as risk management tools or option pricing algorithms. For decades, practitioners have been developing so-called technical analysis, which is a kind of empirical time series analysis based on rudimentary analytical tools. Although some new academic research has analyzed these trading rules,2 they remain controversial and are looked down upon. We hope that this book will put on a new footing many ideas that have been developed in technical analysis.

We have organized this book along the same lines, we first present the empirical regularities, then we construct models, and lastly we test their power to predict market outcomes.

The novelty of high-frequency data demands to take such an approach. This was not usual in econometrics because so little data were available until the late 1980s. It was quite natural that the researchers emphasis was to make sure that the methodology was correct in order to obtain the most information out of the sparse data that were available. Only recently the research community in this field has recognized the importance of the first step: finding empirical facts. This step can already be good research in its own right. A good example is the recent paper by Andersen et al. (2001), where the authors explore in detail the distributional properties of volatility computed from high-frequency data.

Thanks to the development of electronic trading and the existence of various data providers also on the Internet, it is now possible to follow the price formation in real-time. Ideally, the analysis and modeling of the price-generation process should, in real-time, produce results that add value to the raw data. There is strong demand from the market to have, next to the current price, a good assessment of the current risk of the financial asset as well as a reasonable prediction of its future movement. This means that the models should be made amenable to real-time computations and updates. Techniques for doing so will be presented in the remainder of the book. It is possible to develop methods that allow for the easy computation of models and can thus provide almost instantaneous reaction to market events. Although quite popular among practitioners who want to analyze the past developments of prices, those techniques have had little echo, until now, in the academic world. Very few research papers have studied the statistical foundations and properties of those "technical indicators." In this book (Chapter 3) we provide a unified platform for these methods.

1.3 data frequency and market information

Relating the type of data available for researchers, the effects and the models that are discovered and developed with these different samples, provides insight into the development of research in finance. Figure 1.1 illustrates the sample size versus the measurement frequency of some well-known data sets used in finance. The

2 Among others, here is a list of interesting papers on the issue of technical trading models: Neftci (1991), Brock et al. (1992), Taylor and Allen (1992), Levich and Thomas (1993b), Gencay and Stengos (1998), Gencay (1998a,b), Frances and van Griensven (1998), Allen and Karjalainen (1999), Gencay (1999), LeBaron (1999a), Sullivan et al. (1999), and Gencay et al. (2001c, 2002).

FIGURE I. I Available data samples with their typical sizes and frequency. The sample size and the frequency are plotted on a logarithmic scale. The first point corresponds to the O&A database, the last one to the 700 years of yearly data analyzed by Froot et al. (1995), the second to its left to the cotton price data of Mandelbrot (1963), and the daily data are computed from the sample used in Ding et al. (1993) to show long memory in the S&P 500. The text refers to the effects discovered and analyzed in the different segments of these samples.

double logarithmic scale makes the points lie almost on a straight line. The data sample with the lowest frequency is the one used by Froot et al. (1995) of 700 years of annual commodity price data from England and Holland. Beyond 700 years, one is unlikely to find reliable economic or financial data.3 The data with the highest frequency is the Olsen & Associates (O&A) dataset of more than 14 years of high-frequency foreign exchange data. The tick-by-tick data are the highest frequency available. Between those two extremes, one finds the daily series of the Standard & Poors 500 from 1928 to 1991 used by Ding et al. (1993) or the monthly cotton prices used by Mandelbrot (1963) from 1880 to 1940. On this graph, we superimpose those effects that have been identified at these different time scales. One of the questions with data collected over very long periods is whether they really refer to the same phenomenon. Stock indices, for example, change their composition through time due to mergers or the demise of companies. When analyzing the price history of stock indices, the impact of these changes in

, Data can be found in natural sciences such as weather data up to a few hundred thousand years.

Market Microstructure

FIGURE 1.2 Available data samples with their typical sizes and frequency. The sample size and the frequency are plotted on a logarithmic scale. The text refers to the models developed and tested in the different segments of these samples.

composition is not obvious. Wc call this phenomenon the "breakdown of the permanence hypothesis." It is difficult to assess the quality of any inference as the underlying process is not stationary over decades or centuries. At the other end of the frequency spectrum (i.e. with high-frequency data), we are confronted with the details of the price generation process, where other effects, such as how the data arc transmitted and recorded in the data-base (sec Chapter 4) have an impact. With data at frequencies of the order of one hour, a new problem arises, due to the fact that the earth turns and the impact of time zones, where the seasonality of volatility becomes very important (as we shall see in Chapter 5) and overshadows all other effects.

Figure 1.2 relates the data to the models that are typically developed and tested with them. The high-frequency data have opened great possibilities to test market microstructure models, while traditionally low-frequency data are used for testing macroeconomic models. In between lies the whole area of financial and time series modeling, which is typically studied with daily or monthly data as, for instance, option pricing or GARCH models. It is clear from this figure that we have a continuum of both samples and models. The antagonism that is sometimes encountered between time series and market microstructure approaches should slowly vanish with more and more studies combining both with high-frequency