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Recursive stability analysis of linear regression relationships. An exploratory methodology. (English) Zbl 0514.62117


MSC:

62P20 Applications of statistics to economics
62J05 Linear regression; mixed models
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62M20 Inference from stochastic processes and prediction

Citations:

Zbl 0321.62063
Full Text: DOI

References:

[1] Anscombe, P. J., Examination of residuals, Proceedings of the 4th Berkeley symposium on mathematical statistics and probability, 1, 1-36 (1961) · Zbl 0101.35703
[2] Anscombe, P. J.; Tukey, J. W., The examination and analysis of residuals, Technometrics, 5, 141-160 (1963) · Zbl 0118.13903
[3] Bartlett, M. S., On the theoretical specification and sampling properties of autocorrelated time-series, Journal of the Royal Statistical Society, B 8, 26-41 (1946) · Zbl 0063.00228
[4] Bartlett, M. S., An inverse matrix adjustment arising in discriminant analysis, Annals of Mathematical Statistics, 22, 107-111 (1951) · Zbl 0042.38203
[5] Bateman, G., On the power function of the longest run as a test for randomness in a sequence of alternatives, Biometrika, 35, 97-112 (1948) · Zbl 0030.20302
[6] Belsley, D. A.; Kuh, E.; Welsch, R. E., Regression diagnostics: Identifying influential data and sources of collinearity (1980), Wiley: Wiley New York · Zbl 0479.62056
[7] Box, G. E.P.; Cox, D. R., An analysis of transformations, Journal of the Royal Statistical Society, B 26, 211-243 (1964) · Zbl 0156.40104
[8] Box, G. E.P.; Jenkins, G. M., Time series analysis forecasting and control (1969), Holden-Day: Holden-Day San Francisco, CA · Zbl 0109.37303
[9] Box, G. E.P.; Tiao, G. C., Bayesian inference in statistical inference (1973), Addison-Wesley: Addison-Wesley Reading, MA · Zbl 0124.09903
[10] Brown, R. L.; Durbin, J., Methods of investigating whether a regression relationship is constant over time, Mathematical Centre tracts no. 26 (1968), (Amsterdam) · Zbl 0181.22102
[11] Brown, R. L.; Durbin, J.; Evans, J. M., Techniques for testing the constancy of regression relationships over time (with discussion), Journal of the Royal Statistical Society, B 37, 149-192 (1975) · Zbl 0321.62063
[12] Burr, E. J.; Cane, G., Longest run of consecutive observations having a specified attribute, Biometrika, 35, 97-112 (1948) · Zbl 0134.15002
[13] Cameron, N., The stability of Canadian demand for money functions 1954-75, Canadian Journal of Economics, 12, 282-291 (1979)
[14] Chow, C., Tests of equality between sets of coefficients in two linear regressions, Econometrica, 28, 591-605 (1960) · Zbl 0099.14304
[15] Chow, G. C., Analysis and control of dynamic economic systems (1975), Wiley: Wiley New York · Zbl 0314.90001
[16] Cooley, T. F.; Prescott, E. C., Estimation in the presence of stochastic parameter variations, Econometrica, 44, 167-184 (1976) · Zbl 0325.62067
[17] Dempster, A. P., Model searching and estimation in the logic of inference, (Godambe, V. P.; Sprott, D. A., Foundations of statistical inference (1971), Holt, Rinehart and Winston: Holt, Rinehart and Winston Toronto) · Zbl 0169.21301
[18] Dent, W. T.; Styan, G. P.H., Uncorrelated residuals from linear models, Journal of Econometrics, 7, 211-225 (1978) · Zbl 0377.62081
[19] Deshayes, J.; Picard, D., (Tests de rupture dans un modéle, A 288 (1979), Comptes Rendus de l’Académie des Sciences: Comptes Rendus de l’Académie des Sciences Paris), 851-854 · Zbl 0397.62062
[20] Deshayes, J.; Picard, D., Tests de rupture de régression: Comparaisons asymptotiques (1980), Université Paris-Sud (Orsay): Université Paris-Sud (Orsay) Paris, Unpublished manuscript
[21] Duesenberry, The Brookings quarterly econometric model of the United States (1965), Rand McNally: Rand McNally Chicago, IL
[22] Dufour, J.-M., Methods for specification errors analysis with macroeconomic applications, (Ph.D. dissertation (1979), University of Chicago: University of Chicago Chicago, IL)
[23] Dufour, J.-M., Dummy variables and predictive tests for structural change, Economics Letters, 6, 241-247 (1980)
[24] Dufour, J.-M., Rank tests for serial dependence, Journal of Time Series Analysis, 2, 117-128 (1981) · Zbl 0514.62054
[25] Dufour, J.-M., Generalized Chow tests for structural change: A coordinate-free approach, International Economic Review (1981), forthcoming
[26] Dufour, J.-M., The demand for money during the German hyperinflation: A recursive stability analysis, (Discussion paper no. 8130 (1981), Département de Sciences Économiques, Université de Montréal: Département de Sciences Économiques, Université de Montréal Montréal)
[27] Dufour, J.-M., Investment, taxation and econometric policy evaluation: Some evidence on the Lucas critique, (Discussion paper no. 8131 (1981), Département de Sciences Économiques, Université de Montréal: Département de Sciences Économiques, Université de Montréal Montréal)
[28] Duncan, D. B.; Horn, S. D., Linear dynamic recursive estimation form the viewpoint of regression analysis, Journal of the American Statistical Association, 67, 815-821 (1972) · Zbl 0254.62039
[29] Durbin, J., Testing for serial correlation in least squares regression when some of the regressors are lagged dependent variables, Econometrica, 38, 410-421 (1970)
[30] Farebrother, R. W., Recursive residuals — A remark on algorithm AS75: Basic procedures for large, sparse or weighted least squares problems, Applied Statistics, 25, 323-324 (1976)
[31] Farebrother, R. W., An historical note on recursive residuals, Journal of the Royal Statistical Society, B 40, 373-375 (1981)
[32] Farley, J. U.; Hinich, M., Testing for a shifting slope coefficient in a linear model, Journal of the American Statistical Association, 65, 1320-1329 (1970) · Zbl 0214.46502
[33] Farley, J. U.; Hinich, M.; McGuire, T. W., Some comparisons of tests for a shift in the slopes of a multivariate linear time series model, Journal of Econometrics, 3, 297-318 (1975) · Zbl 0318.62074
[34] Fisher, G., Propositions, principles and methods: The linear hypothesis and structural change, (Discussion paper no. 410 (1980), Institute for Economic Research, Queen’s University: Institute for Economic Research, Queen’s University Kingston)
[35] Garbade, K., Two methods for examining the stability of regression coefficients, Journal of the American Statistical Association, 72, 54-63 (1977) · Zbl 0345.62047
[36] Geisser, S., The predictive sample reuse method with applications, Journal of the American Statistical Association, 70, 320-328 (1975) · Zbl 0321.62077
[37] Godolphin, E. J.; de Tullio, M., Invariance properties of uncorrelated residual transformations, Journal of the Royal Statistical Society, B 40, 313-321 (1978) · Zbl 0429.62051
[38] Goldfeld, S. M.; Quandt, R. E., Nonlinear methods in econometrics (1972), North-Holland: North-Holland Amsterdam · Zbl 0231.62114
[39] Hájek, J., A course in nonparametric statistics (1969), Holden-Day: Holden-Day San Francisco, CA · Zbl 0193.16901
[40] Hájek, J.; Šidák, Z., Theory of rank tests (1967), Academic Press: Academic Press New York · Zbl 0161.38102
[41] Harvey, A. C.; Phillips, G. D.A., A comparison of the power of some tests for heteroskedasticity in the general linear model, Journal of Econometrics, 2, 307-316 (1974) · Zbl 0289.62048
[42] Harvey, A. C.; Phillips, G. D.A., Testing for stochastic parameters in regression models, (Q.S.S. discussion paper no. 35 (1977), University of Kent: University of Kent Canterbury) · Zbl 0464.62105
[43] Harvey, A. C.; Phillips, G. D.A., Maximum likelihood estimation of regression models with autoregressive-moving average disturbances, Biometrika, 66, 49-58 (1979) · Zbl 0453.62082
[44] Harvey, A. C., An alternative proof and generalization of a test for structural change, The American Statistician, 30, 122-123 (1976) · Zbl 0336.62060
[45] Harvey, A. C.; Collier, P., Testing for functional misspecification in regression analysis, Journal of Econometrics, 6, 103-119 (1977) · Zbl 0358.62050
[46] Heller, H. R.; Khan, M. S., The demand for money and the term structure of interest rates, Journal of Political Economy, 87, 109-129 (1979)
[47] Heyadat, A.; Robson, D. S., Independent stepwise residuals for testing heteroskedasticity, Journal of the American Statistical Association, 65, 1573-1581 (1970) · Zbl 0225.62084
[48] Hwang, H.-S., A test of a disequilibrium model, Journal of Econometrics, 12, 319-334 (1980) · Zbl 0438.62087
[49] Kagan, A. M.; Linnik, Yu. V.; Rao, C. R., Characterization problems in mathematical statistics (1973), Wiley: Wiley New York · Zbl 0271.62002
[50] Kalman, R. E., A new approach to linear filtering and prediction problems, Transactions ASME Journal of Basic Engineering, 82, 35-45 (1960)
[51] Khan, M. S., The stability of the demand for money function of the United States, Journal of Political Economy, 82, 1205-1219 (1974)
[52] Khan, M. S., The relative stability of velocity and the investment multiplier, Journal of Monetary Economics, 4, 103-119 (1978)
[53] Klotz, J., Small sample power and efficiency for the one-sample Wilcoxon and normal score tests, Annals of Mathematical Statistics, 34, 624-632 (1963) · Zbl 0129.32706
[54] LaMotte, L. R.; McWhorter, A., An exact test for the presence of random-walk coefficients in a linear regression model, Journal of the American Statistical Association, 72, 54-63 (1978)
[55] Leamer, E. E.; Chamberlain, G., Matrix weighted averages and posterior bounds, Journal of the Royal Statistical Society, B 38, 73-84 (1976) · Zbl 0321.62042
[56] Lehmann, E. L., Testing statistical hypotheses (1959), Wiley: Wiley New York · Zbl 0089.14102
[57] Lehmann, E. L., Nonparametrics: Statistical methods based on ranks (1975), Holden-Day: Holden-Day San Francisco, CA · Zbl 0354.62038
[58] Ljung, G. M.; Box, G. E.P., On a measure of lack of fit for stationary time series, Biometrika, 65, 297-303 (1978) · Zbl 0386.62079
[59] Lucas, R., Econometric policy evaluation: A critique, (Carnegie-Rochester conferences on public policy, Vol. 1 (1976), North-Holland: North-Holland Amsterdam), 19-46
[60] McGilchrist, C. A.; Sandland, R. L., Recursive estimation of the general linear model with dependent errors, Journal of the Royal Statistical Society, B 41, 65-68 (1979) · Zbl 0398.62059
[61] Mosteller, F., Note on an application of runs to quality control charts, Annals of Mathematical Statistics, 12, 228-232 (1941) · JFM 67.0458.03
[62] Mosteller, F.; Tukey, J. W., Data analysis and regression (1977), Addison-Wesley: Addison-Wesley Reading, MA
[63] Phillips, G. D.A.; Harvey, A. C., A simple test for serial correlation in regression analysis, Journal of the American Statistical Association, 69, 935-939 (1974) · Zbl 0296.62058
[64] Phillips, G. D.A., Recursions for the two-stage least-squares estimators, Journal of Econometrics, 6, 65-77 (1977) · Zbl 0379.62094
[65] Pizzetti, P., I fondamenti matematici per la critica dei risultati sperimentali (Genoa) (1981), Reprinted in: Atti della Universita di Genova · JFM 24.0204.02
[66] Quandt, R. E., The estimation of the parameters of a linear regression obeying two separate regimes, Journal of the American Statistical Association, 53, 873-880 (1958) · Zbl 0116.37304
[67] Quandt, R. E., Tests of the hypothesis that a linear regression obeys two separate regimes, Journal of the American Statistical Association, 55, 324-330 (1960) · Zbl 0095.13602
[68] Ramsey, J. B., Tests for specification errors in classical least squares analysis, Journal of the Royal Statistical Society, B 31, 350-371 (1969) · Zbl 0179.48902
[69] Ramsey, J. B., Classical model selection through specification error tests, (Zarembka, P., Frontiers of economerics (1974), Academic Press: Academic Press New York), Ch. 1 · Zbl 0179.48902
[70] Riddell, W. C., Recursive estimation algorithms for economic research, Annals of Economic and Social Measurement, 4, 397-406 (1975)
[71] Riddell, W. C., The empirical foundations of the Phillips curve: Evidence from Canadian wage contract data, Econometrica, 47, 1-24 (1979)
[72] Schweder, T., Some ‘optimal’ methods to detect structural shift or outliers in regression, Journal of the American Statistical Association, 71, 491-501 (1976) · Zbl 0361.62058
[73] Singh, B.; Nagar, A. L.; Choudhry, N. K.; Raj, B., On the estimation of structural change: A generalization of the random coefficients regression model, International Economic Review, 17, 340-361 (1976) · Zbl 0357.62040
[74] Stern, R. M.; Baum, C. F.; Greene, M. N., Evidence on structural change in the demand for aggregate U.S. imports and exports, Journal of Political Economy, 87, 179-192 (1979)
[75] Stone, M., Cross-validatory choice and assessment of statistical prediction (with discussion), Journal of the Royal Statistical Society, B 36, 111-147 (1974) · Zbl 0308.62063
[76] Theil, H., Specification errors and the estimation of economic relationships, Review of the International Statistical Institute, 25, 41-51 (1957) · Zbl 0124.36701
[77] Theil, H., The analysis of disturbances in regression analysis, Journal of the American Statistical Association, 60, 1067-1079 (1965)
[78] Theil, H., A simplification of the BLUS procedure for analyzing disturbances, Journal of the American Statistical Association, 63, 242-251 (1968)
[79] Theil, H., Principles of econometrics (1971), Wiley: Wiley New York · Zbl 0221.62002
[80] Tukey, J. W., Exploratory data analysis (1977), Addison-Wesley: Addison-Wesley Reading, MA · Zbl 0409.62003
[81] Tukey, J. W., The future of data analysis, Annals of Mathematical Statistics, 33, 1-67 (1962) · Zbl 0107.36401
[82] Zellner, A., Bayesian analysis of regression error terms, (Discussion paper (1973), H.G.B. Alexander Research Foundation, Graduate School of Business, University of Chicago: H.G.B. Alexander Research Foundation, Graduate School of Business, University of Chicago Chicago, IL) · Zbl 0313.62050
[83] Zellner, A., Bayesian analysis of regression error terms, Journal of the American Statistical Association, 70, 138-144 (1975) · Zbl 0313.62050
[84] Zellner, A., Bayesian and non-Bayesian analysis of the regression model with multivariate Student-\(t\) error terms, Journal of the American Statistical Association, 71, 400-405 (1976) · Zbl 0348.62026
[85] Zellner, A., The sampling distribution of studentized regression residuals, (Discussion paper (1978), H.G.B. Alexander Research Foundation, Graduate School of Business, University of Chicago: H.G.B. Alexander Research Foundation, Graduate School of Business, University of Chicago Chicago, IL)
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