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一个假设的普通最小二乘法(OLS)收入回归模型的平均收入是公司在市场(Mj)和j意想不到的收入变化不相关的。他们之间的相关性可能需要至少两种形式,包含了公司收入的市场指数(Mj)和行业影响。第一个被建设消除(用y-subscript M),但它没有调整由于行业的影响。它被估计的影响,行业可能只占10%的公司收入的变化。为此模型已经采用适当的规范,相信任何偏见的估计不会很显著。然而,随着统计效率模型,检验球和布朗也提出了另一个简单模型的结果,预测收入将与去年相同。预测误差(即意想不到的收入变化)只有前一年以来的收入变化。作为收入的回归模型,股票收益模型包含许多明显违反OLS的假设。市场指数的回归与残余,因为市场指数包含了换取公司j,因为该行业的影响。既不违反是认真的,因为费舍尔的“组合投资业绩指数”(费舍尔,1966)是计算在所有的股票在纽约证券交易所上市(因此只有一小部分股票回报率的指数),也因为这个行业的影响占10%(Brealey,1968)的股票平均收益率的变化。同样,任何偏差对结果影响很小,因为在任何情况下将他的股票回报率回归拟合100多观察.


An assumption for Ordinary Least Squares (OLS) income regression model was that the average income of firm j in the market (Mj) and the unexpected income change were uncorrelated. Correlation between them could take at least two forms, which contained the firm in the market index of income (Mj) and the industry effects at that time. The first had been eliminated by construction (denoted by the y-subscript on M), but it had not been adjusted due to the impact of the industry at that time. It had been estimated that the impact of industry might account for only 10 percent of the variability of the income in a company.For this reason the model had been adopted as appropriate specifications, to believe that any bias in the estimates would not be very significant. However, as the statistical efficiency inspection on the model, Ball and Brown also presented results for another naïve model, which predicted that the income would be the same as last year. The forecast error (i.e. unexpected income change) was only changes in income since the previous year.As was the case with the income regression model, stock returns model contained a number of apparent violations of OLS assumptions. The return of market index was relevant to the residual because the market index contained the return for firm j, and because the industry impacts. Neither violation was serious, because the “Combination Investment Performance Index” of Fisher (Fisher, 1966) was calculated over all stocks listed on the New York Stock Exchange (hence stock returns was only a small portion of the index), and also because the industry impacts accounted for up to 10 percent (Brealey, 1968) of the changes in the rate of return on the average stock. Again, any bias had little effect on the results, because there is in no case was the stock return regression that was fitted over 100 observations


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