scholarly journals One Dimensional Discrete Scan Statistics for Dependent Models and Some Related Problems

Mathematics ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 576
Author(s):  
Alexandru Amarioarei ◽  
Cristian Preda
Keyword(s):  
Moving Average ◽  
Stationary Sequence ◽  
Scan Statistics ◽  
Average Process ◽  
Moving Average Process ◽  
Scan Statistic ◽  
One Dimensional ◽  
The One ◽  
Block Factor ◽  
Dependence Models

The one dimensional discrete scan statistic is considered over sequences of random variables generated by block factor dependence models. Viewed as a maximum of an 1-dependent stationary sequence, the scan statistics distribution is approximated with accuracy and sharp bounds are provided. The longest increasing run statistics is related to the scan statistics and its distribution is studied. The moving average process is a particular case of block factor and the distribution of the associated scan statistics is approximated. Numerical results are presented.

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

scholarly journals Stochastic Interest Rates and Autoregressive Integrated Moving Average Processes

1989 ◽  
Vol 19 (S1) ◽  
pp. 43-50 ◽  
Author(s):  
Jan Dhaene
Keyword(s):  
Interest Rates ◽  
Moving Average ◽  
Practical Method ◽  
Average Process ◽  
Moving Average Process ◽  
Stochastic Interest Rates ◽  
Autoregressive Integrated Moving Average ◽  
Stochastic Interest ◽  
Moving Average Processes

AbstractA practical method is developed for computing moments of insurance functions when interest rates are assumed to follow an autoregressive integrated moving average process.

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.

Sign in / Sign up

Export Citation Format

Share Document