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 ( T S O ) into two time series: time series before structural break ( T S B ) and time series after structural break ( T S A ). 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 ( I M F ) obtained from the T S O , T S B and T S A by using empirical mode decomposition method. H ≈ 0 . 5 for all the IMFs of T S O , T S B and T S A having τ in the range of few days ( D ) to 3 months ( M ) , and H ≥ 0 . 75 for all the IMFs of T S O , T S B and T S A having τ ≥ 5 M . Based on the value of H , the market has been divided into two time horizons: short-term market having 3 D ≥ τ ≥ 3 M and H ≈ 0 . 5 , and long-term market having τ ≥ 5 M 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 ( N V ) 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 N V 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.