Financial Econometrics Study On Ultra-high-frequency Data

This paper studies ultra-high-frequency data modeling and some financial theory testing about random walk,trends and efficiency of technical analysis with Monte Carlo experiment data and empirical data.Ultra-high-frequency data is defined to be a full record of transaction and their associated characteristics. This paper transplants marked point process theory to financial econometrics to analyze ultra-high-frequency data, derives sample function density and its maximum likelihood estimating formulation. Countable and uncountable price conditions are discussed differently. When trade prices are uncountable, and Brown motions, price process and transaction arrival time process are independent each other, we have estimated parameters of sample function density, and taken Guan Dian Dian Zi stock as example to do empirical analysis. The results are that the more the price volatility measured in ultra-high-frequency (UHF) data, the more measured in 5min, 10min, 20min, 30min sampling data than in UHL data, vice versa. The price volatility in 5 min sampling data is nearest to that in UHF data. When prices are countable, we define intensity process different from uncountable condition, describe transaction price jumps with Markov process and insert the process into marked point process, estimate price transfer rate. By Korlgomov front and back differential equation group, we have developed price transfer equation group that can obtain price transfer probabilities. With price transfer probabilities, this paper develops a method to caculate value at risk —— countable conditions method.With Monte Carlo random walk experiment data, we have done Cox-Stuart trend test and efficiency test of moving average method in technical analysis. The results are: it is very common that there are trends in Monte Carlo random walk we can get excessive return with moving average method.Taking Shanghai Stock Index close value time series to contrast with simulated data, with ADF-text and Cox-Stuart trend test we have found that there is an unit root in the time series (1992.5-2002.7), index close value time series walk randomly, and trends are also very common.Disregarding of transaction cost, we get 206% year-return with 5day's moving average method, 193% with 10day's, 181% with 20day's, 171% with 5-10day's, 162% with 5-20day's, 139% with 10-20day's. By comparing test, it has been proved statistically that accumulated returns with moving average transaction method are higher than with "buy and hold" method. Simulated and empirical data test results are contrary to the conclusion in efficiency market hypotheses and random walk theory that if a market is efficient, prices walk randomly, there is no chance to get excessive return. This paper explains this contrary with behaviours financial theory. By developing a method to test price support level and testing, it is found that there are strong supports around 386 in 1993, around 523 in 1994, around 1050 in 1997-1998 in Shanghai Stock Index. According to statistical analysis, 52% retrace ment positions are at 1/2 level, 30% are at 1/3 level, 18% are at 2/3 level. Price increment and transaction volume increment are causes each other according to Granger causality test.