I have 77 observations in my time series data which I obtained from the tsdl library in R. I have also reduced the time window. The data is quarterly average earnings.
library(tsdl) data<-tsdl[] data2<-window(data,end=c(1975,1)) earn<-data2[,3]
I have differenced the data twice and taken a power transformation which lambda equal to -0.03. After differencing, the Dickey-Fuller test has a test statistic of -6.61 and p-value = 0.01.
lam<-BoxCox.lambda(earn) trans.earn<-BoxCox(earn, lambda = lam) nsdiffs(earn) ndiffs(earn) trans<-diff(trans.earn, lag=4, differences = 1) trans<-diff(trans, differences = 1)
I now need to fit AR, MA, ARMA, ARIMA and SARIMA models. Here are the ACF and PACF:
There is a significant spike at lag 4 in the ACF and then at lag 4,6 and 116 in the PACF. I am new to time series and have been struggling with these plots for a while. What do these plots tell me? Is there still some seasonality in my data? What would the p and q be for AR(p) and MA(q) models?
The Ljung-Box Test statistic is 1.14 and has a p-value of 0.29, does this suggest that there is no dependence left in my data? I cannot fit ARMA models? The auto.arima suggest the following model: ARIMA(0,1,1)(0,1,1)