Modelling financial transaction price movements: a dynamic integer count data model

Liesenfeld, Roman; Nolte, Ingmar; Pohlmeier, Winfried

doi:10.1007/s00181-005-0001-1

Cited by 47 publications

(36 citation statements)

References 26 publications

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“…The availability of trade-by-trade (commonly known as ultra high-frequency (UHF)) data on transactions, in the recent decade, has revolutionised data processing and statistical modelling techniques in finance (McCulloch & Tsay, 2001;Tsay, 2005;Liesenfeld, Nolte, & Pohlmeier, 2006;Pacurar, 2008). The unique characteristics of UHF data has introduced new theoretical and computational challenges to both statistical and financial studies (Liesenfeld, Nolte, & Pohlmeier, 2006;Pacurar, 2008;Tsay, 2005).…”

Section: Applicationmentioning

confidence: 99%

“…The unique characteristics of UHF data has introduced new theoretical and computational challenges to both statistical and financial studies (Liesenfeld, Nolte, & Pohlmeier, 2006;Pacurar, 2008;Tsay, 2005). Such data consist of (i) discrete-valued observations, as the price change in consecutive transactions is in a multiple of tick size, where one tick is defined as the minimum amount by which the price of the market can change and (ii) unequally spaced time intervals; see Tsay (2005, Chapter 5) and Liesenfeld, Nolte, and Pohlmeier (2006) and references therein for further details on analysing UHF data sets. Number ( be 0.5 FTSE100 index.…”

Section: Applicationmentioning

confidence: 99%

“…However, considering the size of the data and the fact that most of the values (70%) of index change is zero (no index change), it may be difficult to find suitable diagnostics measures. Here, a randomised version of the PIT is implemented to measure how well the predictive distribution, especially in the tails, is able to explain the density of index change for the next trading day (Liesenfeld, Nolte, & Pohlmeier, 2006). In order to use the PIT, we have to construct intervals based on the cumulative predictive distribution of the ith observed index change and the ith observed index change minus 1, as follows…”

Section: Model Checkingmentioning

confidence: 99%

“…In order to validate the fitted model, we obtain one-step ahead predictions of the index change for the next trading day (March 26, 2008). We assess the performance of the posterior predictive distribution with the probability integral transform (PIT) modified for the case of integer-valued variables (Liesenfeld, Nolte, & Pohlmeier, 2006). Finally, model comparisons were performed using the deviance information criterion (DIC) and the Bayes factor (BF).…”

Section: Introductionmentioning

confidence: 99%

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Bayesian Modelling of Integer Data Using the Generalised Poisson Difference Distribution

Shahtahmassebi¹,

Moyeed²

2014

IJSP

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Integer-valued random variables arising from the difference of two discrete variables can be seen frequently in various applications. In this paper, we obtain the distribution and derive the properties of the difference of two generalised Poisson variables with unequal parameters. This distribution is adopted to model a set of ultra high frequency (UHF) data relating to FTSE100 index futures using covariates. The unique characteristics of UHF data have introduced new theoretical and computational challenges to both statistical and financial studies. Such data consist of discrete-valued observations and unequally spaced time intervals. We also extend the model to its zero inflated version in order to capture the excess of zeros in the given data set. The analysis is carried out in a Bayesian framework using Markov Chain Monte Carlo methods. Various model diagnostics and model comparisons were undertaken which showed that index changes were explained well by the fitted model.

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Section: Applicationmentioning

confidence: 99%

Section: Applicationmentioning

confidence: 99%

Section: Model Checkingmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Bayesian Modelling of Integer Data Using the Generalised Poisson Difference Distribution

Shahtahmassebi¹,

Moyeed²

2014

IJSP

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“…Dynamic extensions of Poisson processes in terms of counting representations are not surveyed in this chapter. Some references reflecting the diversity of approaches are Rydberg and Shephard (2003), Heinen and Rengifo (2003), Liesenfeld, Nolte, and Pohlmeier (2006), and Quoreshi (2006).…”

Section: Types and Representations Of Point Processesmentioning

confidence: 99%

Modelling Financial High Frequency Data using Point Processes

Bauwens

Hautsch

2006

SSRN Journal

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Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in AbstractIn this paper, we give an overview of the state-of-the-art in the econometric literature on the modeling of so-called financial point processes. The latter are associated with the random arrival of specific financial trading events, such as transactions, quote updates, limit orders or price changes observable based on financial high-frequency data. After discussing fundamental statistical concepts of point process theory, we review durationbased and intensity-based models of financial point processes. Whereas duration-based approaches are mostly preferable for univariate time series, intensity-based models provide powerful frameworks to model multivariate point processes in continuous time. We illustrate the most important properties of the individual models and discuss major empirical applications.

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An inflated multivariate integer count hurdle model: an application to bid and ask quote dynamics

Bien

Nolte

Pohlmeier

2011

J of Applied Econometrics

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In this paper we develop a model for the conditional inflated multivariate density of integer count variables with domain Z n . Our modelling framework is based on a copula approach and can be used for a broad set of applications where the primary characteristics of the data are: (i) discrete domain, (ii) the tendency to cluster at certain outcome values and (iii) contemporaneous dependence. These kind of properties can be found for high or ultra-high frequent data describing the trading process on financial markets. We present a straightforward method of sampling from such an inflated multivariate density through the application of an Independence Metropolis-Hastings sampling algorithm. We demonstrate the power of our approach by modelling the conditional bivariate density of bid and ask quote changes in a high frequency setup. We show how to derive the implied conditional discrete density of the bid-ask spread, taking quote clusterings (at multiples of 5 ticks) into account.

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Modelling financial transaction price movements: a dynamic integer count data model

Abstract: Financial transaction prices, Autoregressive conditional multinomial model, GLARMA, Count data, Market microstructure effects, C22, C25, G10,

Cited by 47 publications

References 26 publications

Bayesian Modelling of Integer Data Using the Generalised Poisson Difference Distribution

Bayesian Modelling of Integer Data Using the Generalised Poisson Difference Distribution

Modelling Financial High Frequency Data using Point Processes

An inflated multivariate integer count hurdle model: an application to bid and ask quote dynamics

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