*Review* **Time-Varying Price–Volume Relationship and Adaptive Market Efficiency: A Survey of the Empirical Literature**

#### **Ashok Chanabasangouda Patil 1,***<sup>∗</sup>***,†,‡ and Shailesh Rastogi 2,‡**


Received: 25 May 2019; Accepted: 19 June 2019; Published: 22 June 2019

**Abstract:** This paper conducts a review of the literature on the price–volume relationship and its relation with the implications of the adaptive market hypothesis. The literature on market efficiency is classified as efficient market hypothesis (EMH) studies or adaptive market hypothesis (AMH) studies. Under each class, studies are categorized either as return predictability studies or price–volume relationship studies. Finally, review in each category is analyzed based on the methodology used. Our review shows that the literature on return predictability and price–volume relationship in classical EMH approach is extensive while studies in return predictability in the AMH approach have gained increased attention in the last decade. However, the studies in price–volume relationship under adaptive approach are limited, and there is a scope for studies in this area. Authors did not find any literature review on time-varying price–volume relationship. Authors find that there is a scope to study the nonlinear cross–correlation between price and volume using detrended fluctuation analysis (DFA)-detrended cross–correlational analysis (DXA) in the AMH domain. Further, it would be interesting to investigate whether the same cross–correlation holds across different measures of stock indices within a country and across different time scales.

**Keywords:** market efficiency; price–volume; efficient market hypothesis; adaptive market hypothesis; time-varying or adaptive market efficiency
