scholarly journals The Combined Poisson INMA(q) Models for Time Series of Counts

2015 ◽  
Vol 2015 ◽  
pp. 1-7 ◽  
Author(s):  
Kaizhi Yu ◽  
Hong Zou
Keyword(s):  
Time Series ◽  
Random Vector ◽  
Method Of Moments ◽  
Moving Average ◽  
Numerical Results ◽  
Statistical Properties ◽  
Average Process ◽  
Moving Average Process ◽  
Time Series Of Counts ◽  
Moment Estimators

A new stationaryqth-order integer-valued moving average process with Poisson innovation is introduced based on decision random vector. Some statistical properties of the process are established. Estimators of the parameters of the process are obtained using the method of moments. Some numerical results of the estimators are presented to assess the performance of moment estimators.

scholarly journals Justification of Wold’s Theorem and the Unbiasedness of a Stable Vector Autoregressive Time Series Model Forecasts

2017 ◽  
Vol 6 (2) ◽  
pp. 1
Author(s):  
Iberedem A. Iwok
Keyword(s):  
Time Series ◽  
Moving Average ◽  
Autoregressive Process ◽  
Time Series Model ◽  
Average Process ◽  
Moving Average Process ◽  
Autoregressive Time Series ◽  
Vector Autoregressive ◽  
Vector Autoregressive Process ◽  
Vector Time Series

In this work, the multivariate analogue to the univariate Wold’s theorem for a purely non-deterministic stable vector time series process was presented and justified using the method of undetermined coefficients. By this method, a finite vector autoregressive process of order  [] was represented as an infinite vector moving average () process which was found to be the same as the Wold’s representation. Thus, obtaining the properties of a  process is equivalent to obtaining the properties of an infinite  process. The proof of the unbiasedness of forecasts followed immediately based on the fact that a stable VAR process can be represented as an infinite VEMA process.

A GAMMA MOVING AVERAGE PROCESS FOR MODELLING DEPENDENCE ACROSS DEVELOPMENT YEARS IN RUN-OFF TRIANGLES

2020 ◽  
pp. 1-22
Author(s):  
Luis E. Nieto-Barajas ◽  
Rodrigo S. Targino
Keyword(s):  
Latent Variables ◽  
Moving Average ◽  
Real Data ◽  
Model Parameters ◽  
Average Process ◽  
Moving Average Process ◽  
Data Set ◽  
Run Off ◽  
Average Form ◽  
Reserve Estimates

ABSTRACT We propose a stochastic model for claims reserving that captures dependence along development years within a single triangle. This dependence is based on a gamma process with a moving average form of order $p \ge 0$ which is achieved through the use of poisson latent variables. We carry out Bayesian inference on model parameters and borrow strength across several triangles, coming from different lines of businesses or companies, through the use of hierarchical priors. We carry out a simulation study as well as a real data analysis. Results show that reserve estimates, for the real data set studied, are more accurate with our gamma dependence model as compared to the benchmark over-dispersed poisson that assumes independence.

scholarly journals Wavelet analysis for modeling suspended sediment discharge

2004 ◽  
Vol 35 (2) ◽  
pp. 165-174 ◽  
Author(s):  
Hafzullah Aksoy ◽  
Tanju Akar ◽  
N. Erdem Ünal
Keyword(s):  
Suspended Sediment ◽  
Moving Average ◽  
Haar Wavelet ◽  
Finite Variance ◽  
Sediment Discharge ◽  
Average Process ◽  
Moving Average Process ◽  
Discharge Time ◽  
Data Set ◽  
Environmental Processes

Wavelets, functions with zero mean and finite variance, have recently been found to be appropriate tools in investigating geophysical, hydrological, meteorological, and environmental processes. In this study, a wavelet-based modeling technique is presented for suspended sediment discharge time series. The model generates synthetic series statistically similar to the observed data. In the model in which the Haar wavelet is used, the available data are decomposed into detail functions. By choosing randomly from among the detail functions, synthetic suspended sediment discharge series are composed. Results are compared with those obtained from a moving-average process fitted to the data set.

Moving average process underlying the holographic–optical–tweezers experiments

2014 ◽  
Vol 53 (10) ◽  
pp. B254 ◽  
Author(s):  
Jakub Ślęzak ◽  
Sławomir Drobczyński ◽  
Karina Weron ◽  
Jan Masajada
Keyword(s):  
Optical Tweezers ◽  
Moving Average ◽  
Average Process ◽  
Moving Average Process ◽  
Holographic Optical Tweezers

ARMA processes have maximal entropy among time series with prescribed autocovariances and impulse responses

1985 ◽  
Vol 17 (04) ◽  
pp. 810-840 ◽  
Author(s):  
Jürgen Franke
Keyword(s):  
Time Series ◽  
Impulse Response ◽  
Moving Average ◽  
Autoregressive Process ◽  
Natural Generalization ◽  
Maximal Entropy ◽  
Autoregressive Moving Average ◽  
Moving Average Process ◽  
Arma Process ◽  
Arma Processes

The maximum-entropy approach to the estimation of the spectral density of a time series has become quite popular during the last decade. It is closely related to the fact that an autoregressive process of order p has maximal entropy among all time series sharing the same autocovariances up to lag p. We give a natural generalization of this result by proving that a mixed autoregressive-moving-average process (ARMA process) of order (p, q) has maximal entropy among all time series sharing the same autocovariances up to lag p and the same impulse response coefficients up to lag q. The latter may be estimated from a finite record of the time series, for example by using a method proposed by Bhansali (1976). By the way, we give a result on the existence of ARMA processes with prescribed autocovariances up to lag p and impulse response coefficients up to lag q.

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