Abstract. We measure the price impacts across a correlated financial market by the responses to single and multiple trades. Focusing on the primary responses, we use an event time scale. We quantify the asymmetries of the distributions and of the market structures of cross-impacts, and find that the impacts across the market are asymmetric and non-random. Using spectral statistics and Shannon entropy, we visualize the asymmetric information in market impacts. Also, we introduce an entropy of impacts to estimate the randomness between stocks. We show that the useful information is encoded in the impacts corresponding to the small entropy. The stocks with large number of trades are more likely to impact others, while the less traded stocks have higher probability to be impacted by others.
We empirically analyze the price and liquidity responses to trade signs, traded volumes and signed traded volumes. Utilizing the singular value decomposition, we explore the interconnections of price responses and of liquidity responses across the whole market. The statistical characteristics of their singular vectors are well described by the t location-scale distribution. Furthermore, we discuss the relation between prices and liquidity with respect to their overlapping factors. The factors of price and liquidity changes are non-random when these factors are related to the traded volumes. This means that the traded volumes play a critical role in the price change induced by the liquidity change. In contrast, the two kinds of factors are weakly overlapping when they are related to the trade signs and signed traded volumes. Hence, an imbalance of liquidity is related to the price change.
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