to purchase, when to purchase them, and what assets to divest. These decisions always involve some sort of performance measurement, most typically expected return on the portfolio, and the risk associated with this return (i.e. the standard deviation of the return). Typically the expected return from portfolios comprised of different asset bundles are compared. The unique goals and circumstances of the investor must also be considered. Some investors are more risk averse than others. Mutual funds have developed particular techniques to optimize their portfolio holdings. See fund management for details.

Statistical Process Control

The objective of Statistical Process Control (SPC), is to detect changes in a process that may result from uncontrollable an predictable causes at unknown times. The most important tools for monitoring data are control charts. In principle, a control chart is a decision rule which signals that the process has changed if the control statistic lies outside the control limits. The first control charts were introduced by Shewhart (1926, 1931). Since this pioneering work many other control schemes have been introduced, such as the cumulative sum (CUSUM) chart of Page (1954) and the exponentially weighted moving average (EWMA) chart of Roberts (1959).

Up to the end of the 1980s one of the basic assumptions of nearly all papers was that the underlying observations are independent over time. Only some papers dealt with dependence problem. Goldsmith and Whitfield (1961) investigated the influence of correlation on the CUSUM chart by Monte Carlo simulations. In the same year Page (1961) mentioned: 'The effects of correlated observations have been examined in one case by Goldsmith and Whitfield; wider study is desirable. ' The problem was addressed but one had to wait over 10 years more for the next papers. Then, Bagshaw and Johnson (1974, 1975, 1977) approximated the CUSUM statistic for correlated data by Brownian motion. Rowlands (1976) studied the performance of CUSUM schemes for AR(1) and ARMA (1,1) data (cf. Rowlands and Wetherill (1991)). Furthermore, Nikiforov (1975, 79, 83, 84) wrote a lot about CUSUM charts for ARIMA data. Finally, Vasilopoulos and Stamboulis (1978) proposed modified alart limits for the Shewhart chart in case of dependent data.

 After the more theoretical oriented period of dealing with dependence of the data, in recent years it has been pointed out that quite often the independence assumption is incorrect. Wetherill (1977) reminded in his monography, that observations from modern industrial process are often autocorrelated. Then, in the end of the 1980s treating the dependence problem became very popular. Alwan (1989) analyzed 235 datasets which were frequently used as (standard) SPC examples. It turned out that in about 85% the control limits were misplaced. In nearly the half of these cases neglected correlation was responsible. Now, the problem was realized as severe.

Besides assessing these strong effects of correlation on the control charts as quality control tools in industrial statistics, one has to consider correlation as a typical pattern of data which we can find in medicine, environmental and financial statistics, and in automatic control in engineering. Here time series models are standard.

Many of our papers deal with 'Statistical process control for time series' where recently research is done in the following directions:Monitoring highdimensional time series (O.Bodnar, W.Schmid)
Application of control charts for finance (V. Golosnoy, Y. Okhrin, W. Schmid, I. Yatsyshynets, S. Ragulin)
Characterization of control charts using stochastic ordering (Y. Okhrin, W. Schmid, M. Morais, A. Pacheco)

Environmental Statistics

Environmental statistics are nowadays becoming an interesting field for research. Air pollution, global warming, wind-dynamics, surface structure analysis in nano-space are of interest in environmental statistics.

Many of the well understood models in the area of time-series analysis have to be adapted to spatio-temporal problems such as processes of air pollution.

Publikationen

Ausgewählte Publikationen

Estimation of the global minimum variance portfolio in high dimensions (with T. Bodnar and N. Parolya).

Detection of spatial change points in mean and covariances of multivariate simultaneous autoregressive models, Biometrical Journal, 2016 (with P. Otto).

Spatiotemporal analysis of German real-estate prices, Annals of Regional Science, 2016 (with P. Otto).

Monitoring means and covariances of multivariate nonlinear time series with heavy tails, appears in Communications in Statistics - Theory and Methods, 2015 ( with R. Garthoff).

Multivariate autoregressive extreme value process and its application for modeling the time series properties of the daily asset prices, appears in Communications in Statistics - Theory and Methods, DOI:10.1080/03610926.2013.791370, 2016 (with R. Bodnar and T. Bodnar).

Spatio-temporal statistical analysis of the carbon budget of the terrestrial ecosystem, Statistical Methods and Applications, 25, 143-161, 2016 (with P. Vetter and R. Schwarze).

EWMA control charts for detecting changes in the mean of a long-memory process, Metrika, 79, 267-301, 2016 (with L. Rabyk).

On the misleading signals in simultaneous schemes for the mean vector and covariance matrix of multivariate i.i.d. output, Statistical Papers , 57, 471-498, 2016 (with P. Ramos, M. Morais and A. Pacheco).

Control charts for multivariate nonlinear time series, REVSTAT, 131-144, 2015 (with R. Garthoff and I. Okhrin).

Quality surveillance with EWMA control charts based on exact control limits, Statistical Papers, DOI:10.1007/s00362-014-0612-8, 2015 (with M. Morais and Y. Okhrin).

Behavior of EWMA type charts for small smoothing parameter, Computational Statistics and Data Analysis, 89, 115-125, 2015 (with T. Lazariv and Y. Okhrin).

On the exact solution of the multi-period portfolio choice problem for an exponential utility under return predictability, European Journal of Operational Research, 246, 528-542, 2015 (with T. Bodnar and N. Parolya).

A closed-form solution of the multi-period portfolio choice problem for a quadratic utility function, Annals of Operations Research, 229, 121-158, 2015 (with T. Bodnar and N. Parolya).

Periodic and Long Range Dependent Models for High Frequency Wind Speed Data, Energy, 82, 277-293, 2015 (with D. Ambach)

Discussion on "Recent advances in process monitoring: semi parametric and variable-selection methods for Phase I and Phase II" by Giovanna Capizzi, Quality Engineering, 27, 68-72, 2015.

On the impact of falsely assuming i.i.d output in the probability of misleading signals, REVSTAT, 12, 221-245, 2014. (with M. Morais, P. Ramos and A. Pacheco).

Effcient approximation of the spatial covariance function for large datasets - analysis of atmospheric CO2 concentrations, Journal of Environmental Statistics, 6, 2014 (with P. Vetter and R. Schwarze).

Statistical surveillance of the mean vector and the covariance matrix of nonlinear time series, ASTA - Advances in Statistical Analysis, 98, 225-255, 2014 (with R. Garthoff and I. Okhrin).

Monitoring the mean of multivariate financial time series, Applied Stochastic Models in Business and Industry, 30, 328-340, 2014 (with R. Garthoff and V. Golosnoy).

Asymptotic behavior of the estimated weights and of the estimated performance measures of the minimum VaR and the minimum CVaR optimal portfolios for dependent data, Metrika, 76, 1105-1134, 2013 (with T. Bodnar and T. Zabolotskyy).

On control charts for monitoring the variance of a time series, Journal of Statistical Planning and Inference, 143, 1512-1526, 2013 (with T. Lazariv and S. Zabolotska).

Comparison of some optimization problems in portfolio theory, European Journal of Operational Research, 229, 637-644, 2013 (with T. Bodnar and N. Parolya).

Stochastic ordering in the qualitative assesment of the performance of simultaneous schemes for bivariate processes, Sequential Analysis, 32, 214-229, 2013 (with P. Ramos, M .Morais and A. Pacheco).

On the structure and estimation of hierarchical Archimedian copulas, Journal of Econometrics, 173, 189-204, 2013 (with O. Okhrin and Y. Okhrin).

Properties of hierarchical Archimedian copulas,  Statistics & Risk Modeling, 1001-1034, 2013 (with O. Okhrin and Y. Okhrin).

Statistical surveillance of volatility forecasting models, Journal of Financial Econometrics, 10, 513-543, 2012 (with V. Golosnoy and I. Okhrin).

Minimum VaR and minimum CVaR optimal portfolios: estimators, confidence regions, and tests, Statistics & Risk Modeling, 29, 281-313, 2012 (with T. Bodnar and T. Zabolotskyy).

Limit properties of EWMA charts for stationary processes, Frontiers in Statistical Quality Control, H.-J. Lenz, W. Schmid and P.-Th. Wilrich (Eds.), Physica-Verlag, Heidelberg, 10, 69-83, 2012 (with M. Morais and Y. Okhrin).

Assessing the impact of autocorrelation in misleading signals in simultaneous residual schemes for the process mean and variance: a stochastic ordering approach, Frontiers in Statistical Quality Control, H.-J. Lenz, W. Schmid and P.-Th. Wilrich (Eds.), Physica-Verlag, Heidelberg, 10, 35-52, 2012 (with P. Ramos, M. Morais and A. Pacheco).

CUSUM charts for monitoring the mean of a Gaussian process, Journal of Statistical Planning and Inference, 141, 2055-2070, 2011 (with O. Bodnar).

On the exact distribution of the estimated EU portfolio weights: theory and applications, Statistics & Risk Modeling, 28, 319-342, 2011 (with T. Bodnar).

CUSUM charts for monitoring optimal portfolio weights, Computational Statistics and Data Analysis, 55, 2991-3009, 2011 (with V. Golosnoy and S. Ragulin).

Nonlinear locally weighted kriging prediction for spatio-temporal environmental processes, Environmetrics, 21, 365-381, 2010 (with O. Bodnar).

New characteristics for portfolio surveillance, Statistics, 44, 303-321 (with V. Golosnoy and I. Okhrin), 2010.

Multivariate CUSUM chart: properties and enhancements, AStA - Advances in Statistical Analysis, 93, 263-279, 2009 (with V. Golosnoy and S. Ragulin).

Discussion on "Optimal Sequential Surveillance for Finance, Public Health, and Other Areas" by M. Frisen, Sequential Analysis, 28, 375-380, 2009 (with O. Bodnar).

Misleading signals in simultaneous residual schemes for the mean and the variance of a stationary process, Communications in Statistics - Theory and Methods, 38, 2923-2943, 2009 (with S. Knoth, M. C. Morais and A. Pacheco).

Econometrical analysis of the sample efficient frontier, The European Journal of Finance, 15, 317-335, 2009 (with T. Bodnar).

Statistical inference of the efficient frontier for dependent asset returns, Statistical Papers, 50, 593-604, 2009 (with T. Bodnar and T. Zabolotskyy).

Asset allocation with distorted probability and transaction costs, European Journal of Operational Research,  194, 236-249, 2009 (with R. Kozhan).

Estimation of optimal portfolio compositions for Gaussian returns, Statistics & Decisions, 26, 179-201, 2008 (with T. Bodnar).

Comparing air quality among Italy, Germany, and Poland using BC indexes, Atmospheric Environment, 42, 8412-8421, 2008 (with O. Bodnar, M. Cameletti and A. Fasso).

Discussion on "Is Average Run Length to False Alarm always an Informative Criterion?" by Y. Mei, Sequential Analysis, 27, 392-395, 2008 (with S. Knoth).

EWMA charts for multivariate output: some stochastic ordering results, Communications in Statistics - Theory and Methods, 37, 2653-2663, 2008  (with M.C. Morais, Y. Okhrin and A. Pacheco).

Estimation of the optimal portfolio weights, International Journal of Theoretical and Applied Finance, 11, 249-276, 2008 (with Y. Okhrin).

On the existence of unbiasedestimators for the portfolio weights, AStA - Advances in Statistical Analysis, 92, 29-34, 2007 (with T. Zabolotskyy).

A test for the weights of the global minimum variance portfolio in an elliptical model,  Metrika, 67, 127-143, 2008 (with T. Bodnar).

Surveillance of the mean behaviour of multivariate time series, Statistica Neerlandica, 61, p.383-406, 2007 (with O. Bodnar).

On the stochastic behaviour of the run length of EWMA control schemes for the mean of correlated output in the presence of shifts in sigma, Statistics & Decisions, 24, p.397-413, 2007 (with M.C. Morais, Y. Okhrin and A. Pacheco).

Comparison of different estimation techniques for portfolio selection, Advances in Statistical Analysis (AStA) 91, p.109-127, 2007 (with Y. Okhrin).

EWMA control charts for monitoring optimal portfolio weights, Sequential Analysis, 26, p.195-224, 2007 (with V. Golosnoy).

The distribution of the sample variance of the global minimum variance portfolio in elliptical models, Statistics, 41, p.65-75, 2007 (with T. Bodnar).

Eighty years of control charts, Sequential Analysis 26, p.117-122, 2007.

Discussion on "Sequential Design and Estimation in Heteroscedastic Nonparametric Regression" by S. Efromovich, Sequential Analysis, 26, 53-55, 2007 (with Y. Okhrin).

Distributional properties of portfolio weights, Journal of Econometrics, 134, p.235-256, 2006 (with Y. Okhrin).

EWMA charts for monitoring the mean and autocovariances of stationary processes, Statistical Papers, 47, p.595-630, 2006 (with M. Rosolowski).

Multivariate control charts based on a projection approach, Journal of the German Statistical Society (ASTA), 89, p.75-93, 2005 (with O. Bodnar).

Surveillance of the covariance matrix of multivariate nonlinear time series, Statistics, 39, p.221-246, 2005 (with P. Sliwa).

Monitoring the cross-covariances of a multivariate time series, Metrika, 61, p.89-115, 2005 (with P. Sliwa).

Control charts for time series: a review, Frontiers in Statistical Quality Control, H.-J. Lenz, P.-Th. Wilrich (Eds.), Physica-Verlag, Heidelberg, p.210-236, 2004 (with S. Knoth).

Statistical surveillance of the parameters of a one-factor Cox-Ingersoll-Ross model, Sequential Analysis, 23, p.379-412, 2004 (with D. Tzotchev).

EWMA charts for monitoring the mean and the autocovariances of stationary Gaussian processes, Sequential Analysis, 22, p.257-285, 2003 (with M. Rosolowski).

Tail behaviour of a general family of control charts, Statistics & Decisions, 21, p.77-90, 2003 (with Y. Okhrin).

Monitoring the mean and the variance of a stationary process, Statistica Neerlandica, 56, p.77-100, 2002 (with S. Knoth).

Sequential methods for detecting changes in the variance of economic time series, Sequential Analysis, 20, p.235-262, 2001 (with S. Schipper).

Control charts for GARCH processes, Nonlinear Analysis, 47, p.2049-2060, 2001 (with S. Schipper).

Simultaneous Shewhart-type charts for the mean and the variance of a time series, Frontiers in Statistical Quality Control, H.-J. Lenz, P.-Th. Wilrich (Eds.), Physica-Verlag, Heidelberg, p.61-79, 2001 (with S. Knoth and A. Schöne).

On distributional properties of GARCH processes, Journal of Time Series Analysis, 22, p.339-352, 2001 (with M. Pawlak).

Sequential control of non-stationary processes by kernel control charts, Allgemeines Statistisches Archiv, 84, p.315-336, 2000 (with A. Steland).

On the joint distribution of a quadratic and a linear form in normal variables, Journal of Multivariate Analysis, 72, p.163-182, 2000 (with A. Schöne).

The influence of parameter estimation on the ARL of Shewhart-type charts for time series, Statistical Papers, 41, p.173-196, 2000 (with H. Kramer).

On the run length of the EWMA scheme - a monotonicity result for normal variables, Journal of Statistical Planning and Inference, 79, p.289-297, 1999 (with A. Schöne and S. Knoth).

Monitoring changes in GARCH models, Allgemeines Statistisches Archiv, 83, p.281-307, 1999 (with T. Severin).

On the robustness of Shewhart type charts, Economic Quality Control, 13, p.107-115, 1998 (with H. Kramer).

Statistical process control and its application in finance, Contributions to Economics: Risk Measurement, Econometrics and Neural Networks, Physica-Verlag, Hei, p.83-104, 1998 (with T. Severin).

On the average delay of control schemes, Advances in Stochastic Models for Reliability, Quality and Safety, E. von Collani, J. Franz, U. Jens, p.341-360, 1998 (with H. Kramer).

The effects of autocorrelation on the R-chart and the S²-chart, Sankhyã, Ser. B, 59, p.229-255, 1997 (with R. Amin).

Zur Anwendung der Statistischen Prozesskontrolle in der Wertpapieranalyse, Solutions, 1, p.71-81, 1997 (with T. Severin).

EWMA charts for multivariate time series, Sequential Analysis, 16, p.131-154, 1997 (with H. Kramer).

Some properties of the EWMA control chart in the presence of data correlation, Annals of Statistics, 25, p.1277-1283, 1997 (with A. Schöne).

CUSUM control schemes for Gaussian processes, Statistical Papers, 38, p.191-217, 1997.

On EWMA charts for time series, Frontiers in Statistical Quality Control, H.-J. Lenz, P.-T. Wilrich (Eds.), Physica-Verlag, Heidelb, p.115-137, 1997.

A comparison of several procedures for identifying outliers in contaminated ARMA processes, Computational Statistics, 11, p.175-195, 1996 (with T. Flak and R. Sigmund).

Univariate und bivariate GARCH-Modelle zur Schätzung des Beta-Faktors, Finanzmarkt und Portfolio Management, 10, p.45-52, 1996 (with F. Herrmann and R. Zagst).

An outlier test for linear processes - II. Large contamination, Metrika, 43, p.31-42, 1996 (with T. Flak).

An outlier test for time series based on a 2-sided predictor, Journal of Time Series Analysis, 17, p.497-510, 1996.

Extreme sums of strictly stationary sequences of m-dependent variables, Sankhyã, Ser. A, 57, p.186-201, 1995 (with T. Flak).

On the run length of a Shewhart chart for correlated data, Statistical Papers, 36, p.111-130, 1995.

Robustness of the standard deviation and other measures of dispersion, Biometrical Journal, 36, p.411-427, 1994 (with W. Gaus and J. Högel).

An outlier test for linear processes, Metrika, 40, p.299-318, 1993 (with T. Flak).

An optimal decision rule for identifying outliers in time series, Österreichische Zeitschrift für Statistik und Informatik, 22, p.119-133, 1992.

How to locate outliers in a time series if a starting-block is present, Sankhyã, Ser. B, 53, p.359-383, 1991.

Discussion of a LR test for detecting outliers in time series data, Statistics & Decisions, 8, p.271-294, 1990.

Outliers in a multivariate autoregressive-moving average process, Stochastic Processes and their Applications, p.117-133, 1990.

Identification of a type I outlier in an autoregressive model, Statistics, 20, p.531-545, 1989.

Asymptotical behaviour of a test of discordancy for an increasing number of outliers, Statistics & Decisions, 6, p.245-260, 1988.

The multiple outlier problem in time series analysis, Australian Journal of Statistics, 28, p.400-413, 1986.

Lebenslauf / Vita

Akademischer Werdegang

Studium: Mathematik-Studium an der Universität Ulm von 1977-1982
Promotion: Promotion zum Dr. rer. nat. an der Universität Ulm im Jahr 1984 zum Thema "Lokalisierung von Ausreißern bei autoregressiven Prozessen"
Habilitation: Habilitation im Jahr 1991, Titel der Habilitationsschrift: "Ausreißertests und Ausreißeridentifkation bei Zeitreihen"
Venia legendi für das Fachgebiet Mathematik
 

Akademische Positionen

2013, 2014, 2015: Gastprofessor an der Universität Bergamo, Italien
1999-2000, 2007-2009: Sprecher des Graduiertenkollegs "Kapitalmärkte und Finanzwirtschaft im erweiterten Europa"
seit 1996: Vorsitzender des Promotionsausschusses der Wirtschaftswissenschaftlichen Fakultät
1995-1999, seit 2011: Vorsitzender der Stipendienvergabekommission der EUV
seit Okt. 1995: Professor für Statistik an der Europa-Universität Frankfurt (Oder)
SoSe 1995: Professur (Vertretung) an der Europa-Universität Frankfurt (Oder)
WS 1994/95: Professur (Vertretung) an der Universität Stuttgart
WS 1993/94: Lehrauftrag an der Universität Konstanz
WS 1991/92: Professur (Vertretung) an der Universität Trier
1984-1995: Wissenschaftlicher Mitarbeiter an der Universität Ulm