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

Drost, Feike C.; Akker, R. van den; Werker, Bas J. M.

doi:10.1111/j.1467-9868.2008.00687.x

Cited by 65 publications

(52 citation statements)

References 40 publications

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“…The bias in d found in this study for INARFIMA(0,d,0) appears to be much smaller than the corresponding bias for in ARFIMA(0,d,0) (Drost et al 2009). Besides different data generating process between these studies, the reasons behind these large differences may depend on the choice of constant terms, estimators and start values or in combination of all these.…”

Section: A Brief Monte Carlo Experimentscontrasting

confidence: 55%

“…Smith et al (1996) studied the bias and misspecification in ARFIMA models. Drost et al (2009) investigated finite sample behaviour of semiparametric integer-valued AR(p) models while Bra¨nna¨s and Quoreshi (2010) studied finite lag misspecification when the data is generated according to an infinite-lag INMA model. In this brief Monte Carlo experiment we study the bias, MSE, Ljung-Box statistics, AIC and SBIC properties of the CLS estimators for finite-lag specifications, when data is generated according to INARFIMA (0,d,0).…”

Section: A Brief Monte Carlo Experimentsmentioning

confidence: 99%

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A long-memory integer-valued time series model, INARFIMA, for financial application

Quoreshi

2012

Quantitative Finance

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A model to account for the long-memory property in a count data framework is proposed and applied to high-frequency stock transactions data. By combining features of the INARMA and ARFIMA models, an Integer-valued Auto Regressive Fractionally Integrated Moving Average (INARFIMA) model is proposed. The unconditional and conditional first-and second-order moments are given. The CLS, FGLS and GMM estimators are discussed. In its empirical application to two stock series for AstraZeneca and Ericsson B, we find that both series have a fractional integration property.

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Section: A Brief Monte Carlo Experimentscontrasting

confidence: 55%

Section: A Brief Monte Carlo Experimentsmentioning

confidence: 99%

A long-memory integer-valued time series model, INARFIMA, for financial application

Quoreshi

2012

Quantitative Finance

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“…That the general topic remains of interest today is evidenced by the important recent contributions of, inter alia , Drost et al . () and McCabe et al . ().…”

Section: Introductionmentioning

confidence: 87%

Efficient Method of Moments Estimators for Integer Time Series Models

Martin

Tremayne

Jung

2014

Journal Time Series Analysis

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The parameters of integer autoregressive models with Poisson, or negative binomial innovations can be estimated by maximum likelihood where the prediction error decomposition, together with convolution methods, is used to write down the likelihood function. When a moving average component is introduced this is not the case. To address this problem an efficient method of moment estimator is proposed where the estimated standard errors for the parameters are obtained using subsampling methods. The small sample properties of the estimator are investigated using Monte Carlo methods, while the approach is demonstrated using two well‐known examples from the time series literature.

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“…Drost et al. (2009) established asymptotic normality and efficiency for the NPMLE in the INAR class.…”

Section: Probabilistic Forecasting In the Integer Auto‐regressive mentioning

confidence: 99%

Efficient Probabilistic Forecasts for Counts

McCabe

Martin

Harris

2011

Journal of the Royal Statistical Society Series B: Statistical Methodology

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Efficient probabilistic forecasts of integer-valued random variables are derived. The optimality is achieved by estimating the forecast distribution non-parametrically over a given broad model class and proving asymptotic (non-parametric) efficiency in that setting.The method is developed within the context of the integer auto-regressive class of models, which is a suitable class for any count data that can be interpreted as a queue, stock, birth-and-death process or branching process. The theoretical proofs of asymptotic efficiency are supplemented by simulation results that demonstrate the overall superiority of the non-parametric estimator relative to a misspecified parametric alternative, in large but finite samples. The method is applied to counts of stock market iceberg orders. A subsampling method is used to assess sampling variation in the full estimated forecast distribution and a proof of its validity is given.

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

Cited by 65 publications

References 40 publications

A long-memory integer-valued time series model, INARFIMA, for financial application

A long-memory integer-valued time series model, INARFIMA, for financial application

Efficient Method of Moments Estimators for Integer Time Series Models

Efficient Probabilistic Forecasts for Counts

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