From the bird’s eye to the microscope: A survey of new stylized facts of the intra-daily foreign exchange markets
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paper_title: Naive Trading Rules in Financial Markets and Wiener-Kolmogorov Prediction Theory: A Study of "Technical Analysis."

paper_content:

This article attempts a formal study of technical analysis, which is a class of informal prediction rules, often preferred to Wiener-Kolmogorov prediction theory by participants of financial markets. Yet Wiener-Kolmogorov prediction theory provides optimal linear forecasts. This article investigates two issues that may explain this contradiction. First, the article attempts to devise formal algorithms to represent various forms of technical analysis in order to see if these rules are well defined. Second, the article discusses under which conditions (if any) technical analysis might capture those properties of stock prices left unexploited by linear models of Wiener-Kolmogorov theory. Copyright 1991 by University of Chicago Press.
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paper_title: A Theory of Intraday Patterns: Volume and Price Variability

paper_content:

This article develops a theory in which concentrated-trading patterns arise endogenously as a result of the strategic behavior of liquidity traders and informed traders. Our results provide a partial explanation for some of the recent empitical findings concerning the patterns of volume and price variability in intraday transaction data. In the last few years, intraday trading data for a number of securities have become available. Several empirical studies have used these data to identify various patterns in trading volume and in the daily behavior of security prices. This article focuses on two of these patterns; trading volume and the variability of returns. Consider, for example, the data in Table 1 concerning shares of Exxon traded during 1981.1 The U-shaped pattern of the average volume of shares traded-namely, the heavy trading in the beginning and the end of the trading day and the relatively light trading in the middle of the day-is very typical and has been documented in a number of studies. [For example,Jain andJoh (1986) examine hourly data for the aggregate volume on the NYSE, which is reported in the Wall StreetJournal, and find the same pattern.] Both the variance of price changes
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paper_title: Posted versus effective spreads: Good prices or bad quotes?☆

paper_content:

Abstract When trades are executed inside the posted bid-ask spread, the posted spread is no longer an accurate measure of transactions costs faced by investors. Using two samples of market orders, one based on orders submitted by retail brokers and one based on orders submitted electronically to the NYSE, we document a significant difference between the posted spread and the effective spread paid by investors. For most orders, the effective spread averages half the posted spread. In addition, when the posted spread widens, only 10 to 22% of the increase appears in the effective spread. These results have significant implications for any empirical work that uses the posted spread as a measure of the cost of trading. Our findings also document a significant difference in the expected execution price across exchanges. This finding is robust to controls for the type of order, and implies that U.S. equity markets are not completely integrated.
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paper_title: Every minute counts in financial markets

paper_content:

Abstract This paper represents an introductory study of ultra high frequency, minuute-by-minute data, for forex spot rates (bid-ask Reuters quotes) on three days, Autumn 1987. The frequency of price revision, size of spread, and statistical characteristics are measured. The series exhibit (time varying) leptokurtosis, unit roots, and first-order negative correlation, the latter especially in disturbed ‘jumpy’ markets. The effect of time aggregation on these characteristics is examined, and variance ratios are analyzed. Multivariate analysis revealed significant relationships between lagged exchange rates, both the own rate and the key deutsche mark/US dollar rate, and the current spot rate.
---
paper_title: Bid-ask spreads and volatility in the foreign exchange market. An empirical analysis

paper_content:

Abstract Consistent with the implications from a simple asymmetric information model for the bid-ask spread, we present empirical evidence that the size of the bid-ask spread in the foreign exchange market is positively related to the underlying exchange rate uncertainty. The estimation results are based on an ordered probit analysis that captures the discreteness in the spread distribution, with the uncertainty of the spot exchange rate being quantified through a GARCH type model. The data sets consists of more than 300,000 continuously recorded Deutschemark/dollar quotes over the period from April 1989 to June 1989.
---
paper_title: Trading Patterns and Prices in the Interbank Foreign Exchange Market

paper_content:

The behavior of quote arrivals and bid-ask spreads is examined for continuously recorded deutsche mark-dollar exchange rate data over time, across locations, and by market participants. A pattern in the intraday spread and intensity of market activity over time is uncovered and related to theories of trading patterns. Models for the conditional mean and variance of returns and bid-ask spreads indicate volatility clustering at high frequencies. The proposition that trading intensity has an independent effect on returns volatility is rejected but holds for spread volatility. Conditional returns volatility is increasing in the size of the spread. Copyright 1993 by American Finance Association.
---
paper_title: Generalized Autoregressive Conditional Heteroskedasticity

paper_content:

The present paper proposes a generalization of the canonical AutoRegressive Conditional Heteroskedasticity (ARCH) model by extending the conditional variance equation toward past conditional variances. The stationarity conditions and autocorrelation structure of the Generalized AutoRegressive Conditional Heteroskedastic (GARCH) model are derived. Using an empirical example of uncertainty of the inflation rate the paper demonstrates that the GARCH model provides a better fit and a more plausible learning mechanism than the ARCH model.
---
paper_title: The Message in Daily Exchange Rates: A Conditional-Variance Tale

paper_content:

Formal testing procedures confirm the presence of a unit root in the autoregressive polynomial of the univariate time series representation of daily exchange-rate data. The first differences of the logarithms of daily spot rates are approximately uncorrelated through time, and a generalized autoregressive conditional heteroscedasticity model with daily dummy variables and conditionally t-distributed errors is found to provide a good representation to the leptokurtosis and time-dependent conditional heteroscedasticity. The parameter estimates and characteristics of the models are found to be very similar for six different currencies. These apparent stylized facts carry over to weekly, fortnightly, and monthly data in which the degree of leptokurtosis and time-dependent heteroscedasticity is reduced as the length of the sampling interval increases.
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paper_title: The behavior of intra-daily exchange rates

paper_content:

Abstract The behavior of exchange rates is examined as they evolve continuously over time. The data consist of Swiss franc/U.S. dollar rates for nine days during the years 1978–1980 as quoted by a major Swiss dealer operating on the interbank market. Since this market is highly organized, the observations are market prices at the same time. The distributions of relative changes in exchange rates measured over one minute are highly leptokurtic. The normal distribution is rather rapidly approached when the measurement interval is lengthened from one up to ten minutes. Time series analysis reveals that the natural logarithms of exchange rates are adequately described by a random walk, the same stochastic process as has been found for daily, weekly, monthly and quarterly observations. For short time intervals, significant autocorrelations sometimes occur at the first few lags, which are, however, not stable enough over time to form a basis for reliable forecasts.
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paper_title: Statistical study of foreign exchange rates, empirical evidence of a price change scaling law, and intraday analysis☆

paper_content:

Abstract In this paper we present a statistical analysis of four foreign exchange spot rates against the U.S. Dollar with several million intra-day prices over 3 years. The analysis also includes gold prices and samples of daily foreign exchange prices over 15 years. The mean absolute changes of logarithmic prices are found to follow a scaling law against the time interval on which they are measured. This empirical law holds although the distributions of the price changes strongly differ for different interval sizes. Systematic variations of the volatility are found even during business hours by an intra-day analysis of price changes. Seasonal heteroskedasticity is observed with a period of one day as well as one week as the result of an analogous intra-week analysis; taking this into account is necessary for any future study of intra-day price change distributions and their generating process. The same type of analysis is also made for the bid-ask spreads.
---
paper_title: Trading Patterns and Prices in the Interbank Foreign Exchange Market

paper_content:

The behavior of quote arrivals and bid-ask spreads is examined for continuously recorded deutsche mark-dollar exchange rate data over time, across locations, and by market participants. A pattern in the intraday spread and intensity of market activity over time is uncovered and related to theories of trading patterns. Models for the conditional mean and variance of returns and bid-ask spreads indicate volatility clustering at high frequencies. The proposition that trading intensity has an independent effect on returns volatility is rejected but holds for spread volatility. Conditional returns volatility is increasing in the size of the spread. Copyright 1993 by American Finance Association.
---
paper_title: Every minute counts in financial markets

paper_content:

Abstract This paper represents an introductory study of ultra high frequency, minuute-by-minute data, for forex spot rates (bid-ask Reuters quotes) on three days, Autumn 1987. The frequency of price revision, size of spread, and statistical characteristics are measured. The series exhibit (time varying) leptokurtosis, unit roots, and first-order negative correlation, the latter especially in disturbed ‘jumpy’ markets. The effect of time aggregation on these characteristics is examined, and variance ratios are analyzed. Multivariate analysis revealed significant relationships between lagged exchange rates, both the own rate and the key deutsche mark/US dollar rate, and the current spot rate.
---
paper_title: Statistical study of foreign exchange rates, empirical evidence of a price change scaling law, and intraday analysis☆

paper_content:

Abstract In this paper we present a statistical analysis of four foreign exchange spot rates against the U.S. Dollar with several million intra-day prices over 3 years. The analysis also includes gold prices and samples of daily foreign exchange prices over 15 years. The mean absolute changes of logarithmic prices are found to follow a scaling law against the time interval on which they are measured. This empirical law holds although the distributions of the price changes strongly differ for different interval sizes. Systematic variations of the volatility are found even during business hours by an intra-day analysis of price changes. Seasonal heteroskedasticity is observed with a period of one day as well as one week as the result of an analogous intra-week analysis; taking this into account is necessary for any future study of intra-day price change distributions and their generating process. The same type of analysis is also made for the bid-ask spreads.
---
paper_title: Generalized Autoregressive Conditional Heteroskedasticity

paper_content:

The present paper proposes a generalization of the canonical AutoRegressive Conditional Heteroskedasticity (ARCH) model by extending the conditional variance equation toward past conditional variances. The stationarity conditions and autocorrelation structure of the Generalized AutoRegressive Conditional Heteroskedastic (GARCH) model are derived. Using an empirical example of uncertainty of the inflation rate the paper demonstrates that the GARCH model provides a better fit and a more plausible learning mechanism than the ARCH model.
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paper_title: The Interaction Between the Frequency of Market Quotations, Spread and Volatility in the Foreign Exchange Market

paper_content:

There is an empirical relationship between volatility, average spread, and number of quotations in the foreign exchange spot market. The estimation procedure involves two steps. In the first one the optimal functional form between these variables is determined through a maximization procedure of the unrestricted VAR, involving the Box—Cox transformation. The second step uses the two-stage least squares method to estimate the transformed variables in a simultaneous equation system framework. The results indicate that the number of quotations successfully approximates activity in the spot market. Furthermore, the number of quotations and temporal dummies reduce significantly the conditional heteroskedasticity e⁄ect. We also discuss information aspects of the model as well as its implications for financial informational theories. Inter- and intra-day patterns of the three variables are also revealed.
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paper_title: Stock Market Prices Do Not Follow Random Walks: Evidence from a Simple Specification Test

paper_content:

In this paper, we test the random walk hypothesis for weekly stock market returns by comparing variance estimators derived from data sampled at different frequencies. The random walk model is strongly rejected for the entire sample period (1962-1985) and for all sub-periods for a variety of aggregate returns indexes and size-sorted portfolios. Although the rejections are largely due to the behavior of small stocks, they cannot be ascribed to either the effects of infrequent trading or time-varying volatilities. Moreover, the rejection of the random walk cannot be interpreted as supporting a mean-reverting stationary model of asset prices, but is more consistent with a specific nonstationary alternative hypothesis.
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paper_title: Trading Patterns and Prices in the Interbank Foreign Exchange Market

paper_content:

The behavior of quote arrivals and bid-ask spreads is examined for continuously recorded deutsche mark-dollar exchange rate data over time, across locations, and by market participants. A pattern in the intraday spread and intensity of market activity over time is uncovered and related to theories of trading patterns. Models for the conditional mean and variance of returns and bid-ask spreads indicate volatility clustering at high frequencies. The proposition that trading intensity has an independent effect on returns volatility is rejected but holds for spread volatility. Conditional returns volatility is increasing in the size of the spread. Copyright 1993 by American Finance Association.
---
paper_title: Fighting the arch–enemy with mathematics‘

paper_content:

This is an account of theoretical and applied statistical work done in connection with the problem how to determine a safe height for the sea dikes in the Netherlands
---
paper_title: Every minute counts in financial markets

paper_content:

Abstract This paper represents an introductory study of ultra high frequency, minuute-by-minute data, for forex spot rates (bid-ask Reuters quotes) on three days, Autumn 1987. The frequency of price revision, size of spread, and statistical characteristics are measured. The series exhibit (time varying) leptokurtosis, unit roots, and first-order negative correlation, the latter especially in disturbed ‘jumpy’ markets. The effect of time aggregation on these characteristics is examined, and variance ratios are analyzed. Multivariate analysis revealed significant relationships between lagged exchange rates, both the own rate and the key deutsche mark/US dollar rate, and the current spot rate.
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paper_title: Market structure and inefficiency in the foreign exchange market

paper_content:

This paper investigates the intradaily operational efficiency of the U. S. foreign exchange market by conducting computer simulation experiments with market structure (the numbers of market?makers, brokers and customers). The results indicate significant operational inefficiencies which can be explained by temporary inventory imbalances inherent in a decentralized market. The results also suggest that much of this inefficiency could be alleviated through a centralization of price information.
---
paper_title: Trading Patterns and Prices in the Interbank Foreign Exchange Market

paper_content:

The behavior of quote arrivals and bid-ask spreads is examined for continuously recorded deutsche mark-dollar exchange rate data over time, across locations, and by market participants. A pattern in the intraday spread and intensity of market activity over time is uncovered and related to theories of trading patterns. Models for the conditional mean and variance of returns and bid-ask spreads indicate volatility clustering at high frequencies. The proposition that trading intensity has an independent effect on returns volatility is rejected but holds for spread volatility. Conditional returns volatility is increasing in the size of the spread. Copyright 1993 by American Finance Association.
---
paper_title: Statistical study of foreign exchange rates, empirical evidence of a price change scaling law, and intraday analysis☆

paper_content:

Abstract In this paper we present a statistical analysis of four foreign exchange spot rates against the U.S. Dollar with several million intra-day prices over 3 years. The analysis also includes gold prices and samples of daily foreign exchange prices over 15 years. The mean absolute changes of logarithmic prices are found to follow a scaling law against the time interval on which they are measured. This empirical law holds although the distributions of the price changes strongly differ for different interval sizes. Systematic variations of the volatility are found even during business hours by an intra-day analysis of price changes. Seasonal heteroskedasticity is observed with a period of one day as well as one week as the result of an analogous intra-week analysis; taking this into account is necessary for any future study of intra-day price change distributions and their generating process. The same type of analysis is also made for the bid-ask spreads.
---
paper_title: Bid-ask spreads and volatility in the foreign exchange market. An empirical analysis

paper_content:

Abstract Consistent with the implications from a simple asymmetric information model for the bid-ask spread, we present empirical evidence that the size of the bid-ask spread in the foreign exchange market is positively related to the underlying exchange rate uncertainty. The estimation results are based on an ordered probit analysis that captures the discreteness in the spread distribution, with the uncertainty of the spot exchange rate being quantified through a GARCH type model. The data sets consists of more than 300,000 continuously recorded Deutschemark/dollar quotes over the period from April 1989 to June 1989.
---
paper_title: Every minute counts in financial markets

paper_content:

Abstract This paper represents an introductory study of ultra high frequency, minuute-by-minute data, for forex spot rates (bid-ask Reuters quotes) on three days, Autumn 1987. The frequency of price revision, size of spread, and statistical characteristics are measured. The series exhibit (time varying) leptokurtosis, unit roots, and first-order negative correlation, the latter especially in disturbed ‘jumpy’ markets. The effect of time aggregation on these characteristics is examined, and variance ratios are analyzed. Multivariate analysis revealed significant relationships between lagged exchange rates, both the own rate and the key deutsche mark/US dollar rate, and the current spot rate.
---
paper_title: Statistical study of foreign exchange rates, empirical evidence of a price change scaling law, and intraday analysis☆

paper_content:

Abstract In this paper we present a statistical analysis of four foreign exchange spot rates against the U.S. Dollar with several million intra-day prices over 3 years. The analysis also includes gold prices and samples of daily foreign exchange prices over 15 years. The mean absolute changes of logarithmic prices are found to follow a scaling law against the time interval on which they are measured. This empirical law holds although the distributions of the price changes strongly differ for different interval sizes. Systematic variations of the volatility are found even during business hours by an intra-day analysis of price changes. Seasonal heteroskedasticity is observed with a period of one day as well as one week as the result of an analogous intra-week analysis; taking this into account is necessary for any future study of intra-day price change distributions and their generating process. The same type of analysis is also made for the bid-ask spreads.
---
paper_title: The Message in Daily Exchange Rates: A Conditional-Variance Tale

paper_content:

Formal testing procedures confirm the presence of a unit root in the autoregressive polynomial of the univariate time series representation of daily exchange-rate data. The first differences of the logarithms of daily spot rates are approximately uncorrelated through time, and a generalized autoregressive conditional heteroscedasticity model with daily dummy variables and conditionally t-distributed errors is found to provide a good representation to the leptokurtosis and time-dependent conditional heteroscedasticity. The parameter estimates and characteristics of the models are found to be very similar for six different currencies. These apparent stylized facts carry over to weekly, fortnightly, and monthly data in which the degree of leptokurtosis and time-dependent heteroscedasticity is reduced as the length of the sampling interval increases.
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paper_title: The Variation of Certain Speculative Prices

paper_content:

The purpose of this chapter is to present and test a new model of price behavior in speculative markets. The principal feature of this model is that starting from the Bachelier process as applied to InZ(t) instead of Z(t), the Gaussian distribution is replaced throughout by another family of probability laws to be referred to as stable Paretian. In a somewhat complex way, the Gaussian is a limiting case of this new family, so the new model proposed in this chapter is actually a generalization of the continuous random walk of Bachelier.
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paper_title: Meteor Showers or Heat Waves? Heteroskedastic Intra-Daily Volatility in the Foreign Exchange Market

paper_content:

This paper defines and tests a form of market efficiency called market dexterity which requires that asset prices adjust instantaneously and completely in response to new information. Examining the behavior of the yen/dollar exchange rate while each of the major markets are open it is possible to test for informational effects from one market to the next. Assuming that news has only country specific autocorrelation such as a heat wave. any intra-daily volatility spillovers (meteor showers) become evidence against market dexterity. ARCII models are employed to model heteroskedasticity across intra-daily market segments. Statistical tests lead to the rejection of the heat wave and therefore the market dexterity hypothesis. Using a volatility type of vector autoregression we examine the impact of news in one market on the time path of volatility in other markets.
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paper_title: Generalized Autoregressive Conditional Heteroskedasticity

paper_content:

The present paper proposes a generalization of the canonical AutoRegressive Conditional Heteroskedasticity (ARCH) model by extending the conditional variance equation toward past conditional variances. The stationarity conditions and autocorrelation structure of the Generalized AutoRegressive Conditional Heteroskedastic (GARCH) model are derived. Using an empirical example of uncertainty of the inflation rate the paper demonstrates that the GARCH model provides a better fit and a more plausible learning mechanism than the ARCH model.
---
paper_title: The Message in Daily Exchange Rates: A Conditional-Variance Tale

paper_content:

Formal testing procedures confirm the presence of a unit root in the autoregressive polynomial of the univariate time series representation of daily exchange-rate data. The first differences of the logarithms of daily spot rates are approximately uncorrelated through time, and a generalized autoregressive conditional heteroscedasticity model with daily dummy variables and conditionally t-distributed errors is found to provide a good representation to the leptokurtosis and time-dependent conditional heteroscedasticity. The parameter estimates and characteristics of the models are found to be very similar for six different currencies. These apparent stylized facts carry over to weekly, fortnightly, and monthly data in which the degree of leptokurtosis and time-dependent heteroscedasticity is reduced as the length of the sampling interval increases.
---
paper_title: Statistical study of foreign exchange rates, empirical evidence of a price change scaling law, and intraday analysis☆

paper_content:

Abstract In this paper we present a statistical analysis of four foreign exchange spot rates against the U.S. Dollar with several million intra-day prices over 3 years. The analysis also includes gold prices and samples of daily foreign exchange prices over 15 years. The mean absolute changes of logarithmic prices are found to follow a scaling law against the time interval on which they are measured. This empirical law holds although the distributions of the price changes strongly differ for different interval sizes. Systematic variations of the volatility are found even during business hours by an intra-day analysis of price changes. Seasonal heteroskedasticity is observed with a period of one day as well as one week as the result of an analogous intra-week analysis; taking this into account is necessary for any future study of intra-day price change distributions and their generating process. The same type of analysis is also made for the bid-ask spreads.
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paper_title: The Fractal Geometry of Nature

paper_content:

"...a blend of erudition (fascinating and sometimes obscure historical minutiae abound), popularization (mathematical rigor is relegated to appendices) and exposition (the reader need have little knowledge of the fields involved) ...and the illustrations include many superb examples of computer graphics that are works of art in their own right." Nature
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paper_title: A chaotic model of the exchange rate: The role of fundamentalists and chartists

paper_content:

A monetary model of the exchange rate is constructed in which “fundamentalists” and “chartists” interact. It is shown that the non-linearity of this speculative dynamics leads to chaotic motion of the exchange rate. The model is also capable of generating some of the stylized facts of exchange rate dynamics. Copyright Kluwer Academic Publishers 1993
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paper_title: The Price Variability-Volume Relationship on Speculative Markets

paper_content:

This paper concerns the relationship between the variability of the daily price change and the daily volume of trading on the speculative markets. Our work extends the theory of speculative markets in two ways. First, we derive from economic theory the joint probability distribution of the price change and the trading volume over any interval of time within the trading day. And second, we determine how this joint distribution changes as more traders enter (or exit from) the market. The model's parameters are estimated by FIML using daily data from the 90-day T-bills futures market. The results of the estimation can reconcile a conflict between the price variability-volume relationship for this market and the relationship obtained by previous investigators for other speculative markets. THIS PAPER CONCERNS the relationship between the variability of the daily price change and the volume of trading on speculative markets. Previous empirical studies [2, 3, 6, 12, 14, 16] of both futures and equity markets always find a positive association between price variability (as measured by the squared price change Ap2) and the trading volume.2 There are two explanations for the relationship. Clark's [2] explanation, which is secondary to his effort to explain why the probability distribution of the daily price change is leptokurtic, emphasizes randomness in the number of within-day transactions. In Clark's model the daily price change is the sum of a random number of within-day price changes. The variance of the daily price change is thus a random variable with a mean proportional to the mean number of daily transactions. Clark argues that the trading volume is related positively to the number of within-day transactions, and so the trading volume is related positively to the variability of the price change. The second explanation is due to Epps and Epps [6]. Their model examines the mechanics of within-day trading. The change in the market price on each within-day transaction or market clearing is the average of the changes in all of the traders' reservation prices. Epps and Epps assume there is a positive relationship between the extent to which traders disagree when they revise their reservation prices and the absolute value of the change in the market price. That is, an increase in the extent to which traders disagree is associated with a larger absolute price change. The price variability-volume relationship arises, then, because the volume of trading is positively related to the extent to which traders disagree when they revise their reservation prices.
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paper_title: A Low-Dimensional Fractal Attractor in the Foreign Exchange Markets?

paper_content:

This paper deals with the determination of the presence of a low-dimensional fractal attractor in the foreign exchange (FX) markets. In addition to endogenous nonlinear dynamics, we allow for the presence of a small stochastic component by using two nonlinear filters in conjunction with the correlation dimension methodology. Besides, we avoid the small sample bias present in most studies by using a very large dataset of intra-daily returns for the major currencies against the USD. We also test the absolute value of the returns as a measure of the volatility process. Our main trust of findings is the absence of a low-dimensional attractor both for the FX returns and their absolute values. In other words, nonlinear structural models cannot be used to describe the FX markets. Moreover, the only distinguishable feature seems to be the strong autocorrelation of the volatility which is in line with the time-series approach of the ARCH-class of stochastic models.
---
paper_title: The Message in Daily Exchange Rates: A Conditional-Variance Tale

paper_content:

Formal testing procedures confirm the presence of a unit root in the autoregressive polynomial of the univariate time series representation of daily exchange-rate data. The first differences of the logarithms of daily spot rates are approximately uncorrelated through time, and a generalized autoregressive conditional heteroscedasticity model with daily dummy variables and conditionally t-distributed errors is found to provide a good representation to the leptokurtosis and time-dependent conditional heteroscedasticity. The parameter estimates and characteristics of the models are found to be very similar for six different currencies. These apparent stylized facts carry over to weekly, fortnightly, and monthly data in which the degree of leptokurtosis and time-dependent heteroscedasticity is reduced as the length of the sampling interval increases.
---
paper_title: The statistical distribution of exchange rates: Empirical evidence and economic implications

paper_content:

The abundant evidence that changes in exchange rates have distributions with fatter tails than the normal distribution has led researchers to consider non-normal distributions, including the Student, the stable Paretian and mixtures of distributions. This paper compares the empirical fits of three non-normal candidates and the normal distribution for daily changes in the logarithms of exchange rates, using maximum likelihood estimation of the parameters and chi-square goodness-of-fit tests. The Student and mixture of two normals provide the best fits, but there is evidence that the distribution parameters may vary over time.
---
paper_title: Bid-ask spreads and volatility in the foreign exchange market. An empirical analysis

paper_content:

Abstract Consistent with the implications from a simple asymmetric information model for the bid-ask spread, we present empirical evidence that the size of the bid-ask spread in the foreign exchange market is positively related to the underlying exchange rate uncertainty. The estimation results are based on an ordered probit analysis that captures the discreteness in the spread distribution, with the uncertainty of the spot exchange rate being quantified through a GARCH type model. The data sets consists of more than 300,000 continuously recorded Deutschemark/dollar quotes over the period from April 1989 to June 1989.
---
paper_title: Fighting the arch–enemy with mathematics‘

paper_content:

This is an account of theoretical and applied statistical work done in connection with the problem how to determine a safe height for the sea dikes in the Netherlands
---
paper_title: Trading Patterns and Prices in the Interbank Foreign Exchange Market

paper_content:

The behavior of quote arrivals and bid-ask spreads is examined for continuously recorded deutsche mark-dollar exchange rate data over time, across locations, and by market participants. A pattern in the intraday spread and intensity of market activity over time is uncovered and related to theories of trading patterns. Models for the conditional mean and variance of returns and bid-ask spreads indicate volatility clustering at high frequencies. The proposition that trading intensity has an independent effect on returns volatility is rejected but holds for spread volatility. Conditional returns volatility is increasing in the size of the spread. Copyright 1993 by American Finance Association.
---
paper_title: The statistical properties of daily foreign exchange rates: 1974–1983

paper_content:

Abstract This paper examines the statistical properties of daily rates of change of five foreign currencies from 1974 to 1983. The main purpose is to discriminate between two competing explanations for the observed heavy tails of the distribution: that the data are independently drawn from a heavy tail distribution which remains fixed over time, and that the data come from distributions which vary over time. Evidence point to the rejection of the first hypothesis. Further investigations show that the rejection can be attributed to changing means and variances in the data, which can be described by a simple statistical model.
---
paper_title: A chaotic model of the exchange rate: The role of fundamentalists and chartists

paper_content:

A monetary model of the exchange rate is constructed in which “fundamentalists” and “chartists” interact. It is shown that the non-linearity of this speculative dynamics leads to chaotic motion of the exchange rate. The model is also capable of generating some of the stylized facts of exchange rate dynamics. Copyright Kluwer Academic Publishers 1993
---
paper_title: Generalized Autoregressive Conditional Heteroskedasticity

paper_content:

The present paper proposes a generalization of the canonical AutoRegressive Conditional Heteroskedasticity (ARCH) model by extending the conditional variance equation toward past conditional variances. The stationarity conditions and autocorrelation structure of the Generalized AutoRegressive Conditional Heteroskedastic (GARCH) model are derived. Using an empirical example of uncertainty of the inflation rate the paper demonstrates that the GARCH model provides a better fit and a more plausible learning mechanism than the ARCH model.
---
paper_title: The Message in Daily Exchange Rates: A Conditional-Variance Tale

paper_content:

Formal testing procedures confirm the presence of a unit root in the autoregressive polynomial of the univariate time series representation of daily exchange-rate data. The first differences of the logarithms of daily spot rates are approximately uncorrelated through time, and a generalized autoregressive conditional heteroscedasticity model with daily dummy variables and conditionally t-distributed errors is found to provide a good representation to the leptokurtosis and time-dependent conditional heteroscedasticity. The parameter estimates and characteristics of the models are found to be very similar for six different currencies. These apparent stylized facts carry over to weekly, fortnightly, and monthly data in which the degree of leptokurtosis and time-dependent heteroscedasticity is reduced as the length of the sampling interval increases.
---
paper_title: Optimal Transparency in a Dealership Market with an Application to Foreign Exchange

paper_content:

This paper addresses the issue of optimal transparency in a multiple-dealer market. In particular, we examine the question: Would risk-averse dealers prefer ex-ante that signed order flow were observable? We answer this question with the solution to a mechanism design problem. The resulting incentive-efficient mechanism is one in which signed order flow is not observable. Rather, dealers prefer a slower pace of price discovery because it induces additional risk-sharing. Specifically, slower price discovery permits additional trading with customers prior to revelation; this reduces the variance of unavoidable position disturbances, thereby reducing the market making risk inherent in price discovery. We then apply the framework to the spot foreign exchange market in order to understand better the current degree of transparency in that market.
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Title: From the bird’s eye to the microscope: A survey of new stylized facts of the intra-daily foreign exchange markets

Section 1: Introduction
Description 1: Introduce the background, scope, and purpose of the survey of intra-daily foreign exchange (FX) markets, emphasizing the significance of intra-daily data and its implications for understanding market behavior.

Section 2: Description of the FX market and the data set
Description 2: Summarize essential descriptive knowledge of the FX market, the main source and type of data available, and the unique information content of intra-daily data compared to daily data.

Section 3: Definition of the variables of interest
Description 3: Provide explicit definitions for key variables under study including price, change of price, volatility, relative spread, tick frequency, volatility ratio, and directional change frequency, and discuss their relevance.

Section 4: Stylized facts
Description 4: Present a new set of stylized facts describing the characteristics of the FX market, grouped into distributional properties, price formation process, and time series properties.

Section 5: Conclusion
Description 5: Summarize the insights gained from the intra-daily analysis of the FX market, highlighting key challenges, the impact of heterogeneity among market participants, and directions for future research.

Section 6: Appendix 2
Description 6: Provide a detailed definition of the directional change frequency along with a schematic example of its implementation.