We typically divide the markets into 2 regimes: trending or mean-reverting. In a recent paper [1], the authors not only divided the markets into these 2 regimes but also added a third one, a so-called random walk regime.

*Investors generally go long when the market is rising and short when the market is falling. In order to implement trading strategies more effectively, it is very important to mine the market direction and the timing of long and short positions. This article divides the direction of the market into three categories: Random Walk (RW), Trend Following (TF) caused by negative reflection, and Mean Reverting (MR) caused by overreaction.*

Usually, we utilize the Autocorrelation function or Hurst exponent in order to characterize the markets. There exist, however, other methods that can be used for this purpose, such as

- Push-Response test,
- Variance-Ratio test, and
- P+/P- test.

These methods were utilized in the above-mentioned article.

*Push-Response Test, Variance Ratio Test, and P+, P- Test are used to determine the direction of the market, and finally formulate specific trading strategies according to the market type to achieve profitability. This article summarizes the market of certain indexes of US futures, such as HO, GC, etc., which have TF trends in recent years. Taking the ES (E-mini S&P 500) contract as an example, the results show that ES has a trend of TF in the last 6 years, and a trend of MR in 97-09. This article proposes quantitative strategies based on TF and MR market respectively, and applies it to the ES index to verify the effectiveness of the trading strategies.*

After analyzing the market characteristics, the authors developed two low-frequency trading strategies, one is a trend-following (TF) strategy, and the other is a mean-reverting (MR) one. The Sharpe ratios of the TF and MR strategies are 2.8 and 0.14 respectively.

From the results, we notice that the TF strategy has a much higher risk-adjusted return than the MR one. It is a surprise to us. This is probably due to the fact that the authors developed trading strategies that include commodities, and not just stock market indices.

**References**

[1] C. Zheng, G. Gan, J. Zhao, H. Li, *Mining Market Directions: A Type of Trading Strategy for Trend Following and Mean Reverting Index*, 2021 International Conference on Electronic Commerce, Engineering Management and Information Systems.