I had a monthly river temperature (408 values, separated 360 for modeling). Then I deseasonalized and transformed it to a normal time series by a plotting position technique. Now I need to fit an ARMA model to the time series which I got. These plots show the time series which I want to fit a model, ACF and PACF plots.
According to the results I tried fitting ARMA(2,0,0) and ARIMA(1,0,1) using
arima(TS, c(2,0,0)) in R. but both models were very bad fit. For example, AR(2) results are like this (I just plotted a portion of results for a better view)
The only explanation that I can think of is this: the results of my
KPSS test and
ADF test is stationarity for whole data, but If I apply the test on the different portions of data (like last 50 or 70 values) it will result in nonstationarity.
So, Is my conclusion correct? or there is something else wrong with my modeling?
If I am right how can I model a time series which has different form of nonstationarity in different parts of the data?
I attached the excel file of my time series in this link: time series data (csv)