A geographical model for the daily and weekly seasonal volatility in the foreign exchange market

Dacorogna, Michel M.; Müller, Ulrich; Nagler, Robert J.; Olsen, Richard B.; Pictet, Olivier V.

doi:10.1016/0261-5606(93)90004-u

Cited by 519 publications

(339 citation statements)

References 12 publications

Supporting

Mentioning

301

Contrasting

Unclassified

Order By: Relevance

“…In these studies, it is often concluded that log-squared, squared, or absolute returns are highly persistent processes. Therefore the dynamic evolution of volatility could be best described by a long-memory process [see Dacorogna et al (1993), Ding, Granger, and Engle (1993), Andersen and Bollerslev (1997), and Lobato and Savin (1998)]. The most popular long-memory models for volatilities are the fractionally integrated GARCH (FIGARCH) models of Baillie, Bollerslev, and Mikkelsen (1996) and Bollerslev and Mikkelsen (1996) and the long-memory stochastic volatility (LMSV) model proposed independently by Breidt, Crato, and de Lima (1998) and Harvey (1998).…”

Section: Introductionmentioning

confidence: 99%

Properties of the Sample Autocorrelations of Nonlinear Transformations in Long-Memory Stochastic Volatility Models

Pérez¹

2003

Journal of Financial Econometrics

View full text Add to dashboard Cite

The autocorrelations of log-squared, squared, and absolute financial returns are often used to infer the dynamic properties of the underlying volatility. This article shows that, in the context of long-memory stochastic volatility models, these autocorrelations are smaller than the autocorrelations of the log volatility and so is the rate of decay for squared and absolute returns. Furthermore, the corresponding sample autocorrelations could have severe negative biases, making the identification of conditional heteroscedasticity and long memory a difficult task. Finally, we show that the power of some popular tests for homoscedasticity is larger when they are applied to absolute returns.keywords: absolute transformation, Box-Ljung text, conditional heteroscedasticity, log-squared transformation, Peña Rodriguez test, squared observations. It is by now rather popular to measure the volatility of financial returns by some nonlinear transformations as, for example, log-squared, squared, or absolute returns. Consequently the autocorrelations of these transformations have often been used to test for the presence of conditional heteroscedasticity and to model and estimate the volatility [see, e

show abstract

Section: Introductionmentioning

confidence: 99%

Properties of the Sample Autocorrelations of Nonlinear Transformations in Long-Memory Stochastic Volatility Models

Pérez¹

2003

Journal of Financial Econometrics

View full text Add to dashboard Cite

show abstract

“…The volatility is of practical importance since it quantifies the risk related to assets [1]. Unlike price changes that are correlated only on very short time scales [2] (a few minutes), the absolute values of price changes (which are closely related to the volatility) show correlations on time scales up to many years [3][4][5].Here we study in detail the volatility of the S&P 500 index of the New York stock exchange, which represents the stocks of the 500 largest U.S. companies. Our study is based on a data set over 13 years from January 1984 to December 1996 reported at least every minute (these data extend by 7 years the data set previously analyzed in [6]).…”

mentioning

confidence: 99%

Volatility distribution in the S&P500 stock index

Cizeau

Liu

Meyer

et al. 1997

Physica A: Statistical Mechanics and its Applications

204

View full text Add to dashboard Cite

We study the volatility of the S&P500 stock index from 1984 to 1996 and find that the volatility distribution can be very well described by a log-normal function. Further, using detrended fluctuation analysis we show that the volatility is powerlaw correlated with Hurst exponent α ∼ = 0.9.The volatility is a measure of the mean fluctuation of a market price over a certain time interval T . The volatility is of practical importance since it quantifies the risk related to assets [1]. Unlike price changes that are correlated only on very short time scales [2] (a few minutes), the absolute values of price changes (which are closely related to the volatility) show correlations on time scales up to many years [3][4][5].Here we study in detail the volatility of the S&P 500 index of the New York stock exchange, which represents the stocks of the 500 largest U.S. companies. Our study is based on a data set over 13 years from January 1984 to December 1996 reported at least every minute (these data extend by 7 years the data set previously analyzed in [6]).We calculate the logarithmic incrementswhere Z(t) denotes the index at time t and ∆t is the time lag; G(t) is the relative price change ∆Z/Z in the limit ∆t → 0. Here we set ∆t = 30 min, wellPreprint submitted to Elsevier Preprint August 15, 1997above the correlation time of the price increments; we obtain similar results for other choices of ∆t (larger than the correlation time).Over the day, the market activity shows a strong "U-shape" dependence with high activity in the morning and in the afternoon and much lower activity over noon. To remove artificial correlations resulting from this intra-day pattern of the volatility [7][8][9][10], we analyze the normalized functionwhere A(t) is the mean value of |G(t)| at the same time of the day averaged over all days of the data set.We obtain the volatility at a given time by averaging |g(t)| over a time window T = n · ∆t with some integer n, Figure 1 shows (a) the S&P500 index and (b) the signal v T (t) for a long averaging window T = 8190 min (about 1 month). The volatility fluctuates strongly showing a marked maximum for the '87 crash. Generally periods of high volatility are not independent but tend to "cluster". This clustering is especially marked around the '87 crash, which is accompanied by precursors (possibly related to the oscillatory patterns postulated in [11]). Clustering occurs also in other periods (e.g. in the second half of '90), while there are extended periods where the volatility remains at a rather low level (e.g. the years of '85 and '93). Fig. 2a shows the scaled probability distribution P (v T ) for several values of T . The data for different averaging windows collapse to one curve. Remarkably, the scaling form is log-normal, not Gaussian. In the limit of very long averaging times, one expects that P (v T ) becomes Gaussian, since the central limit theorem holds also for correlated series [12], with a slower convergence than for non-correlated processes [13,14]. For the times considered here, ...

show abstract

“…For example, Johansen and Sornette (2000) find that such asset return innovations exhibit strong positive correlations exactly at the time of extreme events. Dacorogna et al (1993) find the same for FX returns. Muzy et al (2001) and Breymann et al (2000) show that the return volatility displays different long-term correlations from large to small time scales.…”

Section: Introductionmentioning

confidence: 55%

Multi-Fractal Spectral Analysis of the 1987 Stock Market Crash

Los

Yalamova

2004

SSRN Journal

View full text Add to dashboard Cite

The multifractal model of asset returns captures the volatility persistence of many financial time series. Its multifractal spectrum computed from wavelet modulus maxima lines provides the spectrum of irregularities in the distribution of market returns over time and thereby of the kind of uncertainty or "randomness" in a particular market. Changes in this multifractal spectrum display distinctive patterns around substantial market crashes or "drawdowns." In other words, the kinds of singularities and the kinds of irregularity change in a distinct fashion in the periods immediately preceding and following major market drawdowns. This paper focuses on these identifiable multifractal spectral patterns surrounding the stock market crash of 1987. Although we are not able to find a uniquely identifiable irregularity pattern within the same market preceding different crashes at different times, we do find the same uniquely identifiable pattern in various stock markets experiencing the same crash at the same time. Moreover, our results suggest that all such crashes are preceded by a gradual increase in the weighted average of the values of the Lipschitz regularity exponents, under low dispersion of the multifractal spectrum. At a crash, this weighted average irregularity value drops to a much lower value, while the dispersion of the spectrum of Lipschitz exponents jumps up to a much higher level after the crash. Our most striking result, however, is that the multifractal spectra of stock market returns are not stationary. Also, while the stock market returns show a global Hurst exponent of slight persistence 0.5 < H < 0.7, these spectra tend to be skwed towards anti-persistence in the returns.

show abstract

A geographical model for the daily and weekly seasonal volatility in the foreign exchange market

Cited by 519 publications

References 12 publications

Properties of the Sample Autocorrelations of Nonlinear Transformations in Long-Memory Stochastic Volatility Models

Properties of the Sample Autocorrelations of Nonlinear Transformations in Long-Memory Stochastic Volatility Models

Volatility distribution in the S&P500 stock index

Multi-Fractal Spectral Analysis of the 1987 Stock Market Crash

Contact Info

Product

Resources

About