The forecasting of stock prices dynamics is a challenging task since these kinds of financial datasets are characterized by irregular fluctuations, nonlinear patterns, and high uncertainty changes. Deep neural network models, particularly the LSTM (Long Short Term Memory) algorithm, have been increasingly used by researchers and practitioners to analyze, trade, and predict financial time series, defining a new essential tool in several sectors' decision-making processes. The primary purpose of this paper focuses on a multivariate forecast of the U.S. stock index S&P500, using Nasdaq, Dow Jones, and U.S. treasury bills for three months yields of the secondary market series, with daily and weekly data, between January 2018 and July 2021. With the support of a hybrid windowed VECM (Vector Error Correction Model) trend corrected by an LSTM recurrent neural network, we consistently obtain low MAPE forecast errors (around 4%), even including the COVID-19 crises. In addition, nonlinear Granger causality, based on transfer entropy, was tested between the periods with strong intervention by the Federal Bank, concluding that yields variation Granger causes the stock indices returns. In contrast, this causal relationship outside these periods was inverted, with the indices' returns causing yields variation.

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Deep learning,stock markets,VECM,forecasting