An Innovative Estimation Approach

• Activity Number: 472
• Type: Contributed
• Date/Time: Wednesday, August 1, 2012 : 8:30 AM to 10:20 AM
• Sponsor: Business and Economic Statistics Section
• Author(s): Yang Yu*+ and John Chen
• Companies: Bowling Green State University and Bowling Green State University
• Keywords: Skew-Normal ; MLE ; Algorithm

Abstract

When analyzing volatility forecasting bi-variate time series with applications in investment, option pricing and risk management, S. Poon and Clive Granger (2006) advocated the use of a skew-t model, which has a corresponding skew normal family proposed in Chen (2010). The new skew-normal distribution has two pieces defined, respectively, for x < µ and x>= µ, where µ is the location parameter. In addition there are two parameters, the variance t and the skewness parameter ?. In the conventional method of MLE to estimate the three parameters, the explicit forms of algebraic solutions for this new family do not exist. In this talk, a new MLE method of estimation is derived. We established an algorithm to seek the overall MLE from the local MLE when the location parameter is restricted in a partition of the sample space. Following that, the MLEs of t and ? can be consequently computed. Compared with the conventional skew-normal model (which has singular information matrix in the MLE process), the advantage of this new skew-normal family is that the maximum likelihood estimators can be found by the new algorithm.