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.
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
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.
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)
2.
c.
-
Single equation regression methods
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)
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, 535550. (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 discretetime semiparametric hazard model. Accepted by Quantitative Finance. (SSCI)
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)
- M&M 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
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)
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 ()
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)
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)
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
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
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.
11. Path analysis
In this section, path analysis will be
discussed.
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
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.
References
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semiparametric hazard model. Accepted by Quantitative Finance. (SSCI)
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semiparametric method. Accepted by Journal of Empirical Finance. (SSCI)
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