What can wavelets reveal about SOFIX?

Abstract

The current paper investigates the major index of the Bulgarian Stock Exchange with respect to the presence of long- range dependence and principal predictability of the index. The wavelet transform is utilized in order to carry out the investigation since it is a well-suited tool for the analysis of fractal processes and sheds additional light to the term structure of the index. In recent papers Lomev and co-writers (1-3) confirm the presence of long-range dependence (LRD) of SOFIX on other East-European stock exchange indexes. The presence of LRD is closely related to persistency, that is, positive values are likely to be followed by positive values and negative values are likely to be followed by negative values. The latter implies that the chance to predict correctly the future direction of the process is greater than 50%. Actually, the problem of predictability of SOFIX has been already investigated by Lomev and Ivanov (4) and it turns out that the index is predictable. From this point of view the current paper utilizes the wavelet transform in two directions. Firstly, LRD presence for SOFIX is detected. Secondly, wavelet-based forecasts are developed for the index, in order to test it for principal predictability and to investigate its term structure. A good reasoning behind the application of the wavelet transform is that it is a proper tool for the analysis of financial data. On one hand financial data incorporates information about decisions and actions taken by market participants, operating over different time horizons and on the other hand the wavelet transform of some series decomposes the original sequence over a range of frequency scales. The wavelet transform may be continuous or discrete; however for empirical purposes the discrete wavelets transform (DWT) is preferred. Different algorithms are developed for the implementation of DWT, each one having its advantages and drawbacks. A detailed discussion may be found for example in (5), (6). The current investigation utilizes the triangle algorithm of Mallat (7) for the detection of LRD and the a trous wavelet transform (6) for prediction purposes.