Analyzing Sequence Data with Markov Chain Models in Scientific Experiments

Toddlers strategically adapt their information search

Adaptive information seeking is essential for humans to effectively navigate complex and dynamic environments. Here, we developed a gaze-contingent eye-tracking paradigm to examine the early emergence of adaptive information-seeking. Toddlers (N = 60, 18-36 months) and adults (N = 42) either learnt that an animal was equally likely to be found in any of four available locations, or that it was most likely to be found in one particular location. Afterwards, they were given control of a torchlight, which they could move with their eyes to explore the otherwise pitch-black task environment. Eye-movement data and Markov models show that, from 24 months of age, toddlers become more exploratory than adults, and start adapting their exploratory strategies to the information structure of the task. These results show that toddlers' search strategies are more sophisticated than previously thought, and identify the unique features that distinguish their information search from adults'.

High-frequency stock market order transitions during the US-China trade war 2018: A discrete-time Markov chain analysis

Statistical analysis of high-frequency stock market order transaction data is conducted to understand order transition dynamics. We employ a first-order time-homogeneous discrete-time Markov chain model to the sequence of orders of stocks belonging to six different sectors during the US-China trade war of 2018. The Markov property of the order sequence is validated by the Chi-square test. We estimate the transition probability matrix of the sequence using maximum likelihood estimation. From the heatmap of these matrices, we found the presence of active participation by different types of traders during high volatility days. On such days, these traders place limit orders primarily with the intention of deleting the majority of them to influence the market. These findings are supported by high stationary distribution and low mean recurrence values of add and delete orders. Further, we found similar spectral gap and entropy rate values, which indicates that similar trading strategies are employed on both high and low volatility days during the trade war. Among all the sectors considered in this study, we observe that there is a recurring pattern of full execution orders in the Finance & Banking sector. This shows that the banking stocks are resilient during the trade war. Hence, this study may be useful in understanding stock market order dynamics and devise trading strategies accordingly on high and low volatility days during extreme macroeconomic events.