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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).

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.

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.

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.

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.

Influencer marketing mediated by social media is prevalent in social commerce. Micro-, meso- and macro-influencers all play an irreplaceable role in marketing. The purpose of this paper is to explore how companies with limited budgets choose influencers according to products' various levels of brand familiarity.

This study constructs an evolutionary game model of influencer marketing based on evolutionary game theory on complex networks. This model initiates various networks to demonstrate how influencers disseminate information and constructs update mechanisms to depict how individuals react to this information based on individuals' information utility and friends' strategies.

Simulation results suggest that companies should invest more in macro-influencers than in meso-influencers, however investing all in macro-influencers is not a good choice. The investment in meso-influencers will increase as brand familiarity decreases, whereas it will not exceed investment in macro-influencers. Furthermore, the accumulation of micro-influencers can accelerate the marketing process.

This study examines the combined effects of micro-influencers, meso-influencers and macro-influencers in marketing by simulating the marketing process initiated by influencers on social media.