1. Introduction

Fund managers and investors began many years ago to take into account the Islamic component of the GCC stock markets in order to benefit from the diversification opportunities offered by the Islamic stock markets for their investments in equity markets. This can improve the return and reduce the risk associated with their investments. However, these investors are also concerned about linkage aspects of those markets in relation with the international ones regarding integration and shock transmission, in particular, during the financial crisis.

Given the evidence of frequent crises taking place all over the world, our study, therefore, attempts to evaluate the stability of one particular market (Islamic GCC through beta values) with unique characteristics and experience of rapid growth recently, which is the Islamic capital market.

Given these unique features, i.e. the lower leverage, smaller size of firms, and under-diversification of the market, our study has the main objective of investigating the impact of crisis on different Islamic stock markets and, if this case is true, to discover channels of transmission of shocks across borders. We analyse four Islamic region-indices (US, Eurozone, Asia Pacific, and ASEAN) between 2006 and 2011 to examine the multi-horizon nature of the interconnection and the relationships (based on betas) during a time encompassing the global financial crisis 2008.

To the best of our knowledge, the wavelet methodology adopted in our study is one the most advanced state-of-the-art econometric techniques recently imported to finance from engineering.

As regards the methodology, our study is the first attempt to perform multitimescale analysis using wavelet decomposition as one of the latest techniques in finance to decompose any observed variable on a scale-by-scale basis to capture both time domain and frequency domain simultaneously. This may provide the ability to distinguish between short-run frequencies (speculative behaviours, market sentiment, liquidity preferences, cross-border asset trading, etc.) and long-run frequencies (economic fundamentals).

Since wavelets are localized in both time and scale, they can be used to decompose any observed variable on a scale-by-scale basis across different time horizons without losing any information and without having to assume stationarity.

It is known that heterogeneous investors are highly interested in making decisions over different time horizons (1-2 days, 2-4 days, 4-8 days, 8-16 days, 16-32 days, etc.), and want to operate on different time scales switching from investment activity (coarsest scales) to speculative behaviour, cross-border asset trading or liquidity preferences (small time scales).