Empirical Analysis of Random Walks in Financial Market Microstructure

Thesis Abstract

This study investigates whether stock price movements in contemporary financial markets exhibit random-walk characteristics within the microstructure context, addressing the problem that microstructural frictions and high-frequency trading may induce departures from idealized random-walk behavior and thus affect market efficiency. The aim is to empirically assess the persistence of random-walk properties in intraday price series and to identify how order flow, liquidity provision, and trading venue structure modulate these properties. Specific objectives include (1) testing the random-walk hypothesis across multiple time scales (1-second, 5-second, 1-minute) for a broad panel of liquid equities; (2) examining the impact of bid-ask bounce, inventory holding costs, and market maker latency on return autocorrelations; (3) evaluating the role of order flow imbalance and trade-size distributions in shaping microstructure-noise; (4) comparing random-walk characteristics across trades-through systems (continuous trading vs. auction mechanims) and venues (ECNs vs. primary exchanges); and (5) integrating theoretical perspectives from the efficient market hypothesis and market microstructure theory to interpret empirical results. A quantitative, observational research design is employed, drawing on high-frequency tick data from a representative sample of 120 liquid US equities over a 36-month window (January 2021 to December 2023). The population comprises all price ticks, quotes, and trade executions recorded on major U.S. venues, with a stratified sampling approach used to ensure sectoral diversity and varying liquidity profiles. Data collection sources include consolidated tape data for trades and quotes, order book snapshots, and venue-reported latency metrics provided by [Data Provider], yielding a dataset of approximately 150 million trades and 1.2 billion quote updates. Instrumentation involves meticulous data cleaning to remove outliers, misprints, and non-trading hours, followed by synchronization of trade and quote messages using a microsecond time-stamp framework. The analysis integrates multiple established methodologies. First, fractional integration and variance-ratio tests (Barndorff-Nielsen et al.; Lo) are used to detect long memory and deviations from a pure random-walk process in log price returns across scales. Second, intraday autocorrelation and liquidity-adjusted return models (Aït-Sahalia and Yu; Madhavan) control for microstructure noise and bid-ask bounce, while Shapiro–Franke-type tests assess efficiency under market frictions. Third, nonlinear time-series techniques—including surrogate data tests and entropy measures (Permutation Entropy, Sample Entropy)—evaluate the robustness of randomness against regime shifts associated with liquidity droughts and news events. Fourth, multivariate regression and generalized method of moments (GMM) frameworks test the influence of order flow imbalance, queue position, and latency on short-horizon return predictability, with robustness checks for heteroskedasticity and autocorrelation (Newey-West adjustments). Finally, a cross-venue comparison employs hierarchical linear models to discern structural differences between continuous trading and call-auction periods. Expected findings anticipate partial rejections of the naive random-walk hypothesis at the sub-minute level, with returns exhibiting short-term dependence attenuated as sampling frequency increases, consistent with microstructure noise theory. It is anticipated that higher order-flow imbalance and larger trade sizes will amplify return autocorrelations and bid-ask bounce effects, while improved latency and tighter quotes will reduce microstructure-induced predictability. The study also expects variation across venues and trading regimes, with auction-based periods showing stronger mean reversion tendencies relative to continuous trading. The results are likely to reveal that randomness in price movements is scale- and regime-dependent, aligning with theories of market efficiency tempered by information asymmetry and liquidity constraints under market microstructure. Contributions to knowledge include (i) a comprehensive, scale-specific assessment of random-walk properties in U.S. equity microstructures using a large, high-resolution dataset; (ii) empirical quantification of the roles played by liquidity provision, order flow, and latency in shaping short-horizon price dynamics; and (iii) an integrated framework that reconciles efficient-market expectations with microstructure frictions, informing models of price formation and tests of market efficiency. The study concludes with pragmatic recommendations for market designers, traders, and regulators, emphasizing the importance of latency management, order routing transparency, and venue-specific liquidity provision strategies to preserve or enhance informational efficiency at granular time scales.