Basket trading under co-integration with the logistic mixture autoregressive model
AbstractIn this paper, we propose a co-integration model with a logistic mixture auto-regressive equilibrium error (co-integrated LMAR), in which the equilibrium relationship among cumulative returns of different financial assets is modelled by a logistic mixture autoregressive time series model. The traditional autoregression (AR) based unit root test (ADF test), used in testing co-integration, cannot give a sound explanation when a time series passes the ADF test. However, its largest root in the AR polynomial is extremely close to, but less than, one, which is most likely the result of a mixture of random-walk and mean-reverting processes in the time series data. With this background, we put an LMAR model into the co-integration framework to identify baskets that have a large spread but are still well co-integrated. A sufficient condition for the stationarity of the LMAR model is given and proved using a Markovian approach. A two-step estimating procedure, combining least-squares estimation and the Expectation-Maximization (EM) algorithm, is given. The Bayesian information criterion (BIC) is used in model selection. The co-integrated LMAR model is applied to basket trading, which is a widely used tool for arbitrage. We use simulation to assess the model in basket trading strategies with the statistical arbitrage feature in equity markets. Data from several sectors of the Hong Kong Hang Seng Index are used in a simulation study on basket trading. Empirical results show that a portfolio using the co-integrated LMAR model has a higher return than portfolios selected by traditional methods. Although the volatility in the return increases, the Sharpe ratio also increases in most cases. This risk--return profile can be explained by the shorter converging period in the co-integrated LMAR model and the larger volatility in the ‘mean-reverting’ regime.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
Bibliographic InfoArticle provided by Taylor & Francis Journals in its journal Quantitative Finance.
Volume (Year): 11 (2011)
Issue (Month): 9 (July)
Contact details of provider:
Web page: http://www.tandfonline.com/RQUF20
You can help add them by filling out this form.
reading list or among the top items on IDEAS.Access and download statisticsgeneral information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Michael McNulty).
If references are entirely missing, you can add them using this form.