Emergence of Statistically Validated Financial Intraday Lead-Lag Relationships

Abstract

According to the leading models in modern finance, the presence of intraday lead-lag relationships between financial assets is negligible in efficient markets. With the advance of technology, however, markets have become more sophisticated. To determine whether this has resulted in an improved market efficiency, we investigate whether statistically significant lagged correlation relationships exist in financial markets. We introduce a numerical method to statistically validate links in correlationbased networks, and employ our method to study lagged correlation networks of equity returns in financial markets. Crucially, our statistical validation of lead-lag relationships accounts for multiple hypothesis testing over all stock pairs. In an analysis of intraday transaction data from the periods 2002-2003 and 2011-2012, we find a striking growth in the networks as we increase the frequency with which we sample returns. We compute how the number of validated links and the magnitude of correlations change with increasing sampling frequency, and compare the results between the two data sets. Finally, we compare topological properties of the directed correlation-based networks from the two periods using the in-degree and out-degree distributions and an analysis of three-node motifs. Our analysis suggests a growth in both the efficiency and instability of financial markets over the past decade.

Information-theoretic approach to lead-lag effect on financial markets

“…Here we present the methodology of statistically validating lagged correlations for the purpose of network analysis presented in reference [29]. On this basis we will present our extended methodology, which includes non-linear dependencies.…”

“…Curme et al [29] begin the analysis by calculating the matrix of logarithmic returns over given intraday timehorizons. Let us denote the most recent price for stock n occurring on or before time t during the studied period by p n (t).…”

“…On the other hand, very few inquires have been performed looking into networks of lagged correlations [28,29]. The above-described methods of constructing dependency networks cannot be easily extended to the analysis of directed lagged correlations or similarity measures in financial markets.…”

Coupled Network Approach to Predictability of Financial Market Returns and News Sentiments

“…It therefore does not readily extend to the study of lagged correlation networks, in which the correlations are asymmetric: in general, L i,j = L j,i . More generally, such topological methods of filtering a correlation matrix into a network, which depend heavily on the ranking of the measured correlation coefficients, are less robust to statistical uncertainty than other methods, such as applying a threshold to the matrix (Curme et al 2015). This is especially important when studying lagged correlations, which tend to be much lower in magnitude than synchronous correlations.…”

“…But this threshold will vary with the distribution of the signals under consideration, many of which are known to be non-normal (Mantegna & Stanley 2000). To this end, we apply a bootstrapping procedure (Curme et al 2015 in which the rows of the matrix X (t) are shuffled repeatedly in order to construct a distribution for the sample correlation coefficient as measured using uncorrelated signals of the same distribution as the data. We then apply a uniform statistical threshold of p = 0.01, with false discovery rate (FDR) correction for multiple comparisons (Benjamini & Hochberg 1995), to obtain thresholds of measured correlation coefficients that vary for each time series pair.…”