The General Linear Model IV

  • Phoebus Dhrymes


In this chapter we take up the problems occasioned by the failure of the rank condition (for the matrix of explanatory variables). This problem arises as a matter of course in analysis of variance (or covariance) models where some of the variables are classificatory. In this case, we are led to the construction of “dummy” variables representing the classificatory schemes. Since all such classificatory schemes are exhaustive, it is not surprising that the “dummy” variables are linearly dependent and, thus, the rank condition for the data matrix fails.


  1. 6.
    APT Analytics Guide. (2011). SunGard APT, London
  2. 15.
    Ashley, R., & Ye, H. (2012). On the granger causality between median inflation and price dispersion. Applied Economics, 44, 4221–4238.CrossRefGoogle Scholar
  3. 21.
    Beaton, A. E., & Tukey, J. W. (1974). The fitting of power series, meaning polynomials, illustrated on Bank-spectroscopic data. Technometrics, 16, 147–185.CrossRefGoogle Scholar
  4. 26.
    Benjamini, Y., & Hochberg, Y. (1995). Controlling the false discovery rate: A practical and powerful approach to multiple testing. Journal of the Royal Statistical Society, Series B, 57, 289–300.Google Scholar
  5. 33.
    Blin, J. M., Bender, S., & Guerard, J. B. Jr. (1997). Earnings Forecasts, Revisions and Momentum in the Estimation of Efficient Market-Neutral Japanese and U.S. Portfolios. In A. Chen (Ed.), Research in Finance, 15.Google Scholar
  6. 34.
    Bloch, M., Guerard Jr., J. B., Markowitz, H. M., Todd, P., & Xu, G.-L. (1993). A comparison of some aspects of the U.S. and Japanese equity markets. Japan & the World Economy, 5, 3–26.CrossRefGoogle Scholar
  7. 43.
    Brush, J. S., & Boles, K. E. (1988). The predictive power in relative strength and CAPM. Journal of Portfolio Management, 20–23.Google Scholar
  8. 44.
    Brush, J. S. (2001). Price Momentum: A Twenty-Year Research Effort. Columbine Newsletter Special Issue.Google Scholar
  9. 50.
    Chan, L. K. C., Hamao, Y., & Lakonishok, J. (1991). Fundamentals and stock returns in Japan. Journal of Finance, 46, 1739–1764.CrossRefGoogle Scholar
  10. 51.
    Chan, L. K. C., Lakonishok, J., & Hamao, Y. (1993). Can Fundamentals Predict Japanese Stock Returns. Financial Analysts Journal.Google Scholar
  11. 71.
    Conner, G., & Korajczyk, R. A. (2010). Factor models in portfolio and asset pricing theory. In J. Guerard (Ed.), The handbook of portfolio construction: Contemporary applications of Markowitz techniques. New York: Springer.Google Scholar
  12. 76.
    Cragg, J. G., & Malkiel, B. G. (1968). The consensus and accuracy of some predictions of the growth of corporate earnings. Journal of Finance, 23, 67–84.CrossRefGoogle Scholar
  13. 79.
    Deng, S., & Min, X. (2013). Applied optimization in global efficient portfolio construction using earnings forecasts. Journal of Investing, 23, 104–114.CrossRefGoogle Scholar
  14. 83.
    Dhrymes, P. J., Friend, I., Gultekin, B., & Gultekin, M. (1984). A critical reexamination of the empirical evidence on the APT model. Journal of Finance, 39, 323–346.CrossRefGoogle Scholar
  15. 84.
    Dhrymes, P. J., Friend, I., Gultekin, B., & Gultekin, M. (1985). New tests of the APT and their implications. Journal of Finance, 40, 659–674.CrossRefGoogle Scholar
  16. 86.
    Dhrymes, P. J., & Guerard Jr., J. B. (2017). Returns, risk, portfolio selection, and evaluation. In J. Guerard (Ed.), Portfolio construction, Measurment, and efficiency: Essays in honor of Jack Tteynor. New York: Springer.Google Scholar
  17. 103.
    Efron, B. (1982). The jackknife, the bootstrap, and other resampling plans. Philadelphia: Society for Industrial and Applied Mathematics.CrossRefGoogle Scholar
  18. 105.
    Elton, E. J., & Gruber, M. J. (1972). Earnings estimates and the accuracy of Expectational data. Management Science, 18, B409–B424.CrossRefGoogle Scholar
  19. 106.
    Elton, E. J., Gruber, M. J., & Gultekin, M. (1981). Expectations and share prices. Management Science, 27, 975–987.CrossRefGoogle Scholar
  20. 107.
    Elton, E. J., Gruber, M. J., Brown, S. J., & Goetzman, W. N. (2007). Modern portfolio theory and investment analysis (7th ed.). New York: Wiley.Google Scholar
  21. 112.
    Fama, E. F., & MacBeth, J. D. (1973). Risk, return, and equilibrium: Empirical tests. Journal of Political Economy, 81, 607–636.CrossRefGoogle Scholar
  22. 116.
    Fama, E. F., & French, K. R. (2008). Dissecting anomalies. Journal of Finance, 63, 1653–1678.CrossRefGoogle Scholar
  23. 118.
    Farrell Jr., J. L. (1997). Portfolio management: Theory and applications. New York: McGraw-Hill/ Irwin.Google Scholar
  24. 119.
    Farrer, D. E., & Glauber, R. R. (1967). Multicollinearity in regression analysis: The problem revisited. The Review of Economics and Statistics, 49, 92–107.CrossRefGoogle Scholar
  25. 121.
    Ferson, W. E., & Harvey, C. R. (1991b). Sources of predictability in portfolio returns. Financial Analysts Journal, 47, 49–56.CrossRefGoogle Scholar
  26. 122.
    Ferson, W. E., & Harvey, C. R. (1995). Explaining the predictability of asset returns. In A. Chen (Ed.), Research in finance (Vol. 11). Westport, Ct: JAI Press.Google Scholar
  27. 125.
    Fisher, L., & Lorie, J. H. (1964). Rates of return on Investments in Common Stocks. Journal of Business, 7, 1–21.Google Scholar
  28. 135.
    Geary, R. C., & Leser, C. E. V. (1968). Significance tests in multiple regression. The American Statistician, 22, 20–21.Google Scholar
  29. 137.
    Graham, B., & Dodd, D. (1934). Security analysis: Principles and technique. New York: McGraw-Hill Book Company.Google Scholar
  30. 139.
    Granger, C. W. J. (1969). Investigating casual relations by economic models and cross-spectral methods. Econometrica, 37, 424–438.CrossRefGoogle Scholar
  31. 145.
    Granger, C. W. J. (1989a). Invited review: Combining forecasts-twenty years later. Journal of Forecasting, 8, 167–173.CrossRefGoogle Scholar
  32. 148.
    Grinhold, R., & Kahn, R. (1999). Active portfolio management. New York: McGraw-Hill/Irwin.Google Scholar
  33. 149.
    Guerard Jr., J. B., & Horton, R. L. (1984a). The management f executive compensation in large, dynamic firms: A ridge regression estimation. Communications is Statistics, 13, 183–190.CrossRefGoogle Scholar
  34. 150.
    Guerard Jr., J. B., & Horton, R. L. (1984b). The management f executive compensation in large, dynamic firms: A further look. Communications is Statistics, 13, 441–448.Google Scholar
  35. 154.
    Guerard Jr., J. B., Gultekin, M., & Stone, B. K. (1997). The role of fundamental data and analysts’ earnings breadth, forecasts, and revisions in the creation of efficient portfolios. In A. Chen (Ed.), Research in finance (Vol. 15). Greenwich, CT: JAI Press.Google Scholar
  36. 156.
    Guerard Jr., J. B., & Mark, A. (2003). The optimization of efficient portfolios: The case for a Quadratic R&D Term. In Research in Finance, 20, 213–247.CrossRefGoogle Scholar
  37. 158.
    Guerard Jr., J. B. (2010). The handbook of portfolio construction: Contemporary applications of Markowitz techniques. New York: Springer. Chapter 3.CrossRefGoogle Scholar
  38. 159.
    Guerard Jr., J. B. (2012). Global earnings forecast efficiency. In J. Kensinger (Ed.), Research in finance (Vol. 28). Dublin: Emerald.CrossRefGoogle Scholar
  39. 160.
    Guerard Jr., J. B., Gultekin, M. N., & Xu, G. (2012). Investing with momentum: The past, present, and future. Journal of Investing, 21, 68–80.CrossRefGoogle Scholar
  40. 161.
    Guerard Jr., J. B., Rachev, R. T., & Shao, B. (2013). Efficient global portfolios: Big data and investment universe. IBM Journal of Research and Development, 57(5), 11.CrossRefGoogle Scholar
  41. 162.
    Guerard Jr., J. B., Markowitz, H. M., & Xu, G. (2015). Earnings forecasting in a global stock selection model and efficient portfolio construction and management. International Journal of Forecasting, 31, 550–560.CrossRefGoogle Scholar
  42. 174.
    Hastie, T., Tibshirani, R., & Friedman, J. (2016). The elements of statistical learning: Data mining, inference, and prediction (2nd ed.). New York: Springer. 11th printing.Google Scholar
  43. 175.
    Haugen, R. A., & Baker, N. (1996). Communality in the determinants of expected results. Journal of Financial Economics, 41, 401–440.CrossRefGoogle Scholar
  44. 177.
    Haugen, R., & Baker, N. (2010). Case closed. In J. B. Guerard (Ed.), The handbook of portfolio construction: Contemporary applications of Markowitz techniques. New York: Springer.Google Scholar
  45. 178.
    Hawawini, G., & Keim, D. B. (1995). On the predictability of common stock returns: World-wide evidence. In R. A. Jarrow, V. Maksimovic, & W. T. Ziemba (Eds.), Handbooks in operations research and management science: Finance (Vol. 9, pp. 497–537). Amsterdam: Elsevier.Google Scholar
  46. 183.
    Hendry, D. F., & Doornik, J. A. (2014). Empirical model discovery and theory evaluation. Cambridge: MIT Press.CrossRefGoogle Scholar
  47. 186.
    Hoerl, A. E. (1962). Application of ridge analysis to regression problems. Chemical Engineering Progress, 58, 54–59.Google Scholar
  48. 187.
    Hoerl, A. E., & Kennard, R. W. (1970a). Ridge regression: Biased estimation of nonorthogonal problems. Technometrics, 12, 55–69.CrossRefGoogle Scholar
  49. 195.
    Keane, M. P., & Runkle, D. E. (1998). Are financial analysts’ forecasts of corporate profits rational? The Journal of Political Economy, 106, 768–805.CrossRefGoogle Scholar
  50. 197.
    King, R., Plosser, C., & Stock, J. (1991). Stochastic trends and economic fluctuations. American Economic Review, 81, 819–840.Google Scholar
  51. 207.
    Lakonishok, J., Shleifer, A., & Vishny, R. W. (1994). Contrarian investment, extrapolation and risk. Journal of Finance, 49, 1541–1578.CrossRefGoogle Scholar
  52. 208.
    Latane, H. A. (1959). Criteria for choice among risky ventures. Journal of Political Economy, 67, 144–155.CrossRefGoogle Scholar
  53. 209.
    Latane, H. A., Tuttle, D. L., & Jones, C. P. (1975). Security analysis and portfolio management (2nd ed.). New York: The Roland Press.Google Scholar
  54. 211.
    Leamer, E. E. (1972). A class of informative priors and distributed lag analysis. Econometrica, 40, 1059–1081.CrossRefGoogle Scholar
  55. 212.
    Leamer, E. E. (1973). Multicollinearity: A Bayesian interpretation. Review of Economics and Statistics, 55, 371–380.CrossRefGoogle Scholar
  56. 213.
    Leamer, E. E. (1978). Specification searches: Ad hoc inference with nonexperimental data. New York: Wiley.Google Scholar
  57. 219.
    Lim, T. (2001). Rationality and analysts’ forecast bias. Journal of Finance, 56, 369–385.CrossRefGoogle Scholar
  58. 222.
    Lintner, J. (1965b). Security prices, risk, and the maximum gain from diversification. Journal of Finance, 20, 587–615.Google Scholar
  59. 232.
    Markowitz, H. M. (1952). Portfolio selection. Journal of Finance, 7, 77–91.Google Scholar
  60. 233.
    Markowitz, H. M. (1956). The optimization of a quadratic function subject to linear constraints. Naval Research Logistics Quarterly, 3, 111–133.CrossRefGoogle Scholar
  61. 234.
    Markowitz, H. M. (1959). Portfolio selection: Efficient diversification of investment, Cowles foundation monograph no.16. New York: John Wiley & Sons.Google Scholar
  62. 235.
    Markowitz, H. M. (1976). Investment in the Long run: New evidence for an old rule. Journal of Finance, 31, 1273–1286.CrossRefGoogle Scholar
  63. 236.
    Markowitz, H. M. (1987). Mean-variance analysis in portfolio choice and capital markets. Oxford: Basil Blackwell.Google Scholar
  64. 237.
    Markowitz, H. M., & Xu, G. (1994). Data mining corrections. Journal of Portfolio Management, 21, 60–69.CrossRefGoogle Scholar
  65. 253.
    Mossin, J. (1966). Equilibrium in a capital asset market. Econometrica, 34, 768–783.CrossRefGoogle Scholar
  66. 270.
    Rosenberg, B. (1974). Extra-market components of covariance in security returns. Journal of Financial and Quantitative Analysis, 9, 263–274.CrossRefGoogle Scholar
  67. 271.
    Rosenberg, B., & Marathe, V. (1979). Tests of capital asset pricing hypotheses. In H. Levy (Ed.), Research in finance (Vol. 1). Westport, Ct: JAI Press.Google Scholar
  68. 272.
    Ross, S. A. (1976). The arbitrage theory of capital asset pricing. Journal of Economic Theory, 13, 341–360.CrossRefGoogle Scholar
  69. 273.
    Ross, S. A., & Roll, R. (1980). An empirical investigation of the arbitrage pricing theory. Journal of Finance, 35, 1071–1103.CrossRefGoogle Scholar
  70. 277.
    Rudd, A., & Rosenberg, B. (1979). Realistic Portfolio Optimization. In E. Elton & M. Gruer (Eds.), Portfolio theory, 25 years after. Amsterdam: North-Holland.Google Scholar
  71. 279.
    Rudd, A., & Clasing, H. K. (1982). Modern portfolio theory: The principles of investment management. Homewood, IL: Dow-Jones Irwin.Google Scholar
  72. 286.
    Sharpe, W. F. (1963). A simplified model for portfolio analysis. Management Science, 9, 277–293.CrossRefGoogle Scholar
  73. 287.
    Sharpe, W. F. (1964). Capital asset prices: A theory of market equilibrium under conditions of risk. Journal of Finance, 19, 425–442.Google Scholar
  74. 288.
    Sharpe, W. F. (1966). Mutual fund performance. Journal of Business: A Supplement, 1(2), 119–138.CrossRefGoogle Scholar
  75. 304.
    Tibshirani, R. (1996). Regression shrinkage and selection via the lasso. Journal of the Royal Statistical Association, Series B, 58, 267–288.Google Scholar
  76. 306.
    Treynor, J. L. (1965). How to rate Management of Investment Funds. Harvard Business Review, 43, 63–75.Google Scholar
  77. 307.
    Treynor, J. L., & Mazuy, K. K. (1966). Can mutual funds outguess the market. Harvard Business Review, 44, 131–136.Google Scholar
  78. 325.
    Wheeler, L. B. (1994). Changes in consensus earnings estimates and their impact on stock returns. In B. Bruce & C. B. Epstein (Eds.), The handbook of corporate earnings analysis. Chicago: Probus.Google Scholar
  79. 326.
    Williams, J. B. (1938). The theory of investment value. Cambridge: Harvard University Press.Google Scholar
  80. 331.
    Wonnacott, T. H., & Wonnacott, R. J. (1981). In E. Robert (Ed.), Regression: A second course in statistics. Malabar, FL: Krieger Publishing Company.Google Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Phoebus Dhrymes
    • 1
  1. 1.New YorkUSA

Personalised recommendations