First‐order rounded integer‐valued autoregressive (RINAR(1)) process

Kachour, Maher; Yao, Jianfeng

doi:10.1111/j.1467-9892.2009.00620.x

Cited by 52 publications

(42 citation statements)

References 19 publications

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“…As for the proof of the first conclusion, we follow the basic strategy of Kachour (2009) given in the proof of his Proposition 1. However, our assumptions posed for Theorem 1 are much weaker than those in Kachour (2009), and hence the proof needs more details. For any k 2 Z þ and 8 x 2 R p , we define…”

Section: Proof Of Theoremmentioning

confidence: 99%

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Analysis of accumulated rounding errors in autoregressive processes

Li¹,

Bai²

2011

Journal of Time Series Analysis

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In considering the rounding impact of an autoregressive (AR) process, there are two different models available to be considered. The first assumes that the dynamic system follows an underlying AR model and only the observations are rounded up to a certain precision. The second assumes that the updated observation is a rounded version of an autoregression on previous rounded observations. This article considers the second model and examines behaviour of rounding impacts to the statistical inferences. The conditional maximum-likelihood estimates for the model are proposed and their asymptotic properties are established, including strong consistency and asymptotic normality. Furthermore, both the classical AR model and the ordinary rounded AR model are no longer reliable when dealing with accumulated rounding errors. The three models are also applied to fit the Ocean Wave data. It turns out that the estimates under distinct models are significantly different. Based on our findings, we strongly recommend that models for dealing with rounded data should be in accordance with the actions of rounding errors.

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Section: Proof Of Theoremmentioning

confidence: 99%

“…Recently, a similar model was introduced by Kachour and Yao (2009) as where [·] is the rounding operator to the nearest integer, and { ɛ t } is a sequence of centered integer‐valued i.i.d. random variables.…”

Section: Introductionmentioning

confidence: 99%

Analysis of accumulated rounding errors in autoregressive processes

Li¹,

Bai²

2011

Journal of Time Series Analysis

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“…For classification it is common to threshold Gaussian process regression (Chu & Ghahramani, 2005;Ghosal & Roy, 2006). Kachour & Yao (2009) rounded a real discrete autoregressive process to induce an integervalued time series. Canale & Dunson (2011) used rounding of continuous kernel mixture models to induce nonparametric models for count distributions.…”

Section: Introductionmentioning

confidence: 99%

Nonparametric Bayes modelling of count processes

Canale¹,

Dunson²

2013

Biometrika

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SUMMARY 10Data on count processes arise in a variety of applications, including longitudinal, spatial and imaging studies measuring count responses. The literature on statistical models for dependent count data is dominated by models built from hierarchical Poisson components. The Poisson assumption is not warranted in many applications, and hierarchical Poisson models make restrictive assumptions about over-dispersion in marginal distributions. This article proposes a class of 15 nonparametric Bayes count process models, which are constructed through rounding real-valued underlying processes. The proposed class of models accommodates applications in which one observes separate count-valued functional data for each subject under study. Theoretical results on large support and posterior consistency are established, and computational algorithms are developed using Markov chain Monte Carlo. The methods are evaluated via simulation studies and 20 illustrated through application to longitudinal tumor counts and asthma inhaler usage.

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“…Moreover, somehow Markov Chain includes autocorrelation function (ACF), where the next observation depends only on the current observation. There is one alternative approach named integer-valued autoregressive model (INAR) introduced by McKenzie, Alzaid and Al-osh [16], which may improve our method, because we find the significant ACF at lag 1, 2, and 3 while applying global default counts from 1920-2000.…”

Section: Further Workmentioning

confidence: 99%

Modeling and Forecasting Corporate Default Counts Using Hidden Markov Model

Lü¹,

Cheng²

2015

JOEBM

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Abstract-In this paper, a Hidden Markov Model is employed to fit global, U.S. and European annual corporate default counts. The Expectation-Maximization algorithm is applied to calibrate all parameters while the standard errors of the estimated parameters are conducted by Monte Carlo method. Parametric bootstraps are used to compute the nonlinear forecasts. The empirical results show that the Hidden Markov model is useful in distinguishing the periods of expansion from the periods of recession (relative to the points identified by the NBER). Moreover, it obtains relatively satisfactory forecasts especially in capturing the state switching while incorporating more original observations. IndexTerms-Corporate default counts, expectation-maximization algorithm, hidden Markov model, parametric bootstrap. I. INTRODUCTIONThe issue regarding estimating potential risk levels and forecasting default events of financial assets has increasingly became the interest of many financial, economic, and mathematical researchers in contemporary society. Previously, due to the achievement of Moody [1], the Binomial Expansion Technique (BET) was created to estimate the expected loss of collateralized bond and loan obligations (CBOs and CLOs). However, it is ideal that there exists a pure binomial distribution with independent defaults. With the introduction of diversity score which is used to distinguish a smaller portfolio of independent and homogenous financial assets, it is easier to assume that all these financial assets (bonds and loans) have the same default probability and default independently, resulting in the binominal distribution regarding the quantity of observed default events in single time stage. More importantly, as mentioned by Düllmann [2], some shortages of BET method can be optimized to some extent by the model created by Davis and Lo [3]. In particular, it was related to infectious defaults which increase the default risk of other financial assets. There are two types of risk (normal risk and enhanced risk, respectively), and the latter risk level is enhanced by multiplying infectious factor k. In this case, the similar approach named Hidden Markov Model will be used to detect risk periods in the economy, and related parameters are estimated by Expectation-Maximization algorithm (EM algorithm). More importantly, what this paper pays more attention to concerns corporate default counts forecast, which is different from emphasizing on estimation process and detection of expansion and recession periods in previous researches. The forecast process is achieved by the parametric bootstrap approach according to Tsay [4], which is used to perform the nonlinear forecasts.The content of this paper is divided into six aspects. Detailed methods or approaches utilized in this article will be included and explained in Section II and the simulation part Section III is to test the effectiveness of parameter estimation. Then imperial analysis in Section IV incorporates some small related aspects, data introduction, for example. S...

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First‐order rounded integer‐valued autoregressive (RINAR(1)) process

Cited by 52 publications

References 19 publications

Analysis of accumulated rounding errors in autoregressive processes

Analysis of accumulated rounding errors in autoregressive processes

Nonparametric Bayes modelling of count processes

Modeling and Forecasting Corporate Default Counts Using Hidden Markov Model

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