Integer-valued moving average modelling of the number of transactions in stocks

Brännäs, Kurt; Quoreshi, Shahiduzzaman

doi:10.1080/09603107.2010.498343

Cited by 67 publications

(51 citation statements)

References 24 publications

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“…(1999); an application to psychometrics in Böckenholt (1999a), an application to environmentology in Thyregod et al. (1999); recent applications to economics in, for example, Böckenholt (1999b), Berglund and Brännäs (2001), Brännäs and Hellström (2001), Rudholm (2001), Böckenholt (2003), Brännäs and Shahiduzzaman (2004), Freeland and McCabe (2004), Gourieroux and Jasiak (2004) and McCabe and Martin (2005); and Pickands and Stine (1997) and Ahn et al. (2000) considered queueing applications.…”

Section: Introduction and Notationmentioning

confidence: 99%

Efficient Estimation of Auto-Regression Parameters and Innovation Distributions for Semiparametric Integer-Valued AR(p) Models

Drost

Akker

Werker

2008

Journal of the Royal Statistical Society Series B: Statistical Methodology

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Integer-valued auto-regressive (INAR) processes have been introduced to model non-negative integer-valued phenomena that evolve over time. The distribution of an INAR(p) process is essentially described by two parameters: a vector of auto-regression coefficients and a probability distribution on the non-negative integers, called an immigration or innovation distribution. Traditionally, parametric models are considered where the innovation distribution is assumed to belong to a parametric family. The paper instead considers a more realistic semiparametric INAR(p) model where there are essentially no restrictions on the innovation distribution. We provide an (semiparametrically) efficient estimator of both the auto-regression parameters and the innovation distribution.

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Section: Introduction and Notationmentioning

confidence: 99%

Efficient Estimation of Auto-Regression Parameters and Innovation Distributions for Semiparametric Integer-Valued AR(p) Models

Drost

Akker

Werker

2008

Journal of the Royal Statistical Society Series B: Statistical Methodology

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“…Asymmetric responses on the volatility are also commonly observed in the analysis of time series representing the number of intra-day transactions in stocks, in which the numbers are typically quite small as reported in [1]. As an illustration of this kind of data we present in Fig.…”

Section: Introductionmentioning

confidence: 96%

Time Series Analysis and Forecasting

Rojas¹,

Pomares²

2016

Contributions to Statistics

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Abstract. The Asymmetric Power Arch representation for the volatility was introduced by Ding et al. [4] in order to account for asymmetric responses in the volatility in the analysis of continuous-valued financial time series like, for instance, the log-return series of foreign exchange rates, stock indices or share prices. As reported by Brännäs and Quoreshi [1], asymmetric responses in volatility are also observed in time series of counts such as the number of intra-day transactions in stocks. In this work, an asymmetric power autoregressive conditional Poisson model is introduced for the analysis of time series of counts exhibiting asymmetric overdispersion. Basic probabilistic and statistical properties are summarized and parameter estimation is discussed. A simulation study is presented to illustrate the proposed model. Finally, an empirical application to a set of data concerning the daily number of stock transactions is also presented to attest for its practical applicability in data analysis.

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“…It should also be mentioned that the AIC of ARMA models has been used in the INARMA literature (e.g. [16]). …”

Section: Empirical Analysismentioning

confidence: 99%

“…For an INARMA(p,q) process of (11), the aggregated process over a forecast horizon can be written as: (16) Now, if we assume that ∑ (18) with the parameters as shown in Table 1 (see Appendix B for the proof).…”

Section: Proofmentioning

confidence: 99%