Financial Econometrics and Statistics: Past, Present, and Future

1
Financial Econometrics and Statistics Past,
Present, and Future

• By
• Dr. Cheng-Few Lee
• Distinguished Professor of Finance, Rutgers
  University, USA
• Editor, Review of Quantitative Finance and
  Accounting
• Editor, Review of Pacific Basin Financial Markets
  and Policies

To be presented at the The 4th NCTU
International Finance Conference on January 7,
2011.
2
Outline

• 1. Introduction
• 2. Single equation regression methods
• 3. Simultaneous equation models
• 4. Panel data analysis
• 5. Alternative methods to deal with measurement
  error
• 6. Time series analysis
• 7. Spectral Analysis
• 8. Statistical distributions
• 9. Principle components and factor analyses
• 10. Non-parametric, Semi-parametric, and GMM
  analyses
• 11. Path analysis
• 12. Cluster analysis
• 13. Summary and concluding remarks

3
1. Introduction

• Financial econometrics and statistics
  have become more important for empirical research
  in both finance and accounting. Asset pricing and
  corporate finance research have used both
  econometrics and statistics, such as single
  equation multiple regression, simultaneous
  regression, panel data analysis. Portfolio theory
  and management have used different statistics
  distributions, such as normal distribution,
  stable distribution, and log normal distribution.
  Options and futures have used binomial
  distribution, log normal distribution,
  non-central chi square distribution, and so on.
  Auditing has used sampling technique to determine
  the sampling error for auditing. The main purpose
  of this handbook is to review financial
  econometrics and statistics used in the research
  of finance and accounting for last five decades.
  Some suggestions to apply these techniques in
  future research are also recommended.
• The second section of this paper will
  discuss alternative single equation regression
  estimation methods. Section 3 will discuss
  simultaneous equation models. Section 4 will
  discuss panel data analysis. Section 5 will
  discuss alternative methods to deal with
  measurement error. Section 6 will discuss time
  series analysis. Section 7 will discuss spectral
  Analysis. Section 8 will discuss statistical
  distribution. Section 9 will discuss principle
  components and factor analyses. Section 10 will
  discuss non-parametric, semi-parametric, and GMM
  analyses. Section 11 will discuss path analysis.
  Section 12 will discuss cluster analysis.
  Finally, section 13 will summarize the paper.

4
2. Single equation regression methods

• In this section, we will discuss important issues
  related to single equation regression estimation
  method. They are (a) heteroskedasticity, (b)
  specification error, (c) measurement error, (d)
  quantile regression, and (e) testing structural
  change.
• a. Heteroskedasticity
• - White method
• - Newey-West method
• b. Specification error
• - Thursby, JASA (1985)
• - Alternative Specifications and Estimation
  Methods for Determining Random Beta Coefficients
  Comparison and Extensions, (with Robert C.R.
  Rkok and David C. Cheng), Journal of Financial
  Studies, October 1996
• - Power of Alternative Specification Errors
  Tests in Identifying Misspecified Market Models,
  (with David C. Cheng), The Quarterly Review of
  Economics and Business, Fall, 1986.
• - Cheng and Lee, QREB (1986)
• - Maddala et al., Handbook of Statistics 14
  Statistics Methods in Finance (1996)

5
2. Single equation regression methods

• c. Measurement error
• - Lee and Jen, JFQA (1978)
• - Kim, JF (1995)
• - Kim, Handbook of Quantitative Finance and Risk
  Management (2010)
• - Miller and Modigliani, AER (1966)
• d. Quantile regression
• e. Nonlinear regression
• Box-Cox transformation
• - Lee JF (1976)
• - Lee JFQA (1977)
• - Lee JFQA ()
• - Generalized Financial Ratio Adjustment
  Processes and Their Implications, (with Thomas
  J. Frecka), Journal of Accounting Research,
  Spring, 1983.
• - A Generalized Functional Form Approach to
  Investigate the Density Gradient and the Price
  Elasticity of Demand for Housing, (with James B.
  Kau), Urban Studies, April, 1976.
• - Liu (2005)
• - Kau, Lee, and Sirmans. Urban Econometrics
  Model developments and empirical results (1986)

6
2. Single equation regression methods

• f. Testing structural change
• - Yang (1989)
• - Lee et al. (2010) Optimal payout ratio under
• - Lee et al. (2010) Threshold..
• - Chow test and moving chow test
• (Chow, Econometrica, 1960)
• (Strucchange An R Package for Testing for
  Structural Change in Lineaer Regression Models,
  Journal of Statistical Software, 2002)
• - Threshold regression
• (Hansen, Journal of Business Economic
  Statistics, 1997)
• (Hansen, Econometrica, 1996, 2000)
• (Journal of Econometrics, 1999, 2000).
• - Generalize fluctuation test
• (Juan and Hornik, Eonometric Reviews, 1995)
• g. Probit and Logit regression for credit risk
  analysis
• - Hwang, R.C., Cheng, K.F., and Lee, C.F.
  (2009). On multiple-class prediction of issuer
  crediting ratings. Journal of Applied Stochastic
  Models in Business and Industry, 25, 535-550.
  (SCI)
• - Hwang, R.C., Wei, H.C., Lee, J.C., and Lee,
  C.F. (2008). On prediction of financial distress
  using the discrete-time survival model. Journal
  of Financial Studies, 16, 99-129. (TSSCI)
• - Cheng, K.F.,Chu, C.K., and Hwang, R.C. (2009).
  Predicting bankruptcy using the discrete-time
  semiparametric hazard model. Accepted by
  Quantitative Finance. (SSCI)

7
3. Simultaneous equation models

• In this section, we will discuss
  alternative methods to deal with simultaneous
  equation models. There are (a) 2 stage least
  square (2SLS) method, (b) seemly uncorrelated
  regression (SUR) method, (c) 3 stage least square
  (3SLS) method, and (d) disequilibrium estimation
  method.
• a. 2 stage least square (2SLS) method
• - Lee JFQA (1976)
• - MM AER (1966)
• - Chen et al., Corporate Governance and
  International Review (2007)
• b. Seemly uncorrelated regression (SUR) method
• - Lee JFQA (1981)
• c. 3 stage least square (3SLS) method
• - Chen et al., Corporate Governance and
  International Review (2007)
• d. Disequilibrium estimation method
• - Tsai (2005)
• - CW Sealy JF (1979)
• - Lee, Tsai, and Lee, subjected to revision for
  Quantitative Finance (2010)
• - WJ Mayer, Journal of Econometrics, 1989
• - RW David, JBF, 1987
• - C Martin, Review of Economics and Statistics,
  1990

8
4. Panel data analysis

• In this section, we will discuss important
  issues related to panel data analysis. There are
  (a) fixed effect model, (b) random effect model,
  and (c) clustering effect model.
• - Wooldridge, Econometric Analysis of Cross
  Secion and Panel Data, MIT Press (2002)
• - BalTagi, Econometric Analysis of Panel Data,
  Wiley (2008)
• - Hsiao, Analysis of Panel Data, Cambridge
  University Press (2002)
• a. Fixed effect model
• - Lee JFQA (1977)
• - Lee et al. JCF (2010)
• b. Random effect model
• - Lee JFQA (1977)
• c. Clustering effect model of panel data analysis
• - Thompson (2006)
• - Cameron, Gelbach, and Miller (2006)
• - Petersen (2009)

9
5. Alternative methods to deal with measurement
error

• In this section, we will discuss Alternative
  methods to deal with measurement error problem.
  They are (a) LISREL model, (b) multi-factor and
  multi-indicator (MIMIC) model, and (c) partial
  least square method.
• - Lee (1973)
• a. LISREL model
• - Titman and Wessal JF (1988)
• - Chang (1999)
• - Chang and Lee QREF (2008)?
• b. Multi-factor and multi-indicator (MIMIC) model
• - Lee et al. QREB (2009)
• - Wei (1984)
• c. Partial least square method
• - JE Core - Journal of Law, Economics, and
  Organization (2000)
• - Ittner et al. AR (1997)
• - Lambert and Lacker ()

10
6. Time series analysis

• In this section, we will discuss important
  models in time series analysis. They are (a)
  ARIMA, (b) ARCH, (c) GARCH, and (d) Fractional
  GARCH.
• - Anderson, T. W., The statistical Analysis of
  Time Series (1994), Wiley-Interscience.
• - Hamilton, J. D., Time Series Analysis (1994),
  Princeton University Press.
• a. ARIMA
• - Myers, JFM (1991)
• b. ARCH
• - Lien and Shrestha, JFM (2007)
• c. GARCH
• - Lien, JFM (2010)
• d. Fractional GARCH
• - Leon and Vaello-Sebastia, JBF (2009)
• e. Combined forecasting
• - Lee (1996)
• - Lee and Cummins (1998)

11
7. Spectral Analysis

• In this section, we will discuss the spectral
  analysis.
• - Chacko and Viceira, Journal of Econometrics
  (2003)
• - Heston, RFS (1993)
• - Anderson, T. W., The statistical Analysis of
  Time Series (1994)

12
8. Statistical distributions

• In this section, we will discuss different
  statistical distributions. They are (a) binomial
  distribution, (b) poisson distribution, (c)
  normal distribution, (d) log normal distribution,
  (e) Chi-square distribution, (f) non-central
  Chi-square distribution, (g) Wishart
  distribution, (h) stable distribution, and (i)
  other distributions.
• a. Binomial distribution
• - Cox, Ross, and Rubinstein (1979)
• - Rendleman and Barter (1979)
• b. Poisson distribution
• c. Normal distribution
• d. Log Normal distribution
• - Chu (1984)
• e. Chi-square distribution
• f. Non-central Chi-square distribution
• - M. Schroder, Journal of Finance (1989)
• g. Wishart distribution
• - Chen and Lee, Management Science (1981)
• h. Stable distribution
• - E. Fama, JASA (1971)
• i. Other distributions

13
9. Principle components and factor analyses

• In this section, we will discuss principle
  components and factor analyses.
• - Anderson, T. W., An Introduction to
  Multivariate Statistical Analysis (2003),
  Wiley-Interscience.
• a. Principle components
• b. Factor analyses

14
10. Non-parametric, Semi-parametric, and GMM
analyses

• In this section, non-parametric, semi-paprmetric,
  and GMM analyses will be discussed.
• a. Non-parametric analysis
• - Ait-Sahalia and Lo, Journal of Econometrics
  (2000)
• b. Semi-parametric analysis
• - Hwang, R.C., Chung, H., andChu, C.K. (2009).
  Predicting issuer credit ratings using a
  semiparametric method. Accepted by Journal of
  Empirical Finance.
• - Cheng, K.F.,Chu, C.K., and Hwang, R.C. (2009).
  Predicting bankruptcy using the discrete-time
  semiparametric hazard model. Accepted by
  Quantitative Finance.
• - Hwang, R.C., Cheng, K.F., and Lee, J.C.
  (2007). A semiparametric method for predicting
  bankruptcy. Journal of Forecasting, 26, 317-342.
  
• c. GMM analysis
• - Chen et al., Corporate Governance and
  International Review (2007)
• - Brick et al. The Motivations for Issuing
  Putable Debt An Empirical Analysis forthcoming
  for Handbook of Quantitative Finance and
  Econometrics, 2011.

15
11. Path analysis

• In this section, path analysis will be discussed.

16
12. Cluster analysis

• In this section, Cluster analysis will be
  discussed.
• - Brown and Goetzmann (JFE, 1997)
• - Finding Groups in Data An Introduction to
  Cluster Analysis, L Kaufman, Peter J Rousseeuw,
  Wiley, 2005

17
13. Summary and concluding remarks

• In this paper, we have review both financial
  econometrics and statistics methods which has
  been used in finance and accounting research for
  last four decades. In this handbook, we include
  research papers in both finance and accounting
  which present different methodologies in
  detailed. Therefore, it will be very useful to
  researcher when they try to perform similar kind
  of research.

18
References

• Chang, C. F., 1999. Determinants of capital
  structure and management compensation the
  partial least squares approach, Ph.D.
  Dissertation, Rutgers University.
• Cheng, K.F.,Chu, C.K., and Hwang, R.C. (2009).
  Predicting bankruptcy using the discrete-time
  semiparametric hazard model. Accepted by
  Quantitative Finance. (SSCI)
• Chu, C. C., 1984. Alternative methods for
  determining the expected market risk premium
  theory and evidence, Ph.D. Dissertation,
  University of Illinois at Urbana-Champaign.
• Cox, J. C., S. A. Ross, and M. Rubinstein, 1979.
  Option Pricing a simplified approach, Journal
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• Davis, P., 2010. A firm-level test of the CAPM,
  Working paper.
• Hwang, R.C., Cheng, K.F., and Lee, C.F. (2009).
  On multiple-class prediction of issuer crediting
  ratings. Journal of Applied Stochastic Models in
  Business and Industry, 25, 535-550. (SCI)
• Hwang, R.C., Cheng, K.F., and Lee, J.C. (2007).
  A semiparametric method for predicting
  bankruptcy. Journal of Forecasting, 26, 317-342.
  
• Hwang, R.C., Chung, H., and Chu, C.K. (2009).
  Predicting issuer credit ratings using a
  semiparametric method. Accepted by Journal of
  Empirical Finance. (SSCI)
• Hwang, R.C., Wei, H.C., Lee, J.C., and Lee, C.F.
  (2008). On prediction of financial distress using
  the discrete-time survival model. Journal of
  Financial Studies, 16, 99-129. (TSSCI)
• Ittner, C. D., Larcker, D. F., and Rajan, M. V.,
  1997, The choice of performance measure in
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• Kim, D., 2010. Issues related to the
  errors-in-variables problems in asset pricing
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  Management.

19
References

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• Liu, B., 2006. Two essays in financial
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