تجزیه وابستگی روزانه در بازارهای ارز : شواهد از بازار لحظه ای AUD / USD

The local Hurst exponent, a measure employed to detect the presence of dependence in a time series, may also be used to investigate the source of intraday variation observed in the returns in foreign exchange markets. Given that changes in the local Hurst exponent may be due to either a time-varying range, or standard deviation, or both of these simultaneously, values for the range, standard deviation and local Hurst exponent are recorded and analyzed separately. To illustrate this approach, a high-frequency data set of the spot Australian dollar/US dollar provides evidence of the returns distribution across the 24-hour trading ‘day’, with time-varying dependence and volatility clearly aligning with the opening and closing of markets. This variation is attributed to the effects of liquidity and the price-discovery actions of dealers.

Recently, the scope of empirical investigation possible in foreign exchange markets has been expanded by the availability of high-frequency, or tick, data of spot foreign exchange (FX) prices. For example in the financial economics literature, Muller et al. [1], Goodhart and Demos [2], Goodhart and Figliuoli [3], and later Bollerslev and Domowitz [4] and Bollerslev and Melvin [5] focus on quote arrivals (frequency) and the size of the bid-ask spread, which they find varies across the trading day, with higher spreads and volatility at the beginning and end of trading. From a time-series modelling perspective, differences in liquidity and price availability of markets organised around groups of dealers—who possess differing degrees of private information—ensures that prices cannot immediately incorporate all private information in individual trades [6]. Price discovery by these traders may therefore lead to time-series that display statistical properties consistent with dependent processes. Studies investigating the statistical properties of financial series [7], [8], [9], [10] and [11] identify the presence of non-linear dependence, which is a departure from the fair game, or martingale property of asset returns under Fama's [12] Efficient Market Hypothesis. In the econophysics literature, recent studies focusing on the long-range-dependent properties of stock indices by Grau-Carles [13], Costa and Vasconcelos [14], Matos et al [15] and Cajueiro and Tabak [16], [17] and [18] also describe varying levels of long-range dependence. The implications of dependent processes, evident from low- and high- order autocorrelation structures in the data are of particular concern for the volatility-based pricing models (such as option pricing models) typically used in financial markets. Low-order correlations, which tend to exhibit hyperbolic decay, may be associated with short-range memory effects, while long-range memory effects have been linked to the presence of fractal structures. Despite some studies investigating these issues in the major traded currencies such as the euro, Japanese yen, or English pound quoted against the US dollar, there is little information available on the microstructure and statistical properties of trading on the spot Australian dollar against the US dollar (AUD/USD). Extending the work of Batten and Ellis [19] who found weak evidence of positive dependence in the daily spot AUD/USD, this study provides evidence on the intraday behaviour of volatility and links this to the time-varying nature of dependence evident in the series. Measured using the statistical techniques of Hurst [20] and Mandelbrot and Wallis [21], the unique feature of this study is that we decompose the measure of dependence into its underlying components to provide an insight into the cause of the observed variation in volatility and dependence over the 24-hour trading day. The approach differs from recent studies that seek to identify dependence by various methods (see Refs. [13] and [15]) and from those which adopt a rolling sample approach (see Refs. [14], [16], [17] and [22]), the latter of which generally fail to account for the asymptotic behaviour of the Hurst statistic [23] and [24]. First we track the patterns and distributions of price quotes, spreads and returns across the trading day and week. Second we describe the nature and the form of price dependence in the markets. The approach adopted is to investigate the statistical relationship between quote returns across the trading day and week using the rescaled range technique, which is then decomposed to identify the source of the observed time variation. We believe that this is the first study to investigate dependence in this manner. The data employed is time stamped spot AUD/USD price quotes from banks contributing to the Reuters “FX=“page from Friday 5 May 2000 to Thursday 15 June 2000.1 The AUD/USD is the sixth most actively traded currency (after the US dollar, euro, yen, Swiss franc and the Canadian dollar) and is traded 24-hours a day with most trading occurring outside the Australian time zone, in the UK and the US. Although seemingly a short length of physical time, the data set of approximately 30,000 observations is in fact significantly larger than many recently published studies investigating dependence. Furthermore, the large number of observations examined is more than statistically sufficient to enable us to first measure dependence using the Hurst–Mandelbrot–Wallis [20] and [21] method and then decompose it into its component parts: the range and standard deviation of intraday returns. While there are some studies using larger high-frequency data sets than employed herein (see for example Ref. [2]), none investigate the specific issues undertaken in our study. In this way the analysis undertaken is pioneering for highlighting further opportunities to be explored and the results offer hypotheses, which, however tentative, may be subject to further work. The proprietary nature of the information from which the current data set is obtained has largely prevented subsequent and other detailed analyses in other markets. The remainder of the paper is structured as follows: In the next section, the method of calculating dependence and returns is described. In Section 3 the Australian dollar FX market is briefly described, then the characteristics of the quotes in the spot AUD/USD market are established. Then the results from an analysis of variance on the return properties across the trading day and week are presented. The final section allows for some concluding remarks.

The study investigates the source of intraday variation commonly observed in the returns in foreign exchange markets when high-frequency data sets are employed. To illustrate our approach, the differences in returns, volatility and dependence in quotes on the spot AUD/USD exchange rate are compared across the 24-hour trading day. The sample covered tick data from 5 May 2000 to 15 June 2000 and comprised approximately 30,000 observations. Over this period, quote arrival is clearly—and not surprisingly—linked to the opening and closing of key markets in Asia, Europe and the US, with the most dense quote period being late afternoon London as the US markets open. The frequency of quote arrival also varied with the longest time between quotes during the late afternoon trading in the US just prior to the opening of the Australian markets. Attention is drawn to ‘U-shaped’ distribution of volatility over the trading day and the consequent time-varying nature of dependence induced by this variation in volatility. The statistically significant difference in the mean local Hurst exponent across the 24-hour trading day is not attributable to transience in the estimation of the exponent. Decomposing the local exponent into its ‘range’ and ‘standard deviation’ components reveals that changes in the mean standard deviation across the trading day are largely responsible for the variation in the local exponent. In discussion of this finding, three underlying sources of variation in AUD/USD spot volatility are suggested: volatility associated with the absence of quotes, and volatility associated with price-discovery at the start of trading and at the close of markets.