Arthur Magalhães, Adriano Pereira, Marcelo Garcia

A model for price trend forecast is described and tested in series of adjusted closing prices of 15 minute candlesticks concerning 5 shares of the Brazilian market BM&FBovespa. For each time step, the data is first smoothed in a past interval with fixed size by means of Lowess method and then a second order linear differencial equation representing a damped harmonic oscillator is fitted using Levemberg-Marquardt method. Future prices are calculated with the solutions of such equations and price trend forecasts are performed by means of votings involving versions of the model with different parameters. Investment strategies based on stop gain and stop loss are analyzed in two situations: 1) By using a random model; 2) Employing the harmonic oscillator based model. The latter beats the former in all but one case. Price series sthatistics of the case where the random model wins are compared with the others. By considering return and risk, an optimum region in the stop gain-stop loss plane is proposed for employing the model.