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Volatility is a key variable in option pricing, trading and hedging strategies. The purpose of this paper is to improve the accuracy of forecasting implied volatility using an extension of genetic programming (GP) by means of dynamic…
We propose an informal test for stationarity in a time series which checks for the compatibility of nonlinear approximations to the dynamics made in different segments of the sequence. The segments are compared directly, rather than via…
Gaussian processes have become a popular tool for nonparametric regression because of their flexibility and uncertainty quantification. However, they often use stationary kernels, which limit the expressiveness of the model and may be…
This paper proposes an enhanced approach to modeling and forecasting volatility using high frequency data. Using a forecasting model based on Realized GARCH with multiple time-frequency decomposed realized volatility measures, we study the…
We introduce a qualitative, shape-based, timescale-independent time-domain transform used to extract local dynamics from sociotechnical time series---termed the Discrete Shocklet Transform (DST)---and an associated similarity search…
We propose a non-standard subsampling procedure to make formal statistical inference about the business cycle, one of the most important unobserved feature characterising fluctuations of economic growth. We show that some characteristics of…
Linear rate equations are used to describe the cascading decay of an initial heavy cluster into fragments. We consider moments of arbitrary orders of the mass multiplicity spectrum and derive scaling properties pertaining to their time…
Time series data from real-world systems often display non-stationary behavior, indicating varying statistical characteristics over time. This inherent variability poses significant challenges in deciphering the underlying structural…
We introduce a model of DNA sequence evolution which can account for biases in mutation rates that depend on the identity of the neighboring bases. An analytic solution for this class of non-equilibrium models is developed by adopting…
Scattering moments provide nonparametric models of random processes with stationary increments. They are expected values of random variables computed with a nonexpansive operator, obtained by iteratively applying wavelet transforms and…
In this paper, we show that the recent integration of statistical models with deep recurrent neural networks provides a new way of formulating volatility (the degree of variation of time series) models that have been widely used in time…
In this note we show that the locally stationary wavelet process can be decomposed into a sum of signals, each of which following a moving average process with time-varying parameters. We then show that such moving average processes are…
In order to characterise non-equilibrium growth processes, we study the behaviour of global quantities that depend in a non-trivial way on two different times. We discuss the dynamical scaling forms of global correlation and response…
This study investigates temporal variability in U.S. climate using harmonic decomposition techniques, specifically Fourier and wavelet transforms. Monthly temperature, precipitation, and drought index data from the National Oceanic and…
Dynamic heterogeneity has often been modeled by assuming that a single-particle observable, fluctuating at a molecular scale, is influenced by its coupling to environmental variables fluctuating on a second, perhaps slower, time scale.…
Graphical models are ubiquitous for summarizing conditional relations in multivariate data. In many applications involving multivariate time series, it is of interest to learn an interaction graph that treats each individual time series as…
This paper offers a new approach to modeling and forecasting of nonstationary time series with applications to volatility modeling for financial data. The approach is based on the assumption of local homogeneity: for every time point, there…
Real-world time series exhibit temporally structured uncertainty: volatility clusters in turbulent regimes, dissipates in stable periods, and shifts abruptly around structural breaks. Yet many probabilistic forecasting methods estimate…
Many materials, processes, and structures in science and engineering have important features at multiple scales of time and/or space; examples include biological tissues, active matter, oceans, networks, and images. Explicitly extracting,…
A defining feature of non-stationary systems is the time dependence of their statistical parameters. Measured time series may exhibit Gaussian statistics on short time horizons, due to the central limit theorem. The sample statistics for…