Dependent structure and risk analysis of S&P 500 Index's continuously rising returns and continuously falling returns

Purpose The stock market price time series can be divided into two processes: continuously rising and continuously falling. The authors can effectively prevent the stock market from crashing by accurately estimating the risk on continuously rising returns (CRR) and continuously falling returns (CFR). Design/methodology/approach The authors add an exogenous variable into Log-autoregressive conditional duration (Log-ACD) model, and then apply our extended Log-ACD model and Archimedean copula to estimate the marginal distribution and conditional distribution of CRR and CFR. Plus, the authors analyze the conditional value at risk (CVaR) and present back-test results of the CVaR. The back-test shows that our proposed risk estimation method has a good estimation power for the risk of the CRR and CFR, especially the downside risk. In addition, the authors detect whether the dependent structure between the CRR and CFR changes using the change point test method. Findings The empirical results indicate that there is no change point here, suggesting that the results on the dependent structure and risk analysis mentioned above are stable. Therefore, major financial events will not affect the dependent structure here. This is consistent with the point that the CRR and CFR can be analyzed to obtain the trend of stock returns from a more macro perspective than daily stock returns scholars usually study. Practical implications The risk estimation method of this paper is of great significance in understanding stock market risk and can provide corresponding valuable information for investment advisors and public policy regulators. Originality/value The authors defined a new stock returns, CRR and CFR, since it is difficult to analyze and predict the trend of stock returns according to daily stock returns because of the small autocorrelation among daily stock returns.