Estimation of the parameters of vector autoregressive moving average (VARMA) time series model with symmetric stable noise

Author(s):  
Aastha M. Sathe ◽  
Raju Chowdhury ◽  
N. S. Upadhye
2020 ◽  
Author(s):  
Jianqing Qiu ◽  
Huimin Wang ◽  
Tao Zhang ◽  
Changhong Yang

Abstract Background: Influenza is an acute respiratory infection caused by an influenza virus, and the primary intervention strategy is seasonal vaccine. Due to various influenza strains and their rapid mutation each year, how to recognize the key population and timing of the vaccination becomes essential. Considering the importance of finding possible spreading directions and effects of influenza between cities for department of influenza prevention, the construction of influenza transmission network becomes meaningful.Methods: 21 cities in Sichuan province were divided into different learning communities according to whether they were adjacent to each other or not. In each community, the first-order conditional dependencies approximation algorithm was performed to learn the possible structure of the time-lagged correlations between different time series vectors of the ILI estimated weekly number, and the vector autoregressive moving average models were performed for learning the lag orders and parameters of the time-lagged correlations between different time series vectors in each community.Results: It detected a number of significant time-lagged correlations between cities in Sichuan province using two models, and the lag was from 1 week to 3 weeks. The parameters indicating the suspected propagation relationship were between -0.90 and 0.75, and the proportion of the negative values in parameters increased with time. Furthermore, the spreading routes learning from two models were almost in accordance with the traffic network of Sichuan province.Conclusions: This study proposed an innovative framework for exploring the potentially stable transmission routes between different regions and measuring specific size of the transmission effect. It could be used for the infectious disease key area confirmation by considering their adjacent areas’ incidence and the transmission relationship.


2021 ◽  
Vol 16 (3) ◽  
pp. 197-210
Author(s):  
Utriweni Mukhaiyar ◽  
Devina Widyanti ◽  
Sandy Vantika

This study aims to determine the impact of COVID-19 cases in Indonesia on the USD/IDR exchange rate using the Transfer Function Model and Vector Autoregressive Moving-Average with Exogenous Regressors (VARMAX) Model. This paper uses daily data on the COVID-19 case in Indonesia, the USD/IDR exchange rate, and the IDX Composite period from 1 March to 29 June 2020. The analysis shows: (1) the higher the increase of the number of COVID-19 cases in Indonesia will significantly weaken the USD/IDR exchange rate, (2) an increase of 1% in the number of COVID-19 cases in Indonesia six days ago will weaken the USD/IDR exchange rate by 0.003%, (3) an increase of 1% in the number of COVID-19 cases in Indonesia seven days ago will weaken the USD/IDR exchange rate by 0.17%, and (4) an increase of 1% in the number of COVID-19 cases in Indonesia eight days ago will weaken the USD/IDR exchange rate by 0.24%.


2017 ◽  
Vol 6 (2) ◽  
pp. 1
Author(s):  
Iberedem A. Iwok

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.


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