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Marjorie B. McElroy, Edwin Burmeister, Arbitrage Pricing Theory as a Restricted Nonlinear Multivariate Regression Model: Iterated Nonlinear Seemingly Unrelated Regression Estimates, Journal of Business & Economic Statistics, Vol. 6, No. 1 (Jan., 1988), pp. 29-42
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McElroy et al. (1988) studied this question.
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