Now applying simple LSTM on PISCES INTDIAC data set. Next to use the Multivariate with Z, A, B, C, D, E, F PISCES variables from the excel table talked with Raffa

Using the previous methods to apply to pisces variables. First only for one variable INTDIAC, and then adding other variables for a multivariate analysis

Hybrid model, a simple mean of Statistical ARIMA (9.4%) and Sequential ML model LSTM (6.4%), gives a better result with RMSE 5.9%

By defining the autoregression of Z(t) = Y(t) as predictand and Z(t-1)=Y(t-1),A(t),B(t) as predictors to the synthetic data set to apply ARIMA and LSTM models. The RMSE is in the order of 5% ARIMA and 4% LSTM. With HYBRID model, simple averaging the statistical and NN ML models. Next will be uncertainty of forecast, XGBoost, PROPHET, ForrestClassifier Hybrid weighted average, majority voting model ensemble and runnig on MN5 with 9 Billion parameters

By defining the autoregression of Z(t) = Z(t-1) + A(t) + B(t) to the synthetic data set to apply ARIMA and LSTM models. The RMSE is in the order of 8% with HYBRID model, simple mean of statistical and NN ML model, gives a better prediction 3%. Next will be uncertainty of forecast, XGBoost, weighted average, majority voting model ensemble. Hyperparameters and process it on MN5

Adding some noise to the determenistic series. Including the ARIMA search for RMSE min function to evaluate the best  P D Q. Got the Integrated ARIMA(0,2,0) with RMSE of 6% which indicates an I(2) or Differentiation  Function of order 2. Doing a manual MinMaxScaling to rescale the values of LTSM, since the RMSE of normalized values are higher in comparison to the original values, with RMSE of 9% for simple LSTM.

Multivariate timeseries analysis with ARIMA and LSTM on correlated series Z(t) = Y(t) + A(t) + B(t). Next Y(t+1) = Y(t) + A(t+1) + B(t+1)

Using the Weatherbench CNN from ECMWF course Colab that has been applied on ERA5 Geopotential height for PISCES variables and checking if it works

Testing multivariate LSTM and multivariate ARIMA on synthetic time series. The approach works. Next step would be with real PISCES data set. It is still unclear how to weights for linear lag correlation model should be applied. Using just multivariate ARIMA and LSTM or lagged multivariate, where the maximum cross correlation should be the constrain on time lagged external factors?

The Sequential model with LSTM 64 cell delivers a loss of 0.04 but an accuracy on prediction of 60% with RMSE 40%

Trying to figure out what Xtrain ytrain Xtest ytest are....essentially matrix constructions for the Sequential model training

Some minor changes: Convergence criterion for Minima. Take the last 20 steps, exluding the 1st minima at (0,0,0)

Adding prediction and plots for test data set. Playing with parameter settings putting them as constants.

Experimenting with RNNs from Auriel Geron's book examples - Introduction into ML with Scikit-Learn, Keras, Tensorflow - Chapter 15 Working with Sequencec by using RNNs and CNNs