Performance of Bootstrap MCEWMA: Study case of Sukuk Musyarakah data

Abstract

Abstract. Sukuk Musyarakah is one of several instruments of Islamic bond investment in Malaysia, where the form of this sukuk is actually based on restructuring the conventional bond to become a Syariah compliant bond. The Syariah compliant is based on prohibition of any influence of usury, benefit or fixed return. Despite of prohibition, daily returns of sukuk are non-fixed return and in statistic, the data of sukuk returns are said to be a time series data which is dependent and autocorrelation distributed. This kind of data is a crucial problem whether in statistical and financing field. Returns of sukuk can be statistically viewed by its volatility, whether it has high volatility that describing the dramatically change of price and categorized it as risky bond or else. However, this crucial problem doesn't get serious attention among researcher compared to conventional bond. In this study, MCEWMA chart in Statistical Process Control (SPC) is mainly used to monitor autocorrelated data and its application on daily returns of securities investment data has gained widespread attention among statistician. However, this chart has always been influence by inaccurate estimation, whether on base model or its limit, due to produce large error and high of probability of signalling out-of-control process for false alarm study. To overcome this problem, a bootstrap approach used in this study, by hybridise it on MCEWMA base model to construct a new chart, i.e. Bootstrap MCEWMA (BMCEWMA) chart. The hybrid model, BMCEWMA, will be applied to daily returns of sukuk Musyarakah for Rantau Abang Capital Bhd. The performance of BMCEWMA base model showed that its more effective compare to real model, MCEWMA based on smaller error estimation, shorter the confidence interval and smaller false alarm. In other word, hybrid chart reduce the variability which shown by smaller error and false alarm. It concludes that the application of BMCEWMA is better than MCEWMA.

The accuracy of two-sided confidence interval algorithm: an alternative of double bootstrap approach

“…Both of BCa and Studentised are decreased the length estimation as n2 increase from 30 → 60 → 200. As mentioned by [10], theoretical simulation of performance can be describe as size sample increased, the estimation of accuracy will going to be decreased. Moreover, the interesting part of this result is that, BCa interval method is given shorten length either in single or double bootstrap.…”