توزیع ویژگی های نقدینگی بازار سهام

We examine the distribution characteristics of stock market liquidity by employing the generalized additive models for location, scale and shape (GAMLSS) model and three-minute frequency data from Chinese stock markets. We find that the BCPE distribution within the GAMLSS framework fits the distributions of stock market liquidity well with the diagnosis test. We also find that the stock market index exhibits a significant impact on the distributions of stock market liquidity. The stock market liquidity usually exhibits a positive skewness, but a normal distribution at a low level of stock market index and a high-peak and fat-tail shape at a high level of stock market index.

Liquidity can be statistically defined as market width, depth and immediacy, and dynamically defined as market power and resiliency. Among all the liquidity proxies, market depth and width are commonly used in the existing literature. Brockman and Chung [1] investigate the liquidity distribution by employing the high frequency data from the Hong Kong Stock Exchange and find that the intraweek depth follows a reverse UU pattern. Similarly, Plerou et al. [2] reveal that the distribution of the stock price spread has a fat tailed feature and follows a power law. Yan et al. [3] find that the probability distribution of relative changes in returns satisfies a power law form. Ponzi et al. [4] examine the relaxation dynamics of the bid–ask spread and of the midprice after an abrupt change of the spread in a double auction financial market. Mu et al. [5] observe the distributions of trade sizes and trading volumes for 22 Chinese stocks and find that the size distributions for individual stocks has jumps and the probability density functions exhibit power-law tails for large volumes. Kagraoka [6] examines the liquidity processes and reveals the leptokurtic properties of the return distributions. Toth et al. [7] derive a dynamical model of market liquidity and find the average supply/demand profile is V-shaped and disappears close to the current price. Feng et al. [8] develop an agent-based model with stochastic process to show the “fat” tail property in price return distributions. The above studies confirm that the liquidity does not follow the traditional exponential distribution families. In this paper we employ a new approach or a class of GAMLSS models to investigate the distribution of market liquidity, which proves to be a convenient option when the response variable does not follow the exponential family distributions or when the shape of the response variable’s distribution is clearly determined by covariates. Within the GAMLSS framework, we can expand distribution parameters up to four dimensions at a time, which improves the flexibility of analysis. The application of a non-parametric model within the GAMLSS framework avoids modeling with parameters subjectively. In this paper we also show that the GAMLSS framework can compete with traditional linear regression methods for this high-frequency market liquidity data set in terms of forecast accuracy. The remainder of this paper is organized as follows: Section 2 presents the GAMLSS model proposed by Rigby & Stasinopoulos [9]. Section 3 describes the statistical characteristics of the data. Section 4 discusses the empirical results. Section 5 concludes the paper.