Methods and Applications of Statistics in Business, Finance, and Management Science

Preface.

Contributors.

1 Alternatives to Black-Scholes Formulation in Finance.

1.1 Introduction.

1.2 Motivation for Alternative Models.

1.3 Methods of Valuation.

1.4 Stochastic Interest-Rate Models.

1.5 Stochastic Volatility Models.

1.6 Models with Lévy Processes.

2 Analytical Methods of Risk Management: An Engineering Systems Perspective.

2.1 Introduction.

2.2 Risk Management in Engineering Systems.

2.3 Risk Assessment and Analysis.

2.4 Allocating Resources.

2.5 Conclusion.

3 ARCH and GARCH Models.

3.1 Introduction.

3.2 Volatility Clustering.

3.3 GARCH.

3.4 IGARCH.

3.5 EGARCH.

3.6 Alternative Parameterizations.

3.7 Time-Varying Parameter and Bilinear Models.

3.8 Estimation and Inference.

3.9 Testing.

3.10 Empirical Example.

3.11 Future Developments.

4 Bayesian Forecasting.

4.1 Introduction.

4.2 Background.

4.3 Dynamic Bayesian Models.

4.4 Normal Dynamic Linear Models.

4.5 Component Dynamic Linear Models.

4.6 Discounting.

4.7 Intervention.

4.8 Monitoring and Adaptation.

4.9 Mixtures of Dynamic Models.

4.10 Non-normal Nonlinear Models.

4.11 Multivariate Models.

4.12 Computation and Simulation.

4.13 Related Areas.

5 Bayesian Networks.

5.1 Examples and Definitions.

5.2 Constructing Bayesian-Network Models.

5.3 Models Specified by Input Lists.

5.4 Graphically Specified Models.

5.5 Conditionally Specified Models.

5.6 Learning Models from Data.

5.7 Propagation in Bayesian Networks.

5.8 Available Software.

6 Box–Jenkins Model.

6.1 Introduction.

7 Business Forecasting Methods.

7.1 Introduction.

7.2 Trend Curves.

7.3 Exponential Smoothing.

7.4 Exponential Smoothing and Arima Model Building.

7.5 Regression and Econometric Methods.

7.6 Regression and Time-Series Principles.

7.7 Combination of Forecasts.

7.8 Evaluation of Forecasts.

7.9 Summary.

8 Combination of Forecasts.

8.1 Introduction.

8.2 The Theory of Combining.

8.3 Estimators of the Weights.

8.4 An Example.

8.5 Further Extensions.

9 Decision Theory.

9.1 Introduction.

9.2 Parameters, Decisions, and Consequences.

9.3 Utility.

9.4 Components of a Decision Problem.

9.5 Subjective Probability.

9.6 Decision Analysis.

9.7 Statistical Decision Problems.

9.8 Conjugate Families of Prior Distributions.

9.9 Improper Prior Distributions.

9.10 Estimation and Tests of Hypothesis.

9.11 Sequential Decision Problems.

10 Dynamic Programming.

10.1 Introduction.

10.2 Definitions and Examples.

10.3 Some Fundamental Principles.

10.4 The Optimality of Equation and Backward Induction.

10.5 Stationary Plans.

11 Estimation of Travel Distance.

11.1 Introduction.

11.2 Distance Functions.

11.3 Goodness-of-Fit Criteria.

11.4 Areas of Future Research.

12 Financial Time Series.

12.1 Asset Price and Return.

12.2 Fundamental and Technical Analyses.

12.3 Volatility Model.

12.4 High-Frequency Data.

12.5 Continuous-Time Model.

13 Forecasting.

13.1 Introduction.

13.2 Model Components.

13.3 Model Fitting for Forecasting.

13.4 Forecasting Methods.

13.5 Forecast Quality.

14 Foundations of Risk Measurement.

14.1 Introduction.

15 Functional Networks.

15.1 Introduction.

15.2 Elements of Functional Networks.

15.3 Differences Between Standard NNs and FNs.

15.4 Development and Implentation of FNs.

15.5 An Example of Application.

16 Game Theory.

16.1 Introduction.

16.2 Strategies and Payoffs.

16.3 Applications to Statistics.

17 Intervention Model Analysis.

17.1 Introduction.

17.2 Time-Series and Intervention Models.

17.3 Applications and Extensions.

18 Inventory Theory.

18.1 Introduction.

18.2 Historical Background.

18.3 Models with Known Demand.

18.4 Models with Uncertain Demand.

18.5 Conclusion.

19 Manpower Planning.

19.1 Introduction.

19.2 Statistical Analysis of Wastage.

19.3 Markov Models for Graded Systems.

19.4 Renewal Models for Graded Systems.

19.5 Literature.

20 Markov Networks.

20.1 Statement of the Problem.

20.2 Some Basic Concepts of Graphs.

20.3 Constructing Markov Network Models.

20.4 Propagation in markov Networks.

20.5 Available Software.

21 Methods of Estimation of Risks and Analysis of Business Processes.

21.1 Introduction.

21.2 Mathematical Models of Economic Systems in the Form of the Business Processes Portfolio.

21.3 Risks of Economic Systems.

21.4 Economic Systems Factors Analysis.

22 Mining Functional Data in Prediction Markets.

22.1 Introduction.

22.2 Prediction Markets.

22.3 Data.

22.4 Functional Data Analysis.

22.5 Discussion.

23 Models for Bid Arrivals and Bidder Arrivals in Online Auctions.

23.1 Introduction.

23.2 Motivation.

23.3 Features of Bid Arrivals.

23.4 The BARISTA: A Three-Stage Nohomogeneous Poisson Process.

23.5 Relating Bidder Arrivals and Bid Arrivals.

24 Multiserver Queues.

24.1 Introduction.

24.2 Markovian Queues.

24.3 Non-Markovian Queues.

24.4 Other Methods.

25 Multivariate Time-Series Analysis.

25.1 Introduction.

25.2 Stationary Mutivariate Time Series and Their Covariance Properties.

25.3 Some Spectral Characteristics for Stationary Vector Processes.

25.4 Linear Filtering Relations for Stationary Vector Processes.

25.5 Linear Model Representations for Stationary Vector Processes.

25.6 Vecotr Autoregressive Moving Average (ARMA) Model Representations.

25.7 Nonstationary Vector Autoregressive Moving-Average Models.

25.8 Forecasting for Vector Autoregressive Moving-Average Processes.

25.9 Statistical Analysis of Vector Autoregressive Moving-Average Models.

26 Network Analysis.

26.1 Introduction.

27 Network of Queues.

27.1 Introduction.

27.2 Some Background.

27.3 Some Results.

27.4 More General Networks.

27.5 Sojourn Times in Queueing Networks.

27.6 Customer Flow in Networks.

27.7 Other Approaches and Topics.

28 Neural Networks.

28.1 Introduction.

28.2 Feed-Forward Networks.

28.3 Recurrent Networks.

28.4 Associative-Memory Networks and Boltzmann Machines.

28.5 Networks Trained by Unsupervised Learning.

28.6 Use of the Bayesian Approach.

28.7 Conclusion.

29 Newsboy Inventory Problem.

29.1 Introduction.

30 Nonlinear Time Series.

30.1 Introduction.

30.2 Reviews of Linear Time Series.

30.3 Nonparametric Methods.

30.4 Parametric Models.

30.5 Other Surveys and Comparisons.

31 Nonstationary Time Series.

31.1 Introduction.

31.2 Removing Nonstationary Menas and Variances.

31.3 Extensions.

31.4 Homogeneous and Explosive Nonstationarity.

31.5 Differencing.

31.6 Starting Values and Nonstationarity.

31.7 ARIMA Models.

31.8 Sample Autocorrelations--Identifying the Degree of Differencing.

31.9 Estimation of Unit and Explosive Roots.

31.10 Forecasting.

31.11 Variations and Extensions.

31.12 Nonstationary Spectral Analysis.

32 PERT.

32.1 Introduction.

32.2 Finding the Expected Critical Path Length.

32.3 Simulation and Statistical Computations.

32.4 Estimation of Individual Activity Times.

32.5 Conclusions.

33 Prediction and Forecasting.

33.1 Introduction.

33.2 Regression Models.

33.3 Regression and Smoothing Methods for Extrapolating a Single Time Series.

33.4 Forecasts from Univariate Time-Series Models.

33.5 Forecasts from Multivariate Time-Series Models.

33.6 State-Space Models, Kalman Flitering and Bayesian Forecasting.

33.7 Econometric Models.

33.8 Input-Output Tables.

33.9 Turning Points and Business Cycle Indicators.

33.10 Surveys of Anticipations and Intentions.

33.11 Combination of Forecasts.

33.12 Prediction of Qualitative Characteristics.

33.13 Forecast Quality and the Evaluation of Forecasts.

34 Pricing Foreign Exchange Options with Stochastic Volatility.

34.1 Introduction.

34.2 Arbitrage-Free Cross-Currency Markets.

34.3 Stein and Stein Stochastic Volatility Model with Vasicêk Interest Rates.

34.4 Heston's Stochastic Volatility Model with CIR Interest Rates.

34.5 Foreign Exchange Option under Heston Volatility with Constant Interest Rates.

34.6 Concluding Remarks.

35 Probabilistic Expert Systems.

35.1 Introduction.

35.2 Graph Types.

35.3 Conditioal Independence and Markov Properties.

35.4 Specification of Joint Distribution.

35.5 Local Computation Algorithm.

35.6 Extensions.

36 Problem Solving in Statistics.

36.1 Introduction.

36.2 Phase 1: Study Design.

36.3 Phase 2: Data Collection.

36.4 Phase 3: Data Analysis.

36.5 Postprocess Responsibilities.

36.6 Conclusions.

37 Queueing Theory.

37.1 Introduction.

37.2 Subsequent Development of the Simple Queue Model.

37.3 Variants of the Simple Queueing Model.

37.4 Concluding Remarks.

38 Queues and Networks.

38.1 Introduction.

38.2 A Glimpse on Queueing Theory by Example.

38.3 The Vocabulary of Queueing Theory.

38.4 Little's Formulas.

38.5 Markovian Queueing Systems of BD Type.

38.6 General Service Times: The System M/G/1.

38.7 The Systems M/G/c and G/G/c.

38.8 Networks of Queues.

38.9 Approximations and Numerical Methods.

38.10 Simulation.

39 Ranking and Selection Among Mutual Funds.

39.1 Introduction.

39.2 Statistical Underpinnings of Data Mining Using Combinatorial Fusion Algorithm.

39.3 Stochastic Dominance and Asymmetric Attitude Towards Risk.

39.4 Summary and Final Remarks.

40 Risk Theory.

40.1 Introduction.

41 Statistical Consulting.

41.1 Definition.

41.2 What Consultants Do.

41.3 Historical Perspective.

41.4 Skills Needed by a Consultant.

41.5 Consulting and Communication.

41.6 Computers and Consultants.

41.7 Keeping Up with Statistics.

41.8 Ethics.

41.9 Teaching Consulting.

41.10 Rewards of Consulting.

42 Statistical Methods in Inventory Effect and Analysis.

42.1 Introduction.

42.2 Futures Markets.

42.3 Backwardation and Inventory Effect.

42.4 Inventory Effect: A Preliminary Analysis.

42.5 Ordered Bivariate Normal Distribution.

42.6 Bivariate Lognormal Distribution.

42.7 Ordered Bivariate Lognormal Distribution.

42.8 Conclusions.

43 Statistical Methods in Risk Management by Futures Clearinghouses.

43.1 Introduction.

43.2 Margin Requirements.

43.3 Settlement Frequency.

43.4 Capital Requirements.

43.5 Price Limits.

43.6 Position Limits.

43.7 Conclusion.

44 Statistics in Auditing.

44.1 Introduction.

44.2 Study of Internal Control System.

44.3 Study of Account Balances.

44.4 Analytical Review.

45 Statistics in Banking.

45.1 Introduction.

45.2 Further Reading.

46 Statistics in Finance.

46.1 Introduction.

46.2 Regression Analysis and the Market Model.

46.3 Factor, Multiple Discriminant and Logit Applications.

46.4 Time-Series Analyses of Financial Information.

46.5 Statistical Decision Theory and Finance.

47 Statistics in Management Science.

47.1 Introduction.

47.2 Using Regression to Estimate Managerial Decision Rules.

47.3 Using Regression for Input Data in Modeling.

47.4 Construction of Causal Models by Regression.

47.5 Statistical Analysis of Algorithmic Performance Data.

47.6 Sampling Theory.

47.7 Other Statistical Tools.

48 Statistics in Marketing.

48.1 Introduction.

48.2 Some Early Contributions.

48.3 The Uses of Statistics in Marketing Research.

48.4 Sample Survey Methods.

48.5 Multivariate Techniques.

48.6 Forecasting Methods.

48.7 Psychometric Methods in the Measurement of Consumer Perceptions and Preferences.

48.8 Experimentation.

48.9 Probability Models.

49 Statistics of Risk Management.

49.1 Introduction.

49.2 General Concept of Risk Management and Monitoring.

49.3 Scope.

49.4 Evolution of Risk Management.

49.5 Insurance.

49.6 Gambling, Capital Budgeting and Investments.

49.7 Technological Risk Management.

49.8 Low-Probability-High-Consequence Risk Management.

49.9 Environmental Risk and Monitoring Systems.

49.10 Epidemiology and Disease Detection.

49.11 Principles of Statistical Monitoring.

50 Stochastic Differential Equations: Applications in Economics and Management Science.

50.1 Introduction.

50.2 Option Pricing.

50.3 Stochastic Optimal Control.

50.4 Final Remarks.

51 Stochastic Games.

51.1 Introduction.

51.2 Special Cases.

51.3 Computation.

52 Stock Market Price Indexes.

52.1 Introduction.

52.2 Definition and Uses.

52.3 Brief History.

52.4 Main Issues.

52.5 A Numerical Example.

52.6 Two Major Stock Market Price Indexes.

52.7 The S&P 500.

52.8 Comparison of Four International Indexes.

52.9 Stock Market Indexes and Portfolio Analysis.

52.10 Summary.

53 The Black-Scholes Formula and Its Applications in Finance.

53.1 Introduction.

53.2 The Black-Scholes Model.

53.3 European Call and Put Options.

53.4 Some Exotic Options.

53.5 American Options.

53.6 Application to the Modeling of Credit Risk.

53.7 Real Options.

54 Time Series.

54.1 Introduction.

54.2 Examples of Time Series.

54.3 A Historical Perspective.

54.4 Stationarity.

54.5 The Frequency Domain.

54.6 The Time Domain.

54.7 State-Space Models.

54.8 Transfer Functions and Interventions.

54.9 Other Topics.

54.10 Literature.

54.11 Computer Programs.

54.12 Future Developments.

Index.