Essays on Dynamic Efficiency in a Betting Market

Abstract

This thesis introduces a novel framework for modelling the dynamic processes inherent in financial time series, focusing specifically on price fluctuations. The Dynamic Trend Analysis Approach (DTAA) is proposed to address critical issues found in existing literature, such as the ambiguity in the definition of trends and the challenges associated with structural breaks in time series data. Traditional models often rely on proxies like the mean or static trend assumptions, which can lead to substantial bias when trends are present, particularly over longer time intervals, and lake of capture the dynamic characteristics of time series. The DTAA aims to rectify these shortcomings by introducing a new concept: the ”Dynamic Trend” (DT), which captures both the time-varying nature of price movements and the evolving state of the data itself.

The methodology decomposes time series into two key components: the dynamic trend component, which reflects the broader price movements dynamically, and the volatility component, which captures short-term fluctuations. Central to this approach is the establishment of 3 key parameters, the Observer’s Time Points, the Fundamental (Primary) Time Level, and the Horizon. Assuming the Fundamental (Primary) Time Level and Horizon are predetermined, the price changes observed at different Observer’s Time Points vary, which means that the Dynamic Trend at each Observer’s Time Points reflecting the dynamic nature of price movements.

The market dynamic has two aspects, the information incoming and the market state, as shaped by all participant behaviours, evolve over time. Thus, we decompose DT into two dimensions: Information Affect Factor (I AF) and the Market Equilibrium Condition Factor (MECF). These parameters allow for a more nuanced representation of how market participants process and respond to external information, with the DT(I AF and MECF) evolving dynamically as time progresses.

Chapter 2 presents a detailed economic and mathematical definition of the DT concept, providing a theoretical foundation for understanding dynamic price movements.

It also introduces a tangent proxy for approximating the DT, enhancing the precision of time series modelling. Chapter 2 applies the DTAA to assess dynamic efficiency in five distinct betting markets, using a novel decomposition model to examine long-memory properties and informational inefficiencies. By decomposing the time series into trend-free volatility series and DT sequences, this approach overcomes the limitations of existing long-memory models, offering a robust tool for analysing market dynamics.

Chapter 3 explores the dynamic efficiency in betting markets using a novel decomposition model to analyse long-memory properties and informational inefficiency. By identifying integration orders (d) and constructing the degree of market inefficiency (D), it demonstrates that market efficiency improves as betting progresses, with cross-market patterns confirming this gradual increase. Additionally, the chapter introduces the Estimation Score for Integration Orders (ESIO), a method that optimises the combination of window size (WS), bandwidth (BD), and estimator for d. Four estimators (LW, ELW, FELW, Two-Step FELW) are tested, and the combination with the lowest ESIO is selected for each market. Forecasts for the dynamic trend (DT) series in five markets using the FCVAR model show significant cointegrating relationships.

In Chapter 4, the analysis shifts focus to the dynamic interaction between market equilibrium conditions and external information inputs. This chapter emphasises the bounded nature of market responses, revealing how market reaction fluctuate due to the inter-play between market liquidity, and the physical limitations of information processing. The introduction of the Information Affect Factor (I AF) and the Market Equilibrium Condition Factor (MECF) provides a clear framework for understanding the market’s dynamic equilibrium.

Overall, the DTAA framework contributes to the literature by offering a comprehensive method for capturing the structural breaks and dynamic processes in time series data. This method not only improves the robustness of traditional models but also provides new insights into the temporal evolution of market efficiency. It reveals the insight of the information processing in a system in a dynamic way.

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Identifiers

ORCID for Yifu Li: orcid.org/0009-0005-1163-170X

ORCID for Tapas Mishra: orcid.org/0000-0002-6902-2326

ORCID for Ming-Chien Sung: orcid.org/0000-0002-2278-6185

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