Behavior of realized volatility and correlation in exchange markets

We study time-varying realized volatility and related correlation measures as proxies for the true volatility and correlation. We investigate measures of Two-Scale realized Absolute Volatility (TSAV) and correlation (TSACORxy) which are helpful to cope effectively with the problem of market microstructure effects at very high frequency financial time series. The measures are constructed based on subsampling and averaging method so that they possess rather less bias even in presence of market microstructure noise. Absolute transformation of return values has been proved in literature to be more robust than squared transformation when considering large values. With respect to some stylized facts of markets, realized squared correlation does not display dynamic behavior. Motivated by robustness of realized absolute volatility, we study an alternative measure of correlation, built on absolute-transformed volatility. This measure of correlation exhibits experimentally some dynamics and hence some predictability capability on minute-by-minute frequency exchange market data. We show that the distribution of realized correlation series computed based on TSACORxy tends to comply a rightward asymmetric shape implying that upside co-movements are greater than downside ones. Moreover we study the association between realized volatility and correlation. According to the two-scale measure, our findings empirically suggest that when returns in Euro/USD exchange rate are highly volatile, the relation between Euro/USD and Euro/GBP exchange markets is strong, and when Euro/USD calms down, the relationship relaxes.Realized Volatility and Correlation, Long Memory, Scaling Law, Self-Similarity Dimension, Market Microstructure Effects.

Behavior of realized volatility and correlation in exchange markets

We study time-varying realized volatility and related correlation measures as proxies for the true volatility and correlation. We investigate measures of Two-Scale realized Absolute Volatility (TSAV) and correlation (TSACORxy) which are helpful to cope effectively with the problem of market microstructure effects at very high frequency financial time series. The measures are constructed based on subsampling and averaging method so that they possess rather less bias even in presence of market microstructure noise. Absolute transformation of return values has been proved in literature to be more robust than squared transformation when considering large values. With respect to some stylized facts of markets, realized squared correlation does not display dynamic behavior. Motivated by robustness of realized absolute volatility, we study an alternative measure of correlation, built on absolute-transformed volatility. This measure of correlation exhibits experimentally some dynamics and hence some predictability capability on minute-by-minute frequency exchange market data. We show that the distribution of realized correlation series computed based on TSACORxy tends to comply a rightward asymmetric shape implying that upside co-movements are greater than downside ones. Moreover we study the association between realized volatility and correlation. According to the two-scale measure, our findings empirically suggest that when returns in Euro/USD exchange rate are highly volatile, the relation between Euro/USD and Euro/GBP exchange markets is strong, and when Euro/USD calms down, the relationship relaxes

Algorithms for Spectral Analysis of Irregularly Sampled Time Series

In this paper, we present a spectral analysis method based upon least square approximation. Our method deals with nonuniform sampling. It provides meaningful phase information that varies in a predictable way as the samples are shifted in time. We compare least square approximations of real and complex series, analyze their properties for sample count towards infinity as well as estimator behaviour, and show the equivalence to the discrete Fourier transform applied onto uniformly sampled data as a special case. We propose a way to deal with the undesirable side effects of nonuniform sampling in the presence of constant offsets. By using weighted least square approximation, we introduce an analogue to the Morlet wavelet transform for nonuniformly sampled data. Asymptotically fast divide-and-conquer schemes for the computation of the variants of the proposed method are presented. The usefulness is demonstrated in some relevant applications.

Algorithms for Spectral Analysis of Irregularly Sampled Time Series

In this paper, we present a spectral analysis method based upon least square approximation. Our method deals with nonuniform sampling. It provides meaningful phase information that varies in a predictable way as the samples are shifted in time. We compare least square approximations of real and complex series, analyze their properties for sample count towards infinity as well as estimator behaviour, and show the equivalence to the discrete Fourier transform applied onto uniformly sampled data as a special case. We propose a way to deal with the undesirable side effects of nonuniform sampling in the presence of constant offsets. By using weighted least square approximation, we introduce an analogue to the Morlet wavelet transform for nonuniformly sampled data. Asymptotically fast divide-and-conquer schemes for the computation of the variants of the proposed method are presented. The usefulness is demonstrated in some relevant applications