This study focuses on building an algorithmic investment strategy employing a hybrid approach that combines LSTM and ARIMA models referred to as LSTM-ARIMA. This unique algorithm uses LSTM to produce final predictions but boost results of this RNN by adding the residuals obtained from ARIMA predictions among other inputs. The algorithm is tested across three equity indices (S&P 500, FTSE 100, and CAC 40) using daily frequency data spanning from January, 2000 to August, 2023. The architecture of testing is based on the walk-forward procedure which is applied for hyperparameter tunning phase that uses using Random Search and backtesting the algorithms. The selection of the optimal model is determined based on adequately selected performance metrics combining focused on risk-adjusted return measures. We considered two strategies for each algorithm: Long-Only and Long-Short in order to present situation of two various groups of investors with different investment policy restrictions. For each strategy and equity index, we compute the performance metrics and visualize the equity curve to identify the best strategy with the highest modified information ratio. The findings conclude that the LSTM-ARIMA algorithm outperforms all the other algorithms across all the equity indices what confirms strong potential behind hybrid ML-TS (machine learning - time series) models in searching for the optimal algorithmic investment strategies

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