Renewal Sequences With Periodic Dynamics

Fralix, Brian; Livsey, James; Lund, Robert

doi:10.1017/s0269964811000209

Cited by 5 publications

(8 citation statements)

References 14 publications

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“…To calculate

\overset{π}{true} (0)

, one may use

\overset{π}{true} (0) MathClass-rel' MathClass-rel= bold-italic 1 MathClass-rel' ((), bold-italicI MathClass-bin- {MathClass-op\prod}_{ν MathClass-rel= 1}^{T} scriptP (ν) MathClass-bin+ bold-italicJ) MathClass-bin- 1

where 1 is a length‐2 vector of 1 s, I is the 2 × 2 identity matrix, and J is a 2 × 2 matrix of 1 s. For more on stationary distributions of periodic Markov chains, see Fralix et al . () (2012) has not been included in the Reference List, please supply full publication details. and the references therein.…”

Section: Methodsmentioning

confidence: 93%

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Changepoint detection in daily precipitation data

2012

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This paper introduces a method to identify an undocumented changepoint time in a daily precipitation series. A two‐state Markov chain is used to induce dependence in the precipitation amounts; our dynamics allow for seasonality in the daily observations, a structure inherent to many nonequatorial region series. No current precipitation changepoint techniques exist that consider day‐to‐day dependencies, the zero support set aspect (the fact that most measurements are zero), and the periodic dynamics of the problem. The test statistic is constructed by applying cumulative sum methods to a strategically devised set of one‐step‐ahead prediction residuals. The methods are robust to distributional assumptions, requiring only seasonal mean and transition probability estimators. Simulations are presented that demonstrate the efficacy of the methods; application to two daily precipitation series is made. Copyright © 2012 John Wiley & Sons, Ltd.

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“…To calculate

\overset{π}{true} (0)

, one may use

\overset{π}{true} (0) MathClass-rel' MathClass-rel= bold-italic 1 MathClass-rel' ((), bold-italicI MathClass-bin- {MathClass-op\prod}_{ν MathClass-rel= 1}^{T} scriptP (ν) MathClass-bin+ bold-italicJ) MathClass-bin- 1

Section: Methodsmentioning

confidence: 93%

“…where 1 is a length-2 vector of 1 s, I is the 2 2 identity matrix, and J is a 2 2 matrix of 1 s. For more on stationary distributions of periodic Markov chains, see Fralix et al (2012) and the references therein.…”

Section: One-step-ahead Prediction Residualsmentioning

confidence: 99%

Changepoint detection in daily precipitation data

2012

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“…One way simply allows for seasonal covariates via (40). Seasonality in the underlying Bernoulli sequences is also possible and will yield count series with seasonally varying autocorrelations; this avenue was pursued in Fralix, Livsey, and Lund [7].…”

Section: Covariatesmentioning

confidence: 99%

Superpositioned Stationary Count Time Series

Jia

Lund

Livsey

2019

Prob. Eng. Inf. Sci.

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This paper probabilistically explores a class of stationary count time series models built by superpositioning (or otherwise combining) independent copies of a binary stationary sequence of zeroes and ones. Superpositioning methods have proven useful in devising stationary count time series having prespecified marginal distributions. Here, basic properties of this model class are established and the idea is further developed. Specifically, stationary series with binomial, Poisson, negative binomial, discrete uniform, and multinomial marginal distributions are constructed; other marginal distributions are possible. Our primary goal is to derive the autocovariance function of the resulting series.

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“…A different method for constructing seasonal count series uses a periodic renewal point processes as in Fralix et al (2012) and Livsey et al (2018). Here, a zero-one binary sequence {B t } ∞ t =1 is constructed to be periodically stationary and {B 1,t }, {B 2,t }, .…”

mentioning

confidence: 99%

“…Then it is easy to see that X dT +ν is Poisson distributed with mean λ ν P (B ν = 1). Fralix et al (2012), Lund and Livsey (2016), and Livsey et al (2018) show how to produce the classical count marginal distributions (Poisson, binomial, and negative binomial) with this setup and consider {B t } processes constructed by clipping Gaussian processes.…”

mentioning

confidence: 99%

Seasonal Count Time Series

Kong¹,

Lund²

2021

Preprint

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Funding informationThe authors thank NSF support from Grant DMS 21-13592.Count time series are widely encountered in practice. As with continuous valued data, many count series have seasonal properties. This paper uses a recent advance in stationary count time series to develop a general seasonal count time series modeling paradigm. The model permits any marginal distribution for the series and the most flexible autocorrelations possible, including those with negative dependence. Likelihood methods of inference can be conducted and covariates can be easily accommodated. The paper first develops the modeling methods, which entail a discrete transformation of a Gaussian process having seasonal dynamics. Properties of this model class are then established and particle filtering likelihood methods of parameter estimation are developed. A simulation study demonstrating the efficacy of the methods is presented and an application to the number of rainy days in successive weeks in Seattle, Washington is given.

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Renewal Sequences With Periodic Dynamics

Cited by 5 publications

References 14 publications

Changepoint detection in daily precipitation data

Changepoint detection in daily precipitation data

Superpositioned Stationary Count Time Series

Seasonal Count Time Series

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