POISSON MODELS WITH DYNAMIC RANDOM EFFECTS AND NONNEGATIVE CREDIBILITIES PER PERIOD

2020 ◽  
Vol 50 (2) ◽  
pp. 585-618 ◽  
Author(s):  
Jean Pinquet
Keyword(s):  
Time Series ◽  
Random Effects ◽  
Semiparametric Models ◽  
Second Order ◽  
Risk Exposure ◽  
Autocovariance Function ◽  
Poisson Models ◽  
Poisson Distributions ◽  
Short Memory ◽  
Time Invariant

AbstractThis paper provides a toolbox for the credibility analysis of frequency risks, with allowance for the seniority of claims and of risk exposure. We use Poisson models with dynamic and second-order stationary random effects that ensure nonnegative credibilities per period. We specify classes of autocovariance functions that are compatible with positive random effects and that entail nonnegative credibilities regardless of the risk exposure. Random effects with nonnegative generalized partial autocorrelations are shown to imply nonnegative credibilities. This holds for ARFIMA(0, d, 0) models. The AR(p) time series that ensure nonnegative credibilities are specified from their precision matrices. The compatibility of these semiparametric models with log-Gaussian random effects is verified. Gaussian sequences with ARFIMA(0, d, 0) specifications, which are then exponentiated entrywise, provide positive random effects that also imply nonnegative credibilities. Dynamic random effects applied to Poisson distributions are retained as products of two uncorrelated and positive components: the first is time-invariant, whereas the autocovariance function of the second vanishes at infinity and ensures nonnegative credibilities. The limit credibility is related to the three levels for the length of the memory in the random effects. The limit credibility is less than one in the short memory case, and a formula is provided.

HIGHER ORDER COMPLEXITY OF TIME SERIES

2004 ◽  
Vol 14 (08) ◽  
pp. 2979-2990 ◽  
Author(s):  
FANJI GU ◽  
ENHUA SHEN ◽  
XIN MENG ◽  
YANG CAO ◽  
ZHIJIE CAI
Keyword(s):  
Time Series ◽  
Mental Arithmetic ◽  
Higher Order ◽  
Second Order ◽  
Stationary Time Series ◽  
Eeg Signals ◽  
Eyes Closed ◽  
Logistic Mapping ◽  
Original Time ◽  
Different Order

A concept of higher order complexity is proposed in this letter. If a randomness-finding complexity [Rapp & Schmah, 2000] is taken as the complexity measure, the first-order complexity is suggested to be a measure of randomness of the original time series, while the second-order complexity is a measure of its degree of nonstationarity. A different order is associated with each different aspect of complexity. Using logistic mapping repeatedly, some quasi-stationary time series were constructed, the nonstationarity degree of which could be expected theoretically. The estimation of the second-order complexity of these time series shows that the second-order complexities do reflect the degree of nonstationarity and thus can be considered as its indicator. It is also shown that the second-order complexities of the EEG signals from subjects doing mental arithmetic are significantly higher than those from subjects in deep sleep or resting with eyes closed.

Estimation of second-order properties from jittered time series

1996 ◽  
Vol 48 (1) ◽  
pp. 29-48 ◽  
Author(s):  
Peter J. Thomson ◽  
Peter M. Robinson
Keyword(s):  
Time Series ◽  
Second Order

scholarly journals Mixed Models as a Tool for Comparing Groups of Time Series in Plant Sciences

Plants ◽  
2021 ◽  
Vol 10 (2) ◽  
pp. 362
Author(s):  
Ioannis Spyroglou ◽  
Jan Skalák ◽  
Veronika Balakhonova ◽  
Zuzana Benedikty ◽  
Alexandros G. Rigas ◽  
...  
Keyword(s):  
Time Series ◽  
Random Effects ◽  
Mixed Models ◽  
Mixed Model ◽  
Repeated Measurements ◽  
Time Series Models ◽  
Additional Time ◽  
Biotic Stresses ◽  
Viable Solution ◽  
Long Time

Plants adapt to continual changes in environmental conditions throughout their life spans. High-throughput phenotyping methods have been developed to noninvasively monitor the physiological responses to abiotic/biotic stresses on a scale spanning a long time, covering most of the vegetative and reproductive stages. However, some of the physiological events comprise almost immediate and very fast responses towards the changing environment which might be overlooked in long-term observations. Additionally, there are certain technical difficulties and restrictions in analyzing phenotyping data, especially when dealing with repeated measurements. In this study, a method for comparing means at different time points using generalized linear mixed models combined with classical time series models is presented. As an example, we use multiple chlorophyll time series measurements from different genotypes. The use of additional time series models as random effects is essential as the residuals of the initial mixed model may contain autocorrelations that bias the result. The nature of mixed models offers a viable solution as these can incorporate time series models for residuals as random effects. The results from analyzing chlorophyll content time series show that the autocorrelation is successfully eliminated from the residuals and incorporated into the final model. This allows the use of statistical inference.

scholarly journals Tuning of a time-delayed controller for a general class of second-order linear time invariant systems with dead-time

2019 ◽  
Vol 13 (3) ◽  
pp. 451-457 ◽  
Author(s):  
Raul Villafuerte-Segura ◽  
Francisco Medina-Dorantes ◽  
Leopoldo Vite-Hernández ◽  
Baltazar Aguirre-Hernández
Keyword(s):  
General Class ◽  
Dead Time ◽  
Linear Time ◽  
Second Order ◽  
Order Linear ◽  
Linear Time Invariant ◽  
Linear Time Invariant Systems ◽  
Time Invariant

scholarly journals Characterizing sand ripples at equilibrium phases

2013 ◽  
Vol 61 (4) ◽  
pp. 293-298 ◽  
Author(s):  
Jie Qin ◽  
Deyu Zhong ◽  
Guangqian Wang
Keyword(s):  
Time Series ◽  
Random Fields ◽  
Morphological Characteristics ◽  
Structure Functions ◽  
Second Order ◽  
Order Structure ◽  
Two Dimensional ◽  
Sand Ripples ◽  
Digital Elevation ◽  
Equilibrium Phases

Abstract Morphological characteristics of ripples are analyzed considering bed surfaces as two dimensional random fields of bed elevations. Two equilibrium phases are analyzed with respect to successive development of ripples based on digital elevation models. The key findings relate to the shape of the two dimensional second-order structure functions and multiscaling behavior revealed by higher-order structure functions. Our results suggest that (1) the two dimensional second-order structure functions can be used to differentiate the two equilibrium phases of ripples; and (2) in contrast to the elevational time series of ripples that exhibit significant multiscaling behavior, the DEMs of ripples at both equilibrium phases do not exhibit multiscaling behavior.

scholarly journals Assessing the benefit of snow data assimilation for runoff modeling in Alpine catchments

2016 ◽  
Vol 20 (9) ◽  
pp. 3895-3905 ◽  
Author(s):  
Nena Griessinger ◽  
Jan Seibert ◽  
Jan Magnusson ◽  
Tobias Jonas
Keyword(s):  
Time Series ◽  
Data Assimilation ◽  
Hydrological Model ◽  
Temperature Index ◽  
Degree Day ◽  
Index Approach ◽  
Snow Model ◽  
Alpine Catchments ◽  
Time Invariant ◽  
Snowmelt Time

Abstract. In Alpine catchments, snowmelt is often a major contribution to runoff. Therefore, modeling snow processes is important when concerned with flood or drought forecasting, reservoir operation and inland waterway management. In this study, we address the question of how sensitive hydrological models are to the representation of snow cover dynamics and whether the performance of a hydrological model can be enhanced by integrating data from a dedicated external snow monitoring system. As a framework for our tests we have used the hydrological model HBV (Hydrologiska Byråns Vattenbalansavdelning) in the version HBV-light, which has been applied in many hydrological studies and is also in use for operational purposes. While HBV originally follows a temperature-index approach with time-invariant calibrated degree-day factors to represent snowmelt, in this study the HBV model was modified to use snowmelt time series from an external and spatially distributed snow model as model input. The external snow model integrates three-dimensional sequential assimilation of snow monitoring data with a snowmelt model, which is also based on the temperature-index approach but uses a time-variant degree-day factor. The following three variations of this external snow model were applied: (a) the full model with assimilation of observational snow data from a dense monitoring network, (b) the same snow model but with data assimilation switched off and (c) a downgraded version of the same snow model representing snowmelt with a time-invariant degree-day factor. Model runs were conducted for 20 catchments at different elevations within Switzerland for 15 years. Our results show that at low and mid-elevations the performance of the runoff simulations did not vary considerably with the snow model version chosen. At higher elevations, however, best performance in terms of simulated runoff was obtained when using the snowmelt time series from the snow model, which utilized data assimilation. This was especially true for snow-rich years. These findings suggest that with increasing elevation and the correspondingly increased contribution of snowmelt to runoff, the accurate estimation of snow water equivalent (SWE) and snowmelt rates has gained importance.

A note on the asymptotic eigenvalues and eigenvectors of the dispersion matrix of a second-order Stationary Process on a d-dimensional Lattice

1986 ◽  
Vol 23 (02) ◽  
pp. 529-535 ◽  
Author(s):  
R. J. Martin
Keyword(s):  
Time Series ◽  
Stationary Process ◽  
Second Order ◽  
Stationary Time Series ◽  
Stationary Processes ◽  
Dispersion Matrix ◽  
Eigenvalues And Eigenvectors ◽  
Dimensional Lattice ◽  
Stationary Time

A sufficiently large finite second-order stationary time series process on a line has approximately the same eigenvalues and eigenvectors of its dispersion matrix as its counterpart on a circle. It is shown here that this result can be extended to second-order stationary processes on a d-dimensional lattice.

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