David Maneiro 11 4 19 Project 2 1 General National Income has an upward trend but does not seem to have any seasonality effect 2 Looking that the additive and multiplicative decomposition results we see that the graph is supported by the decompositions as we can see there is an upward trend and the seasonal keeps reverting back to the mean Looking at the seasonal component of the multiplicative decomposition we see that the General National Income has very minor if any seasonality effect in Q1 it is slightly above the trend is Q2 and Q3 it is slightly below and in Q4 it is slightly above Due to the minor effect of these number we do not observe them as significant Looking at the seasonal component of the additive decomposition we see that the General National Income has very minor if any seasonality effect which we already saw in the multiplicative decomposition results in Q1 it is slightly above the trend is Q2 and Q3 it is slightly below and in Q4 it is slightly above In Q1 it higher by 7 billion dollars Q2 lower by 9 36 billion dollars Q3 lower again by 1 50 billion dollars and in Q4 it is higher by 3 85 billion dollars 3 Looking at the ACFs and the box tests for the remainders we see that you can use both additive and multiplicative decomposition for General National Income However when looking at the results of the RSME we see that multiplicative decomposition is the better of the two options data read csv file choose header TRUE library ggplot2 library forecast library tseries library TSA GNI ts data GNI frequency 4 start c 2004 04 autoplot GNI xlab Year ylab GNI General National Income has an upward trend but does not seem to have any seasonality effect deGNI1 decompose GNI type multiplicative deGNI2 decompose GNI type additive plot deGNI1 plot deGNI2 s1 deGNI1 seasonal r1 deGNI1 random s2 deGNI2 seasonal r2 deGNI2 random plot s1 plot r1 plot s2 plot r2 s1 r1 s2 r2 ggAcf s1 ggAcf r1 ggAcf s2 ggAcf r2 Box test s1 Box test r1 Box test s2 Box test r2 r1 r1 3 59 r2 r2 3 59 rmse1 sqrt sum r1 2 59 rmse2 sqrt sum r2 2 59 rmse1 rmse2 for rmse pick the lowest one multiplicative at 1 on trend above 1 above trend below 1 below trend numbers after decimal point show by how much percent up or down additive actual data show actually how higher or lower you are compared to the data