I have a time-series data (Fig 1) that clearly look non-stationary on visual analysis. There is a clear trend and seasonality in the time series as shown in the Final figure below. But the ADF test and ACF/PACF show a Stationary time series.
My understanding and interpretation of the results are that over the course of the series, it maintains a mean and variance and hence statistical properties of a Stationary time series !!
Also, I read that the non-stationarity in time-series causes difficulty in prediction. But the LSTM model that I have created with this series (which look non-stationary visually, but comes out to be Stationary statistically), predicts pretty accurately. Is it because the LSTM captures the non-linearity pretty well as compared to the ARIMA models?
The ADF test: it was clearly Stationary with p-value of 3.15e-15 and ADF stats much smaller than 1% critical value of -3.432.
ACF and PACF charts: The chart shows the stationarity as well! ACF chart touched Zero, not instantaneously, but relatively quickly! (AM I STUDYING THE ACF CORRECTLY)?