Choosing the best type of wavelet: Case study-business cycle in Iran

The main purpose of this paper has been determined the best type and length of the wavelet used the case study business cycles of Iran during the period 1978-2010 and on the bases on quarterly data. Therefore Haar, Daubechies, Symmelets, Coiflets and biorthogonal wavelets was used to level 5, and the quarterly log GDP were decomposed to 370 series of (185 series of quarterly business cycle and 185 series of trend). First by using the correlation index, the same series was removed and then by wavelet simulation, series were simulated for the period 2005-2010. Our findings indicate that while the majority of research conducted have chosen Daubechies wavelet, the biorthogonal wavelet have a higher quality and comprehensiveness than the Haar, Daubechies, Symmelets, Coiflets wavelets. The study of types of biorthogonal wavelet shows that bior2.2, bior3.1, bior2.6, bior5.5, bior1.1, bior1.5 and bior1.3 respectively, have the highest quality of decomposition and smoothing the business cycle in Iran. In order to provide more accurate results, the business cycle was also examined on an annual basis. The results showed that the business cycle shows high sensitivity and inverse to the level and type of the selected wavelet. It is proposed that when annual data are used, the choice of wavelet level is low (maximum 3) and If the data is monthly or quarterly, high-level wavelet (minimum of 4) is selected.