Modeling Z-valued time series based on new versions of the Skellam INGARCH model

2021 ◽  
Vol 35 (2) ◽  
Author(s):  
Yan Cui ◽  
Qi Li ◽  
Fukang Zhu
Keyword(s):  
Time Series ◽  
Ingarch Model

Hysteretic Poisson INGARCH model for integer-valued time series

2017 ◽  
Vol 17 (6) ◽  
pp. 401-422 ◽  
Author(s):  
Buu-Chau Truong ◽  
Cathy WS Chen ◽  
Songsak Sriboonchitta
Keyword(s):  
Time Series ◽  
Model Comparison ◽  
Monte Carlo Sampling ◽  
Information Criteria ◽  
Model Parameters ◽  
Modelling Framework ◽  
South Wales ◽  
Proposed Model ◽  
Over Dispersion ◽  
Ingarch Model

This study proposes a new model for integer-valued time series—the hysteretic Poisson integer-valued generalized autoregressive conditionally heteroskedastic (INGARCH) model—which has an integrated hysteresis zone in the switching mechanism of the conditional expectation. Our modelling framework provides a parsimonious representation of the salient features of integer-valued time series, such as discreteness, over-dispersion, asymmetry and structural change. We adopt Bayesian methods with a Markov chain Monte Carlo sampling scheme to estimate model parameters and utilize the Bayesian information criteria for model comparison. We then apply the proposed model to five real time series of criminal incidents recorded by the New South Wales Police Force in Australia. Simulation results and empirical analysis highlight the better performance of hysteresis in modelling the integer-valued time series.

scholarly journals Integer-valued Time Series Model via Generalized Linear Models Technique of Estimation

2018 ◽  
Vol 4 (1) ◽  
pp. 35-43 ◽  
Author(s):  
Rasaki Olawale Olanrewaju
Keyword(s):  
Time Series ◽  
Positive Integer ◽  
Error Term ◽  
Linear Models ◽  
Time Series Data ◽  
Series Data ◽  
Link Function ◽  
Log Linear ◽  
Ingarch Model ◽  
Autoregressive Conditional Heteroscedasticity

The paper authenticated the need for separate positive integer time series model(s). This was done from the standpoint of a proposal for both mixtures of continuous and discrete time series models. Positive integer time series data are time series data subjected to a number of events per constant interval of time that relatedly fits into the analogy of conditional mean and variance which depends on immediate past observations. This includes dependency among observations that can be best described by Generalized Autoregressive Conditional Heteroscedasticity (GARCH) model with Poisson distributed error term due to its positive integer defined range of values. As a result, an integer GARCH model with Poisson distributed error term was formed in this paper and called Integer Generalized Autoregressive Conditional Heteroscedasticity (INGARCH). Iterative Reweighted Least Square (IRLS) parameter estimation technique type of the Generalized Linear Models (GLM) was adopted to estimate parameters of the two spilt models; Linear and Log-linear INGARCH models deduced from the identity link function and logarithmic link function, respectively. This resulted from the log-likelihood function generated from the GLM via the random component that follows a Poisson distribution. A study of monthly successful bids of auction from 2003 to 2015 was carried out. The Probabilistic Integral Transformation (PIT) and scoring rule pinpointed the uniformity of the linear INGARCH than that of the log-linear INGARCH in describing first order autocorrelation, serial dependence and positive conditional effects among covariates based on the immediate past. The linear INGARCH model outperformed the log-linear INGARCH model with (AIC = 10514.47, BIC = 10545.01, QIC = 34128.56) and (AIC = 37588.83, BIC = 37614.28, QIC = 37587.3), respectively.

scholarly journals A New Approach to Integer-Valued Time Series Modeling: The Neyman Type-A INGARCH Model*

2015 ◽  
Vol 55 (2) ◽  
pp. 231-242 ◽  
Author(s):  
Esmeralda Gonçalves ◽  
Nazaré Mendes Lopes ◽  
Filipa Silva
Keyword(s):  
Time Series ◽  
Type A ◽  
Time Series Modeling ◽  
New Approach ◽  
Ingarch Model

The LDE-Type Flare Occurrence (1969-1993)

1994 ◽  
Vol 144 ◽  
pp. 279-282
Author(s):  
A. Antalová
Keyword(s):  
Time Series ◽  
Fourier Analysis ◽  
Sunspot Cycle ◽  
List Type ◽  
Type Number ◽  
Solar Cycles ◽  
Type Iv ◽  
Long Duration ◽  
Cycle Maximum ◽  
Flare Index

AbstractThe occurrence of LDE-type flares in the last three cycles has been investigated. The Fourier analysis spectrum was calculated for the time series of the LDE-type flare occurrence during the 20-th, the 21-st and the rising part of the 22-nd cycle. LDE-type flares (Long Duration Events in SXR) are associated with the interplanetary protons (SEP and STIP as well), energized coronal archs and radio type IV emission. Generally, in all the cycles considered, LDE-type flares mainly originated during a 6-year interval of the respective cycle (2 years before and 4 years after the sunspot cycle maximum). The following significant periodicities were found:• in the 20-th cycle: 1.4, 2.1, 2.9, 4.0, 10.7 and 54.2 of month,• in the 21-st cycle: 1.2, 1.6, 2.8, 4.9, 7.8 and 44.5 of month,• in the 22-nd cycle, till March 1992: 1.4, 1.8, 2.4, 7.2, 8.7, 11.8 and 29.1 of month,• in all interval (1969-1992):a)the longer periodicities: 232.1, 121.1 (the dominant at 10.1 of year), 80.7, 61.9 and 25.6 of month,b)the shorter periodicities: 4.7, 5.0, 6.8, 7.9, 9.1, 15.8 and 20.4 of month.Fourier analysis of the LDE-type flare index (FI) yields significant peaks at 2.3 - 2.9 months and 4.2 - 4.9 months. These short periodicities correspond remarkably in the all three last solar cycles. The larger periodicities are different in respective cycles.

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