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I am working on forecasting a financial index, i tried decomposing the time series using :

from matplotlib import pyplot
from statsmodels.tsa.seasonal import seasonal_decompose
result = seasonal_decompose(dataset, model='multiplicative', freq=12)
result.plot()
pyplot.show()

And i got the following result:

decomposition

The results show that the time series is not stationary and it has a unit root (I used ADF and KPSS tests) and that the mean and std are constant in time!

I am wondering if i should use ARIMA or SARIMA since they are adapted to linear trend (my trend is not linear as shown in the image) or move to using LSTM, NN ... ? Or even ARIMA or SARIMA are not adapted to this type of time series?

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Long Short Term Memory (LSTM) is one option given that you have about 9 years of historical data.

You can take a model comparison approach where you split the data and see which algorithm is best at predicting the hold-out data.

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