The Estimators of Vector Autoregressive Moving Avarege Model VARMA of Lower Order: VARMA (0,1), ARMA (1,0), VARMA (1,1), VARMA (1,2), VARMA (2,1), VARMA (2,2) with Forecasting

Abstract This research includes analyzing the relationship between two financial time series, which is a series of global monthly Silver price in dollar and global monthly gold price in dollar, a Vector Autoregressive Moving Avarege VARMA Model was used to analysis this relationship, for the period from January 2016 to December 2019, it is 48 monthly value, where the data has been transferred to get the Stationarity, Diekey Fuller test for the Stationarity was conducted, lower order VARMA were estimated, the best order for The model was determined through a standard Akaike information AIC, Akaike information corrected AICC, Hannan-Quinn criterion HQC, Schwarz Bayesian criterion SBC, Final prediction error criterion FPE, It turns out that the best model is VARMA(0,1), according to all standards, Some tests were conducted such as Portmanteau test, Jarque - Bera test, Autoregressive Conditional Heteroscdastic ARCH test to residuals for the selected model, with forecasting for the VARMA(0,1) model for the period from Jan 2020 to Jan 2021, It is 12 monthly value, It turns out that there is an increase in volatility for the two price forecasting series with increase in forecasting period. The simulation has been applied using three samples sizes, It turns out that the model is appropriate when the sample size (50), the result has been computed through the SAS. Program.