Abstract
In this paper, regression models with error terms generated by lower order ARMA schemes are analyzed. Methods are discussed for estimating the parameters of the regression coefficients and the ARMA processes. The problem of detecting changes in the regression parameters is considered. A change-detection statistic proposed by MacNeill (1978) for regression problems is modified for application to ARMA processes. The effect of autocorrelated errors on this statistic is briefly discussed.
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References
Bagshaw, M. and Johnson, A. R.: 1977, ‘Sequential Procedures for Detecting Parameters Changes in a Time Series Model’, Journal of the American Statistical Association 72, 593–597.
Box, G. E. P. and Jenkins, G.: 1976, Time Series Analysis: Forecasting and Control, San Francisco, Holden-Day.
Chernoff, H. and Zacks, S.: 1964, ‘Estimating the Current Mean of a Normal Distribution which is Subject to Changes in Time’, Annals of Mathematical Statistics 35, 999–1018.
El-Shaarawi, A. H. and Esterby, S. R.: 1982, Time Series Methods in Hydrosciences, Development in Water Science 17.
Esterby, S. R. and El-Shaarawi, A. H.: 1981, ‘Inference about the Point of Change in a Regression Model’, Applied Statistics 30, 227–285.
Gallant, A. R. and Fuller, W. A.: 1973, ‘Fitting Segmented Polynomial Regression Models Whose Join Points Have to be Estimated’, Journal of the American Statistical Association 68, 144–147.
Gardner, L. A.: 1969, ‘On Detecting Changes in the Mean of Normal Variates’, Annals of Mathematical Statistics 40, 116–126.
Jandhyala, V. K. and MacNeill, I. B.: 1986a, ‘Detection of Parameter Changes at Unknown Times in Linear Regression Models’, Technical Report, The University of Western Ontario.
Jandhyala, V. K. and MacNeill, I. B.: 1986b, ‘A Solution to the Fredholm Integral Equation with Application to Detecting Parameter Changes at Unknown Times in Linear Regression’, Technical Report, The University of Western Ontario.
Kulperger, R. J.: 1985, ‘On the Residuals of Autoregressive Processes and Polynomial Regression’, Stochastic Processes and their Applications 21, 107–118.
Kulperger, R. J.: 1986, ‘Residuals from Regression with Dependent Errors’, Developments in Water Science 27, 318–325.
MacNeill, I. B. (1978a), ‘Properties of Sequences of Partial Sums of Polynomial Regression Residuals with Applications to Test for Change in Regression at Unknown Times’, Annals of Statistics 6, 422–433.
MacNeill, I. B. (1978b), ‘Limit Processes for Sequences of Partial Sums of Regression Residuals’, Annals of Probability 6, 695–698.
MacNeill, I. B. (1982), ‘Detection of Interventions at Unknown Times’, in El-Sharrawi, A. H. and Esterby, S. R. (eds.), Time Series Methods in Hydro Sciences, North Holland Publishing Company, Amsterdam, pp. 16–26.
MacNeill, I. B. (1985), ‘Detecting Unknown Interventions with Application to Forecasting Hydrological Data’, Water Resources Research 21, 785–796.
Page, E. S.: 1955, ‘A Test for a Change in a Parameter Occurring at an Unknown Time Point’, Biometrika 42 523–526.
Quandt, R. E.: 1958, ‘The Estimation of the Parameters of a Linear Regression System Obeying Two Separate Regimes’, Journal of the American Statistical Association 53, 873–880.
Quandt, R. E.: 1960, ‘Test of the Hypothesis that a Linear Regression System Obeys Two Separate Regimes’, Journal of the American Association 55, 324–330.
Robison, D. E.: 1964, ‘Estimates for the Points of Intersection of Two Polynomial Regression’, Journal of the American Association 59, 214–224.
Segen, J. and Sanderson, A. C: 1980, ‘Detecting Change in a Time-Series’, I.E.E.E. Transactions on Information Theory 26, 249–255.
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© 1989 Kluwer Academic Publishers
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Tang, S.M., Macneill, I.B. (1989). The Effect of Autocorrelated Errors on Change-Detection Statistics. In: Chapman, D.T., El-Shaarawi, A.H. (eds) Statistical Methods for the Assessment of Point Source Pollution. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-1960-0_7
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DOI: https://doi.org/10.1007/978-94-009-1960-0_7
Publisher Name: Springer, Dordrecht
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