Stock price process and long memory in trade signs

Kuroda, Koji; Maskawa, Jun-ichi; Murai, Joshin

doi:10.1007/978-4-431-53883-7_4

Cited by 5 publications

(5 citation statements)

References 11 publications

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“…A well-known property of order flow in real financial markets is long memory (Bouchaud et al 2008). This phenomenon can be observed by plotting the autocorrelation function of the time series of trade signs for a particular market over some period (+1 for buyer initiated trades and -1 for seller initiated trades), which typically demonstrates a slow decay in autocorrelation as the number of lags is increased in most empirical investigations (Kuroda et al 2011). Using the measured data and following the method of Lee and Ready (1991), which was also applied to similar datasets in Harvey et al (2017), we classified trades as either buyer or seller initiated and computed the associated trade sign autocorrelation function.…”

Section: Realistic Order Matching Procedures and Price Dynamicsmentioning

confidence: 99%

Can agent-based models probe market microstructure?

Platt

Gebbie

2018

Physica A: Statistical Mechanics and its Applications

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We extend prior evidence that naively using intraday agent-based models that involve realistic ordermatching processes for modeling continuous-time double auction markets seems to fail to be able to provide a robust link between data and many model parameters, even when these models are able to reproduce a number of well-known stylized facts of return time series. We demonstrate that while the parameters of intraday agent-based models rooted in market microstructure can be meaningfully calibrated, those exclusively related to agent behaviors and incentives remain problematic. This could simply be a failure of the calibration techniques used but we argue that the observed parameter degeneracies are most likely a consequence of the realistic matching processes employed in these models. This suggests that alternative approaches to linking data, phenomenology and market structure may be necessary and that it is conceivable that one could construct a useful model that does not directly depend on the nuances of agent behaviors, even when it is known that the real agents engage in complex behaviors.

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Section: Realistic Order Matching Procedures and Price Dynamicsmentioning

confidence: 99%

Can agent-based models probe market microstructure?

Platt

Gebbie

2018

Physica A: Statistical Mechanics and its Applications

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“…Setting gðnÞ ¼ ffiffi ffi n p and using expansion, the property that a ðAÞ ¼ 0 unless A is a cluster, and arguments developed in Kuroda et al (2011), we obtain log ðn;rÞ t 1 ;...;t m ðz 1 ; .…”

Section: Kotecky-preissmentioning

confidence: 99%

“…The method of abstract polymer expansion has been investigated in studies of phase transitions in lattice spin systems (Kotecky and Preiss 1986;Brickmont et al 1985), and applied to finance models for long memory (Kuroda et al 2011(Kuroda et al , 2013.…”

Section: Introductionmentioning

confidence: 99%

Investment time horizon and multifractality of stock price process

Kuroda

2016

Evolut Inst Econ Rev

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We construct a multifractal random walk for a stock trades model with inverse power law interaction. Consider a stock in a stock market and introduce a discrete time model for pair trades [(first trade ! second (reverse) trade] transacted by various types of traders. The type of trader is characterized by the investment time horizon defined as a time difference of the pair trades. We assume that probability distributions of the investment time horizons are given by inverse power law interactions with different exponents depending on the types of traders, and define a discrete time log-volatility process of the stock. Using the method of abstract polymer expansion developed in the study of mathematical physics we obtain a continuous type log-volatility process as a scale limit, and define a logreturn process from time 0 as a stochastic integral with respect to a Brownian motion. We then find a condition of the continuous cascade equation which derives a multifractality in the log-return process. Finally, we construct a multifractal random walk using the martingale convergence theorem.

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“…In the hypothesis of order splitting, investors split their unrevealed hidden order of buying or selling into small pieces before execution. It is proposed by Lillo et al (2005) and used by Kuroda et al (2011Kuroda et al ( , (2013 and Murai (2015). One explanation why investors split their hidden order is because of investors' strategical behavior.…”

Section: Hypotheses On Long Memorymentioning

confidence: 99%

“…Some techniques of the statistical mechanics is effective in the theoretical research (Mantegna et al 200). The method of the cluster expansion which has developed into a study of the statistical mechanics is one of effective techniques (Kuroda et al 2011(Kuroda et al , 2013.…”

Section: Introductionmentioning

confidence: 99%

A model of transaction signs with order splitting and public information

Murai

2016

Evolut Inst Econ Rev

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Applying a method of the cluster expansion developed in a study of statistical mechanics, a new mathematical model has been structured to account for the reason that a time series of transaction signs in financial markets has a long memory property. A basic assumption for the model was that investors split their hidden orders into small pieces before execution. The effect of public information also was taken into consideration. A mathematical expression of investors' investment behavior generates a discrete time stochastic process of cumulative transaction signs. The strong law of large numbers holds for the process: it converges to a trend term almost surely. The distribution of the fluctuation around the trend term weakly converges to the distribution of a superposition of a stochastic integral with respect to a Brownian motion and stochastic integrals with respect to a fractional Brownian motions with Hurst exponents greater than one-half. Namely, increments of the derived process have a long memory property.

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Stock price process and long memory in trade signs

Cited by 5 publications

References 11 publications

Can agent-based models probe market microstructure?

Can agent-based models probe market microstructure?

Investment time horizon and multifractality of stock price process

A model of transaction signs with order splitting and public information

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