Detecting Shifts of Parameter in Gamma Sequences with Applications to Stock Price and Air Traffic Flow Analysis

Abstract

Abstract In this article a technique for detecting shift of scale parameter in a sequence of independent gamma random variables is discussed. Distribution theories and related properties of the test statistic are investigated. Numerical critical points and test powers are tabulated for two specific variables. Other useful techniques are also summarized. The methods are then applied to the analysis of stock-market returns and air traffic flows. These two examples are studied in detail to illustrate the use of the proposed method compared to other available techniques. The empirical examples also illuminate the importance of the treatment of stochastic instability in statistical applications. Key Words: Shift in scale parameterVariance heterogeneityGamma random variablesLocally most powerful testDirichlet variablesMonte Carlo methods