Narrow Results

Based on six large empirical data sets, the financial data sequences are decomposed by Empirical Mode Decomposition (EMD) into various quasi-periodic fluctuation modes, including weekly, half-month, seasonal, about-four-years and so on, which may indicate some abnormal return oscillation patterns. The corresponding average periods are calculated by Fast Fourier Transform Algorithm (FFT), about 6 days for the weekly, about 10 days for the half-month, about 60 days for the seasonal and 1020 days or so for the about-four-years. These obtained results show that the mode periods may be universal for different markets.

Several recently developed chaotic forecasting methods give better results than the random walk forecasts. However they do not take into account specific regularities of stock returns reported in empirical finance literature, such as the calendar effects. In this paper, we present a method for filtering the day-of-the-week and the holiday effect in a time series. Our main objective is twofold. On the one hand we study how the underlying dynamics of the Nasdaq Composite, and TSE 300 Composite returns series can be influenced by the presence of calendar effects. On the other hand we adapt our method to chaotic forecasting. Its computational advantages lead to significant improvements of forecasts.

The paper introduces a method for estimation and reduction of calendar effects from time series, which their fluctuations are governed by a nonlinear dynamical system and additive normal noise. Calendar effects can be considered deviations of the distribution(s) of particular group(s) of observations that have a common characteristic related to the calendar. The concept of this method is the following: since the calendar effects are not related to the dynamics of the time series, the accurate estimation and reduction will result a time series with a smaller amount of noise level (i.e. more accurate dynamics). The main tool of this method is the correlation integral, due to its inherit capability of modeling both the dynamics and the additive normal noise. Experimental results are presented on the Nasdaq Cmp. index.