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

Liesenfeld, Roman; Nolte, Ingmar; Pohlmeier, Winfried

doi:10.1007/978-3-7908-1992-2_8

Cited by 18 publications

(23 citation statements)

References 27 publications

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“…To remedy this, several authors have suggested a randomized PIT. Specifically, if P is the predictive distribution, x ∼ P is the observed count, and v is standard uniform and independent of x , then where we define P −1 = 0, is standard uniform (Smith, 1985; Frühwirth‐Schnatter, 1996; Liesenfeld, Nolte, and Pohlmeier, 2006; Brockwell, 2007). For time series data one typically considers one‐step (or k ‐step) ahead predictions, based on a time series model fitted on past and current data, and checks for the independence of the randomized PIT, in addition to checks for uniformity.…”

Section: Calibration and Sharpnessmentioning

confidence: 99%

“…We now turn to studentized errors. It has frequently been argued that the squared Pearson residual or normalized squared error score , where μ P and σ 2 P denote the mean and the variance of P , ought be approximately one when averaged over the predictions (Carroll and Cressie, 1997; Liesenfeld et al, 2006). Gotway and Wolfinger (2003) call the mean normalized squared error score the average empirical‐to‐model variability ratio , arguing also that it should be close to one.…”

Section: Scoring Rulesmentioning

confidence: 99%

“…where we define P −1 = 0, is standard uniform (Smith, 1985;Frühwirth-Schnatter, 1996;Liesenfeld, Nolte, and Pohlmeier, 2006;Brockwell, 2007). For time series data one typically considers one-step (or k-step) ahead predictions, based on a time series model fitted on past and current data, and checks for the independence of the randomized PIT, in addition to checks for uniformity.…”

Section: Probability Integral Transformmentioning

confidence: 99%

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Predictive Model Assessment for Count Data

2009

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We discuss tools for the evaluation of probabilistic forecasts and the critique of statistical models for count data. Our proposals include a nonrandomized version of the probability integral transform, marginal calibration diagrams, and proper scoring rules, such as the predictive deviance. In case studies, we critique count regression models for patent data, and assess the predictive performance of Bayesian age-period-cohort models for larynx cancer counts in Germany. The toolbox applies in Bayesian or classical and parametric or nonparametric settings and to any type of ordered discrete outcomes.

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Section: Calibration and Sharpnessmentioning

confidence: 99%

Section: Scoring Rulesmentioning

confidence: 99%

Section: Probability Integral Transformmentioning

confidence: 99%

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Predictive Model Assessment for Count Data

2009

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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

2009

Handbook of Financial Time Series

145

121

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In 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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“…where ω is a constant, w(s) denotes a non-negative weight function, and t 0 w(s)dN (s) is the stochastic Stieltjes integral of the process w with respect to the counting process N (t). The process (10) was proposed by Hawkes (1971) and is therefore named a 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%