Identification of short-term and long-term time scales in stock markets and effect of structural break

Abstract

The paper presents the comparative study of the nature of stock markets in short-term and long-term time scales ( τ) with and without structural break in the stock data. Structural break point has been identified by applying Zivot and Andrews structural trend break model to break the original time series (TSO) into two time series: time series before structural break (TSB) and time series after structural break (TSA). In order to identify the τ of short-term and long-term market, the Hurst exponent (H) technique has been applied on the intrinsic mode functions (IMF) obtained from the TSO, TSB and TSA by using empirical mode decomposition method. H≈0.5 for all the IMFs of TSO, TSB and TSA having τ in the range of few days (D) to 3 months (M), and H≥0.75 for all the IMFs of TSO, TSB and TSA having τ≥5M. Based on the value of H, the market has been divided into two time horizons: short-term market having 3D≥τ≥3M and H≈0.5, and long-term market having τ≥5M and H≥0.75. As H≈0.5 in short-term and H≥0.75 in long-term, the market is random in short-term and has long-range correlation in long-term. Robustness of the results has also been verified by using detrended fluctuation exponent (ν) analysis and normalised variance (NV) techniques. We obtained ν≈0.5 for reconstructed short-term time series and ν≈1.68 for long-term reconstructed time series. Separation of short-term and long-term market are also identified using NV technique. The time scales for short-term and long-term markets are independent of structural break happened due to extreme event. The τ obtained using the proposed method for short-term and long-term market may be useful for investors to identify the investment time horizon, and hence to design the investment and trading strategies.