Volatility is an important measure of stock market performance. Competing securities market makers keep abreast of the pace of volatility change by adjusting the bid-ask spreads and bid/ask quotes properly and efficiently. For intradaily high frequency transaction data, the observed volatility of stock returns can be decomposed into the sum of the two components - the realized volatility and the volatility due to microstructure noise. The quote adjustments of the market makers comprise part of the microstructure noise. In this study, we define the ratio of the realized integrated volatility to the observed squared returns as the proportion of realized integrated volatility (PIV). Time series models with generalized error distributed innovations are fitted to the PIV data based on 70-minute returns of NYSE tick-to-tick transaction data. Both retrospective and dynamic online control charts of the PIV data are established based on the fitted time series models. The McNemar test supports that the dynamic online control charts have the same power of detecting out of control events as the retrospective control charts. The Wilcoxon signedrank test is adopted to test the differences between the changes of the market maker volatility and the realized volatility for in-control and out-of-control periods, respectively. The results reveals that the points above the upper control limit are related to the situation when the market makers can not keep up with the realized integrated volatility, whereas the points below the lower control limit indicate excessive reaction of the the market makers.

Taiwan Security Market is a typical order-driven market. The electronic trading system of Taiwan Security Market launched in 1998 significantly reduces the trade matching time (the current matching time is around 20 seconds) and promptly provides updated online trading information to traders. In this study, we establish an online transaction simulation system which can be applied to predict trade prices and study market efficiency. Models are established for the times and volumes of the newly added bid/ask orders on the match list. Exponentially weighted moving average (EWMA) method is adopted to update the model parameters. Match prices are predicted dynamically based on the EWMA updated models. Further, high frequency bid/ask order data are used to find the supply and demand curves as well as the equilibrium prices. Differences between the transaction prices and the equilibrium prices are used to investigate the efficiency of Taiwan Security Market. Finally, EWMA and cusum control charts are used to monitor the market efficiency. In empirical study, we analyze the intra-daily (April, 2005) high frequency match data of Uni-president Enterprises Corporation and Formosa Plastics Corporation.

In security markets, the stock price movements are closely linked to the market information. For example, the subprime mortgage triggered a global financial crisis in 2007. Drops occurred in virtually every stock market in the world. After the Federal Reserve took several steps to address the crisis, the stock markets have been gradually stable. Reaction of the traders to the arrival information results in different patterns of the stock price movements. Thus pattern matching is an important subject in future movement prediction, rule discovery and computer aided diagnosis. In this research, we propose a pattern matching procedure to seize the similar stock price movements of two listed companies during one day. First, the algorithm of searching the longest common subsequence is introduced to sieve out the time intervals where the two listed companies have the same integrated volatility levels and price rise/drop trends. Next we transform the raw price data in the found matching time periods to the Bollinger Band Percent data, then use the power spectrum to extract low frequency components. Adjusted Pearson chi-squared tests are performed to analyze the similarity of the price movement patterns in these periods. We perform the study by simulation investigation first, then apply the procedure to empirical analysis of high frequency transaction data of NYSE.