Related papers: Fundamental Framework for Technical Analysis
We present an empirical study of the subordination hypothesis for a stochastic time series of a stock price. The fluctuating rate of trading is identified with the stochastic variance of the stock price, as in the continuous-time random…
Data normalization is one of the most important preprocessing steps when building a machine learning model, especially when the model of interest is a deep neural network. This is because deep neural network optimized with stochastic…
In setting up a stochastic description of the time evolution of a financial index, the challenge consists in devising a model compatible with all stylized facts emerging from the analysis of financial time series and providing a reliable…
Prices in financial markets exhibit extreme jumps far more often than can be accounted for by external news. Further, magnitudes of price changes are correlated over long times. These so called stylized facts are quantified by scaling laws…
When the number of subjects, $n$, is large, paired comparisons are often sparse. Here, we study statistical inference in a class of paired comparison models parameterized by a set of merit parameters, under an Erd\"{o}s--R\'{e}nyi…
This paper proposes an algorithm based on a staged sliding window Transformer architecture to detect abnormal behaviors in the microstructure of the foreign exchange market, focusing on high-frequency EUR/USD trading data. The method…
Linear models are foundational tools in statistics and ubiquitous across the applied sciences. However, conventional statistical inference -- such as $t$-tests and $F$-tests -- are only valid at fixed sample sizes, making them unsuitable…
We introduce a novel uncertainty principle for generalized graph signals that extends classical time-frequency and graph uncertainty principles into a unified framework. By defining joint vertex-time and spectral-frequency spreads, we…
In recent years, model collapse has become a critical issue in language model training, making it essential to understand the underlying mechanisms driving this phenomenon. In this paper, we investigate recursive parametric model training…
We present cross and time series analysis of price fluctuations in the U.S. Treasury fixed income market. By means of techniques borrowed from statistical physics we show that the correlation among bonds depends strongly on the maturity and…
We develop a general framework for estimating function-valued parameters under equality or inequality constraints in infinite-dimensional statistical models. Such constrained learning problems are common across many areas of statistics and…
Detailed study of multifractal characteristics of the financial time series of asset values and of its returns is performed using a collection of the high frequency Deutsche Aktienindex data. The tail index ($\alpha$), the Renyi exponents…
Empirical process theory for i.i.d. observations has emerged as a ubiquitous tool for understanding the generalization properties of various statistical problems. However, in many applications where the data exhibit temporal dependencies…
The distribution of price returns for a class of uncorrelated diffusive dynamics is considered. The basic assumptions are (1) that there is a "consensus" value associated with a stock, and (2) that the rate of diffusion depends on the…
Data dependencies have been extended to graphs to characterize topological and value constraints. Existing data dependencies are defined to capture inconsistencies in static graphs. Nevertheless, inconsistencies may occur over evolving…
We extend the now classic structural credit modeling approach of Black and Cox to a class of "two-factor" models that unify equity securities such as options written on the stock price, and credit products like bonds and credit default…
We develop inference procedures robust to general forms of weak dependence. The procedures utilize test statistics constructed by resampling in a manner that does not depend on the unknown correlation structure of the data. We prove that…
The prediction of a binary sequence is a classic example of online machine learning. We like to call it the 'stock prediction problem,' viewing the sequence as the price history of a stock that goes up or down one unit at each time step. In…
We propose a unified framework that employs variational inference (VI) with (conditional) normalizing flows (NFs) to train both between-model and within-model proposals for reversible jump Markov chain Monte Carlo, enabling efficient…
This thesis develops exact analytical tools to study strongly correlated stochastic systems, with a focus on extreme value statistics, gap statistics, and full counting statistics in multi-particle processes. A central contribution is the…