The transformation of Z into Z +2 and logarithmic scaling proves to improve the model for ARIMA and LSTM with RMSE < 2%. But this is a matter of close values. Before calculating the true RMSE, we should re-scale to the original values and calculate the correct RMSE.

Now with native values but scaled in order to avoid low numbers and have similar scale of values. Had to add a shift of 2 in order to avoid zero values. ARIMA reaches only 20% RMSE for 7 next step forecast. LSTM reaches 50% RMSE for 15 next steps. For the same next 7 steps LSTM beats the ARIMA with RMSE of 13%. The HYBRID, LSTM + ARIMA gives a mean, that will tend to be in between of them and gives only 18%. A weighted mean RMSE where the weights are the differences of the distance between test values and prediction, might give a better Hybrid, but this Hybrid is not a good approach if one of the predictions is biased and the other one is close to the true. Therefore a weight penalizing the biased forecast might lead to a better approach

Reshape all XARRAYS into PANDAS data frames and normalize and use it for ARIMA and LSTM. ARIMA fails due to normalized data sets with RMSE of 100% and not catching the shape. Normalization is not a good step for ARIMA. LSTM predicts perfectly the shape of time series but since the data were normalized already, the rescaling is incorrect and leads to RMSE of 196%. Next step would be to use unnormalized data for ARIMA and LSTM to be able to rescale it to original values and hence realistic RMSE...

Normalized the time series with MinMaxScaler. For plotting of subplots it takes 50 Minutes, which is way too long, and have to run it on server. ARIMA gave 100% RMSE for non-scaled series. Now with scaling, but there is an issue with indexes for ARIMA....

The 7 variables are now loaded and split into train and test data sets. Subplot the time series with labels and units for a given location and level = 6. Have to run it on MN5

Starting to apply multivariance time series analysis of the PISCES variables. First loading the XARRAYS....

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