Ultra-High Frequency Financial Data Research Articles

Bayesian semi-parametric estimation of compound inhomogeneous Poisson processes for ultra-high frequency financial transaction data

Marked point processes provide a flexible framework for studying ultra-high frequency financial data that records the time and price for each transaction. This paper estimates compound, inhomogeneous Poisson processes (CIPP) where trades arrive according to an inhomogeneous Poisson process, and returns are drawn from a distribution after arrival. The intensity functions have Gaussian process priors to model time-of-day (diurnal) effects, which have bursts of activity at the open and close and a midday lull, and lagged returns from the previous trade, which are idiosyncratic and depend on the stock. The nonparametric density estimator for returns imposes a shape constraint to obtain a unimodal distribution that is asymmetric and leptokurtic. A mixture model separates trades into time sensitive and time insensitive trades with different intensity functions. The latter group tends to have larger orders and higher returns. The proposed model is compared to B-splines and geometric Brownian motion.

Alternative asymptotic inference theory for a nonstationary Hawkes process

The Hawkes process is a popular point process model for events that exhibit a local clustering behaviour. Chen and Hall studied the asymptotic inference theory for a nonstationary Hawkes process where the baseline intensity is proportional to some time-varying function with the proportionality constant n tending to infinity. However, they assumed the excitation kernel to be independent of n, and therefore, as n increases, the waiting times from a baseline event to its excited events are of order OP(1) while the waiting times between baseline events is OP(1/n), suggesting the excitation effect is not local anymore, which defeats the purpose of choosing the exponential excitation kernel in the first place. To avoid this issue, we study the model in a more realistic setting where the excitation kernel also depends on the limit index n, so that the waiting times to excited events are of the same order of magnitude as those between baseline events. We establish consistency and asymptotic normality of the Maximum Likelihood Estimator (MLE). We also propose a score test to assess the constancy of the baseline intensity function and derive the asymptotic properties of the test. We apply the MLE and the score test to ultra-high frequency financial data as well as evaluating their finite sample performance via simulation experiments.

Price change prediction of Ultra high frequency financial data based on temporal convolutional network

Through in-depth analysis of Ultra high frequency (UHF) stock price change data, more reasonable discrete dynamic distribution models are proposed in this paper. Firstly, we classify the price changes into several categories. Then, temporal convolutional network (TCN) is utilized to predict the conditional probability for each category. Furthermore, attention mechanism is added into the TCN architecture to model the time-varying distribution for stock price change data. Empirical research on constituent stocks of Chinese Shenzhen Stock Exchange 100 Index (SZSE 100) found that the TCN framework model and the TCN (attention) framework have a better overall performance than GARCH family models and the long short-term memory (LSTM) framework model for the description of the dynamic process of the UHF stock price change sequence. In addition, the scale of the dataset reached nearly 10 million, to the best of our knowledge, there has been no previous attempt to apply TCN to such a large-scale UHF transaction price dataset in Chinese stock market.

Nonparametric Estimation for Self-Exciting Point Processes—A Parsimonious Approach

There is ample evidence that in applications of self-exciting point-process models, the intensity of background events is often far from constant. If a constant background is imposed that assumption can reduce significantly the quality of statistical analysis, in problems as diverse as modeling the after-shocks of earthquakes and the study of ultra-high frequency financial data. Parametric models can be used to alleviate this problem, but they run the risk of distorting inference by misspecifying the nature of the background intensity function. On the other hand, a purely nonparametric approach to analysis leads to problems of identifiability; when a nonparametric approach is taken, not every aspect of the model can be identified from data recorded along a single observed sample path. In this article, we suggest overcoming this difficulty by using an approach based on the principle of parsimony, or Occam’s razor. In particular, we suggest taking the point-process intensity to be either a constant or to have maximum differential entropy, in cases where there is not sufficient empirical evidence to suggest that the background intensity function is more complex than those models. This approach is seldom, if ever, used for nonparametric function estimation in other settings, not least because in those cases more data are typically available. However, our “ontological parsimony” argument is appropriate in the context of self-exciting point-process models. Supplementary materials are available online.

Inference for a Nonstationary Self-Exciting Point Process with an Application in Ultra-High Frequency Financial Data Modeling

Self-exciting point processes (SEPPs), or Hawkes processes, have found applications in a wide range of fields, such as epidemiology, seismology, neuroscience, engineering, and more recently financial econometrics and social interactions. In the traditional SEPP models, the baseline intensity is assumed to be a constant. This has restricted the application of SEPPs to situations where there is clearly a self-exciting phenomenon, but a constant baseline intensity is inappropriate. In this paper, to model point processes with varying baseline intensity, we introduce SEPP models with time-varying background intensities (SEPPVB, for short). We show that SEPPVB models are competitive with autoregressive conditional SEPP models (Engle and Russell 1998) for modeling ultra-high frequency data. We also develop asymptotic theory for maximum likelihood estimation based inference of parametric SEPP models, including SEPPVB. We illustrate applications to ultra-high frequency financial data analysis, and we compare performance with the autoregressive conditional duration models.

Inference for a Nonstationary Self-Exciting Point Process with an Application in Ultra-High Frequency Financial Data Modeling

Self-exciting point processes (SEPPs), or Hawkes processes, have found applications in a wide range of fields, such as epidemiology, seismology, neuroscience, engineering, and more recently financial econometrics and social interactions. In the traditional SEPP models, the baseline intensity is assumed to be a constant. This has restricted the application of SEPPs to situations where there is clearly a self-exciting phenomenon, but a constant baseline intensity is inappropriate. In this paper, to model point processes with varying baseline intensity, we introduce SEPP models with time-varying background intensities (SEPPVB, for short). We show that SEPPVB models are competitive with autoregressive conditional SEPP models (Engle and Russell 1998) for modeling ultra-high frequency data. We also develop asymptotic theory for maximum likelihood estimation based inference of parametric SEPP models, including SEPPVB. We illustrate applications to ultra-high frequency financial data analysis, and we compare performance with the autoregressive conditional duration models.

The Application of SAS® Hash Object to Ultra-High Frequency Financial Data: A Case Study in Limit Order Book Reconstruction

Over the last decade, the increased availability of ultra-high frequency (UHF) financial data on trades, quotes and order flows in electronic order-driven markets has led to significant innovations in the fields of the empirical microstructure and quantitative analysis of financial markets. Unfortunately, the enormous size of these UHF datasets, usually several million observations per stock per day, has brought up new data processing and handling, in addition to computational challenges. In today’s trading environment, the key challenge posed by UHF data is how one can efficiently and more importantly, quickly exploit a massive dataset to develop consistent and profitable (alpha generating) algorithmic trading strategies. Central to this exercise is the complete and accurate reconstruction of the electronic limit order book (LOB) of order-driven markets. This paper attempts to address the research challenge presented by UHF data by demonstrating the application of SAS® Hash Object to the reconstruction of SETS (Stock Exchange Electronic Trading Service) electronic LOB of the London Stock Exchange (LSE).

Forecasting Irregularly Spaced UHF Financial Data: Realized Volatility vs UHF-GARCH Models

A new literature has been recently devoted to the modeling of ultra-high-frequency (UHF) data. Our first aim is to develop an empirical application of UHF-GARCH models to forecast future volatilities on irregularly spaced data. We also compare the out-sample performance of these generalized autoregressive conditional heteroskedastic (GARCH) models with the realized volatility method. We propose a procedure to account for the time deformation problem and show how to use these models for computing daily Value at Risk (VaR).

Testing the Markov Property With Ultra-High Frequency Financial Data

This paper develops a framework to nonparametrically test whether discretevalued irregularly-spaced financial transactions data follow a Markov process. For that purpose, we consider a specific optional sampling in which a continuous-time Markov process is observed only when it crosses some discrete level. This framework is convenient for it accommodates not only the irregular spacing of transactions data, but also price discreteness. Under such an observation rule, the current price duration is independent of previous price durations given the current price realization. A simple nonparametric test then follows by examining whether this conditional independence property holds. Finally, we investigate whether or not bid-ask spreads follow Markov processes using transactions data from the New York Stock Exchange. The motivation lies on the fact that asymmetric information models of market microstructures predict that the Markov property does not hold for the bid-ask spread. The results are mixed in the sense that the Markov assumption is rejected for three out of the five stocks we have analyzed.

Integrated Volatility and UHF-GARCH Models: A Comparison Using High Frequency Financial Data

A very promising literature has been recently devoted to the modeling of ultra-high-frequency (UHF) data. The main problem encountered to measure volatility dynamics of high-frequency intra-daily data lies in the irregularity at which observations arrive. Engle and Russell (1998) have proposed a new class of point processes with dependent arrival rates: autoregressive conditional duration (ACD) point processes. Engle (2000) has generalized this approach and developed a Ultra-High-Frequency GARCH model. At the same time, Andersen and Bollerslev (1998) and Bollerslev and Wright (2001) have studied the volatility of UHF financial data by introducing the concept of integrated volatility. This integrated volatility is measured by the squared value of intra-daily returns. Our first aim in this paper is to develop an empirical application of ACD GARCH models in forecasting future volatilities. Then we propose another contribution in comparing the performances of ACD GARCH models with the integrated volatility. Therefore we propose a procedure to take into account the calendar effect or the time of day effect. We introduce an adjusted duration to calculate volatilities before comparing volatility forecasts. We show that the models induced by the two approaches lead to poor performances. Nevertheless, our results show that the integrated volatility method tends to outperform UHF-GARCH models.

Quantile estimation in ultra-high frequency financial data: a comparison between parametric and semiparametric approach

In the context of ACD models for ultra-high frequency data different specifications are available to estimate the conditional mean of intertrade durations, while quantiles estimation has been completely neglected by literature, even if to trading extent it can be more informative. The main problem arising with quantiles estimation is the correct specification of durations’ probability law: the usual assumption of Exponentially distributed residuals, is very robust for the estimation of parameters of the conditional mean, but dramatically fails the distributional fit. In this paper a semiparametric approach is formalized, and compared with the parametric one, deriving from Exponential assumption. Empirical evidence for a stock of Italian financial market strongly supports the former approach.