Medium-term cycles in the dynamics of the Dow Jones Index for the period 1985–2019

The problem of showing the existence of cycles in the dynamics of economic systems has attracted the interest of diverse researches in the last century. The motivation relies on the fact that cycles would imply that the evolution of the economic system is intrinsically marked by non-steady growth trends, but by expansion–contraction mechanisms. Inventory Kitchin (∼40 months), fixed investment Juglar (7–11 years), infrastructural Kuznets (15–25 years), and long-term technological Kondratieff (40–60 years) cycles are at the center of the discussion. Commonly, spectral analysis applied to typical economic signals (e.g., GDP, unemployment rate, and industrial output) is used for gaining valuable insights on cyclical movements of the economic activity. However, the analysis is limited by the relatively low size of real data, as economic variables are sampled at low frequencies (annual and quarterly). This work uses stock market variables (returns and traded volume) to explore the existence of cycling behavior. The approach is based on the time variations of the Hurst exponent computed by means of the detrended fluctuation analysis (DFA). The Hurst exponent of the traded volume showed a clear cycle with period ∼8.0 years, while for returns the dominant period was ∼10.5 years, which are within the range of fixed capital investment Juglar cycles. Finally, the use of cycles of the Hurst exponent as a proxy for studying economic recession forecasting is discussed.