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Financial Econometrics and Statistics: Past, Present, and Future

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.

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Financial Econometrics and Statistics: Past, Present, and Future

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  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) - 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

  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 of Financial Economics, 7, 229-263. 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 annual bonus contracts,” Accounting Review 72, 231-255. JE Core - Journal of Law, Economics, and Organization, 2000 “The directors' and officers' insurance premium: an outside assessment of the quality of corporate governance” Kim, D., 1997. “A reexamination of firm size, book-to-market, and earnings price in the cross-section of expected stock returns,” Journal of Financial and Quantitative Analysis, 32(4), 463-489. Kim, D., 2010. “Issues related to the errors-in-variables problems in asset pricing tests,” Handbook of Quantitative Finance and Risk Management.

  19. References Lee, A. C. and J. D. Cummins (1998), “Alternative models for estimating the cost of capital for property/casualty insurers,” Review of Quantitative Finance and Accounting, 10(3), 235-267. Lee, A., 1996. “Cost of capital and equity offerings in the insurance industry,” Ph.D. Dissertation, The University of Pennsylvania in Partial. Lee, C. F. and F. C. Jen, 1978. “Effects of measurement errors on systematic risk and performance measure of a portfolio,” Journal of Financial and Quantitative Analysis, 13(2), 299-312. Lee, C. F., 1973. “Errors-in-variables estimation procedures with applications to a capital asset pricing model,” Ph.D. Dissertation, The State University of New York at Buffalo, 1973. Liu, B., 2006. “Two essays in financial economics: I: Functional forms and pricing of country funds. II: The term structure model of inflation risk premia,” Ph.D. Dissertation, Rutgers University. Maddala, G. S., C. R. Rao, and G. S. Maddala, (1996) “Handbook of Statistics 14: Statistical Methods in Finance,” Elsevier Science & Technology. Miller, M. H. and F. Modigliani, 1966. “Some estimates of the cost of capital to the electric utility industry,” American Economic Review, 56(3), 333-391. Rendleman, R. J., Jr. and B. J. Barter, 1979. “Two-state option pricing,” Journal of Finance, 24, 1093-1110. Rubinstein, M., 1994. “Implied binomial trees,” Journal of Finance, 49, 771-818. Thursby, J. G., 1985. “The relationship among the specification error tests of Hausman, Ramsey and Chow,” Journal of the American Statistical Association, 80(392), 926-928. Tsai, G. M, 2005. “Alternative Dynamic Capital Asset Pricing Models: Theories and Empirical Results,” Ph.D. Dissertation, Rutgers. Wei, K. C., 1984. “The arbitrage pricing theory versus the generalized intertemporal capital asset pricing model: theory and empirical evidence,” Ph.D. Dissertation, University of Illinois at Urbana-Champaign. Yang, C. C., 1989. “The impact of new equity financing on firms’ investment, dividend and bebt-financing decisions,” Ph.D. Dissertation, The University of Illinois at Urbana-Champaign.

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