On Hoover’s Scale-Free Forecast Accuracy Metric MAD/MEAN

In this study, we find that Hoover’s scale-free forecast accuracy metric MAD/MEAN is only recommended when the coefficient of variation (c.v.) is small. Using empirical studies, five near identically and independently distributed (i.i.d.) time series from a popular statistics textbook are observed. We find that 100% of real time series chosen in the textbook have a c.v. less than 1, indicating the applicability of Hoover’s metric in most real data analysis. However, under the market efficiency hypothesis, returns for stocks will follow or approximately follow an i.i.d. normal distribution. There are 3173 stocks in the New York Stock Exchange (NYSE), 3182 stocks in the National Association of Securities Dealers Automated Quotations (NASDAQ), and 2044 stocks in the American Stock Exchange (AMEX). In this study, we observe the c.v.’s of monthly returns of 50 stocks chosen to represent these markets—nineteen stocks are randomly drawn from each of the NYSE and the NASDAQ and twelve stocks are randomly drawn from the AMEX. We find that 100% of these series have a c.v. greater than 1, indicating that Hoover’s metric is not applicable to analyzing returns. Further empirical studies about the returns from Minsville, General Electronic, Goodyear, and Owens studied in Fama (J Bus 38(1):34–105, 1965, J Finance 25(2):383–417, 1970) show that Hoover’s MAD/MEAN is not a good accuracy measure to distinguish different MA methods. We conclude that Hoover’s MAD/MEAN has its merit in general real data analysis as shown in a textbook, but that it is not recommended for analyzing time series for returns in economics and finance.