Erwin Saniga, Nicolas Gressis, Jack Hayya, The Effects of Sample Size and Correlation on the Accuracy of the EV Efficiency Criterion, The Journal of Financial and Quantitative Analysis, Vol. 14, No. 3 (Sep., 1979), pp. 615-628

Stable distributions are becoming increasingly popular as appropriate models for stock price changes and other economic phenomena. As a result, there is an expanding body of literature on inferential procedures for this family of distributions. Computationally simple estimators for the parameters of symmetric stable distributions have been provided by Fama and Roll. Little attention, though, has been given to goodness-of-fit tests for members of this family other than the normal.It is the purpose of this paper to discuss simple goodness-of-fit hypothesis tests using kurtosis, b2, to distinguish among members of the stable family. The b2 tests of hypothesis comprise: 1) a null normal versus a nonnormal symmetric stable alternative; 2) a null nonnormal symmetric stable versus a normal alternative; and 3) a null nonnormal stable versus another nonnormal stable alternative. Tables that give the percentage points of b2 and that are necessary for these tests of hypothesis are given. Apart from providing critical values for the tests, the tables allow the researcher to calculate the power. It will be seen that the b2 test exhibits excellent power.It is then hoped that computational convenience will make b2 an important tool for researchers and practitioners in finance. It is also hoped that the procedures we provide will aid these researchers and practitioners in the construction of appropriate financial models.

Abstract The article comments on the paper "Extending the Applicability of Probabilistic Management Planning and Control Models," by Stephen L. Buzby, which was published in the January 1974 issue of the journal "The Accounting Review." According to the authors, the use of Tchebycheff inequalities has been made obsolete by improvements in statistical techniques. Second, the tests that result from the use of Tchebycheff inequalities are extremely conservative, because they provide excessive protection against type I errors and, consequently, poorer protection against type II errors. Third, Buzby has made several statements relating to the distribution of products of variables which are contradictory to the nature of those distributions as reported in the statistics literature. Buzby states that the distribution of the product of a number of normally and identically distributed random variables is unknown except in the case where each has a mean of zero and where there is equality of variances. In that case, Buzby claims that the product will possess a chi-square distribution. However, this is in error. In the authors' opinion, it is important to keep in mind that the Tchebycheff inequalities are rather loose and inaccurate in calculating probabilities and that they should mostly be used in theoretical proofs.

Abstract The article presents a reply to authors John F. Kottas and Hon-Shiang Lau, on the appropriate size of samples in &chi 2 tests. The paper by FHN falls into the realm of accounting risk analysis. In risk analysis, it attempt to incorporate uncertainty into the decision process and, at the same time, try to make the analysis as simple as possible so that it can be understood by the manager and so that it can be done by those with elementary knowledge in statistics and mathematics. There is, therefore, a need in risk analysis to reduce intractible functions to reasonable approximations, preferably to the normal approximation as it is the most familiar and easiest distribution for the practitioner to use. In simulation experiments, the record has been that the choice of sample size was, for the most part, arbitrary. Better yet would be a choice based on the fulfillment of some important criteria of validity, for example, that the minimum expected frequency in a cell be no less than one in a chi-square goodness-of-fit test.

Abstract This article presents information related to the article "Cost-Volume-Profit Analysis Under Conditions of Uncertainty," by researchers Robert K. Jaedicke and Alexander A. Robichek. The fact that the traditional "cost-volume profit analysis" does not include adjustments for uncertainty severely limits its usefulness. Jaedicke and Robichek explain that if a firm is considering the introduction of two new products with the same expected fixed costs, the same expected selling price per unit, the same expected variable costs per unit and the same expected breakeven sales volume, one may be misled to think that the two products are equally desirable. This is not true for one good reason: determining which product is more desirable depends upon the frequency distributions of all the variables that influence profit, not just their expected values. Furthermore, it is more instructive to compare two profit distributions not only by their expected values but also in terms of their variances. Use of the Jaedicke-Robichek model enables one to compute the expected value and the standard deviation of profit for a given product. This information enables a manager to estimate the probability of achieving the breakeven point, as well as the probability of achieving any level of profit or loss.

This paper deals with the theoretical development of some aspects of the trend removal problem. The objective is to show the difference between the two most popular trend removal methods: first differences and linear least squares regression. On the one hand, we show that if first differences are used to eliminate a linear trend, the series of residuals would be stationary but would not be white noises as they contain a first lag autocorrelation of -0.50. Furthermore, the spectral density function (SDF) of these residuals relative to that of a white noise series would be exaggerated at the high frequency portion and attenuated at the low frequency portion. On the other hand, we show that the regression residuals from the linear detrending of a random walk series would contain large positive autocorrelations in the first few lags. Relative to that of white noises, the SDF of the regression residuals would be exaggerated at the low frequency portion and attenuated at the high frequency portion.