Innovations algorithm for periodically stationary time series

Anderson, Paul L.; Meerschaert, Mark M.; Vecchia, Aldo V.

doi:10.1016/s0304-4149(99)00027-7

Cited by 23 publications

(75 citation statements)

References 21 publications

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“…Estimation of time series regression models are discussed extensively in the literature for a range of models. For example Kedem et al (2002) discuss the estimation for a class of generalized linear time series models and Tesfaye et al (2006) utilizes the "innovation" algorithm developed in Anderson et al (1999) to apply PARMA models to river flow modeling in Fraser River in British Columbia. Since none of these methods are directly applicable to our method in which both the autoregressive coefficients and the volatility vary with time (in a non-linear fashion), below we discuss a simple iterative estimation method which works very efficiently both in simulations and our data analysis.…”

Section: Estimationmentioning

confidence: 99%

Non-linear time-varying stochastic models for agroclimate risk assessment

Hosseini¹,

Takemura

Hosseini

2014

Environ Ecol Stat

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This work develops a model for minimum temperature in order to assess the weather related risk in agriculture industry. Non-linear autoregressive models with time-varying coefficients and volatility with various seasonal components and lags are compared in an appropriate model-selection algorithm using AIC. The optimal model is a time-varying autoregressive model which includes non-linear and seasonallyvarying autoregressive terms as well as time-varying volatility. These models are then used to simulate future weather from which the probabilities of appropriate complex hazard events are estimated.

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Section: Estimationmentioning

confidence: 99%

Non-linear time-varying stochastic models for agroclimate risk assessment

Hosseini¹,

Takemura

Hosseini

2014

Environ Ecol Stat

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“…In practice, a model selection criterion such as AIC or BIC is used to choose the appropriate order of the model (Franses, 1996). Estimation is achieved by computing the exact Gaussian likelihood of PARMA models (Anderson et al, 1999;Lund and Basawa, 2000;Basawa and Lund, 2001). …”

Section: Periodic Arma Modelsmentioning

confidence: 99%

Modelling time series with season‐dependent autocorrelation structure

Tripodis

Penzer²

2009

Journal of Forecasting

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Time series with season-dependent autocorrelation structure are commonly modelled using periodic autoregressive moving average (PARMA) processes. In most applications, the moving average terms are excluded for ease of estimation. We propose a new class of periodic unobserved component models (PUCM). Parameter estimates for PUCM are readily interpreted; the estimated coefficients correspond to variances of the measurement noise and of the error terms in unobserved components. We show that PUCM have correlation structure equivalent to that of a periodic integrated moving average (PIMA) process. Results from practical applications indicate that our models provide a natural framework for series with periodic autocorrelation structure both in terms of interpretability and forecasting accuracy. Copyright © 2008 John Wiley & Sons, Ltd.

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“…. , −1, then for a causal PARMA (p, q) process the covariance matrix k,i is non-singular for every k 1 and each i. Anderson et al [5] show that if EX t = 0 and k,i is nonsingular for each k 1, then the one-step predictorsX i+k , k 0, and their mean-square errors v k,i , k 1, are given by…”

Section: The Innovations Algorithmmentioning

confidence: 99%

“…An important class of stochastic models for describing periodically stationary time series are the periodic ARMA models, in which the model parameters are allowed to vary with the season. Periodic ARMA models are developed by many authors including [1,2,[4][5][6][7]20,[22][23][24]26,28,30,31,[33][34][35][36][37][38][39][40][41].…”

Section: Introductionmentioning

confidence: 99%

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Innovations algorithm asymptotics for periodically stationary time series with heavy tails

Anderson

Kavalieris

Meerschaert

2008

Journal of Multivariate Analysis

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The innovations algorithm can be used to obtain parameter estimates for periodically stationary time series models. In this paper we compute the asymptotic distribution for these estimates in the case where the underlying noise sequence has infinite fourth moment but finite second moment. In this case, the sample covariances on which the innovations algorithm are based are known to be asymptotically stable. The asymptotic results developed here are useful to determine which model parameters are significant. In the process, we also compute the asymptotic distributions of least squares estimates of parameters in an autoregressive model.

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Innovations algorithm for periodically stationary time series

Cited by 23 publications

References 21 publications

Non-linear time-varying stochastic models for agroclimate risk assessment

Non-linear time-varying stochastic models for agroclimate risk assessment

Modelling time series with season‐dependent autocorrelation structure

Innovations algorithm asymptotics for periodically stationary time series with heavy tails

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