The study is aimed at determining the oscillators of crisis manifestations when the Russian economy tries to make transition to the path for accelerating technological development and forming an innovative economy. Short-term cycles were determined in the development of the Russian economy from 1995 to the first half of 2020 through the Fourier spectral analysis. Using the Granger test, causal relationships between the leading indicators of the economic crisis and the real GDP index in Russia were identified and substantiated. They reflect the influence of the key rate dynamics on the volume of lending, savings, investments, the yield on securities and the exchange rate; volumes of bank loans per the share of non-performing and bad loans and innovative development of the economy. Based on the constructed neural models of the oscillator influence on the level of real GDP in Russia, it was determined that the rapid growth of bank and mortgage lending, the devaluation of the ruble, a decreased volume of gross foreign investment and the level of innovative development predetermine crisis manifestations in the national economy. The lags of the influence of changes in the leading indicators of the economic crisis on the development of the economy were calculated. The results obtained can contribute to the effectiveness of the anti-crisis regulation strategy in Russia. They can serve as a basis for increasing the efficiency of long-term innovative development and creating appropriate conditions for increasing the scientific and technological potential of the country. © 2020 by the authors. Licensee MDPI, Basel, Switzerland.