A Research Of Multiplicative Error Model And Its Application

In the 20 years following the publication of the ARCH model in 1982, there has been a vast quantity of research uncovering the properties of competing volatility models. Subsequently, the duration model ACD and many of its derivative models come forth, and have been developed rapidly and successfully. Wide-ranging application to financial data have discovered important stylized facts and illstrated both the strengths and weaknesses of the models. There are now many surveys of this literature. In 2002, Robert Engle published his paper " New Frontiers for ARCH Models ", in which he briefly discussed three high-frequency volatility models, large-scale multivariate ARCH models, and derivatives pricing models. What's more important, in this paper, one further frontier is examined in more detail—application of ACD models to the broad class of non-negative processes, that is Multiplicative Error Model (MEM), which assumes that the evolution of a non-negative valued process can be described by the product of a time varying scale factor (which depends upon the recent past of the series) and a standard positive valued random variable. This class of models have a similar formulation with ACD models, and the ARCH model can be a especial demonstration of MEM. Nowadays, many researches about characteristics of financial market using non-negative processes as tool, just like the absolute return in security market, the financial duration, number of trades, volume and high-low range. The application of MEMs can show its advantage on building models in these fields, describing their statistical characteristics and solving other problems which brought by processing date. Therefore, as a expanded model for the classes of ARCH model and ACD model, MEMs deserve our deeper and particular research.This paper gives the research about building MEM on financial time series, which including the background of model introduction, the setting of basic model, the extension and estimation of model and other restriction conditions of parameters. The author will analyze the univariate MEM, and consider about a mixture-innovation process with a mixture conditional expectation at the same time, which means the univariate mixture-MEM. Then the paper will extend the univariate MEM to the multivariate MEM (which is the vector MEM), and set up the multivariate MEM with innovation process following a mixture-gamma distribution. The author will also use copula function theory in estimating multivariate mixture-MEM in this part. In the empirical analysis part, this paper will use the bivariate MEM with mixture-gamma distribution on two indicator series of the volatility of shanghai stock index, that is the absolute logarithm return series and high-low range series, contrasting the estimation equation by equation and the joint estimation of correlation with copulas. This empirical analysis can fully testify the feasible application of MEM.