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Abstract for "Kolmogorov complexity and Dynamic structures in high frequency data: a newfound land or a dead end?" by Fushing Hsieh
Based on the concept of Kolmogorov complexity, algorithmic statistics in a form of a computer program is proposed as an unified way of computing unknown probabilistic or non-probabilistic dynamic structures of high frequency time series data. Popular model selection techniques, such as AIC, BIC and MDL, all are shown not algorithmic statistics due to their computational infeasibility. We then address a fundamental question: Is there an algorithmic statistic that can extract more computable information of dynamic structure than maximum likelihood approach can? We address this question by comparing two algorithmic statistics: Viterbi and Hierarchical Factor Segmentation (HFS) algorithms, for decoding state-space vector under Hidden Markov Model and beyond. We discuss how to apply HFS algorithm to resolve parametric/non-parametric change-point problems without prior knowledge of number of changes as an example of non-probabilistic dynamic structure. We present applications of HFS algorithm on circadian rhythm by marking out day-and-night rhythmic cycles, on financial stock dynamics by mapping out volatile vs non-volatile periods, and on CpG-island dynamics by segmenting aggregation vs. sparsity of CG di-nucleotidesa on a genomic sequence. We finally postulate the conjecture that high frequency time series data could well be a dead end for R.A. Fisher's likelihood based statistical inferences, but a newfound land for A. N. Kolmogorov's algorithmic statistics before the dawn of quantum computing.