Discrimination Measures for Fractional Integrated Models Based on Wavelets

Discrimination measures have been well developed for stationary time series. However in a large number of phenomena, long-term dependencies are involved. In this article, we are dealing with discrimination of fractional integrated models. Kullback–Leibler and Chernoff's discrimination measures are approximated, using the discrete wavelet transform (DWT) for discrimination of these time series classes. The simulation study indicates low misclassification rate, related to the approximations of Kullback–Leibler and Chernoff discrimination measures. Application to problem of classifying seismic data showed that our procedure performs as well as other procedures.     

Market‐Triggered Changes in Capital Structure: Equilibrium Price Dynamics

We analyze the internal consistency of using the market price of a firm's equity to trigger a contractual change in the firm's capital structure, given that the value of the equity itself depends on the firm's capital structure. Of particular interest is the case of contingent capital for banks, in the form of debt that converts to equity, when conversion is triggered by a decline in the bank's stock price. We analyze the problem of existence and uniqueness of equilibrium values for a firm's liabilities in this context, meaning values consistent with a market‐price trigger. Discrete‐time dynamics allow multiple equilibria. In contrast, we show that the possibility of multiple equilibria can largely be ruled out in continuous time, where the price of the triggering security adjusts in anticipation of breaching the trigger. Our main condition for existence of an equilibrium requires that the consequences of triggering a conversion be consistent with the direction in which the trigger is crossed. For the design of contingent capital with a stock price trigger, this condition may be interpreted to mean that conversion should be disadvantageous to shareholders, and it is satisfied by setting the trigger sufficiently high. Uniqueness follows provided the trigger is sufficiently accessible by all candidate equilibria. We illustrate precise formulations of these conditions with a variety of applications.