Related papers: A Functional Version of the ARCH Model
Training deep learning models that generalize well to live deployment is a challenging problem in the financial markets. The challenge arises because of high dimensionality, limited observations, changing data distributions, and a low…
ARCH and GARCH models assume either i.i.d. or (what economists lable as) white noise as is usual in regression analysis while assuming memory in a conditional mean square fluctuation with stationary increments. We will show that ARCH/GARCH…
In this paper we present a rather general phenomenological theory of tick-by-tick dynamics in financial markets. Many well-known aspects, such as the L\'evy scaling form, follow as particular cases of the theory. The theory fully takes into…
Recent technological developments have enabled us to collect complex and high-dimensional data in many scientific fields, such as population health, meteorology, econometrics, geology, and psychology. It is common to encounter such datasets…
In this paper, we investigate the adequacy testing problem of high-dimensional factor-augmented regression model. Existing test procedures perform not well under dense alternatives. To address this critical issue, we introduce a novel…
The volatility of financial instruments is rarely constant, and usually varies over time. This creates a phenomenon called volatility clustering, where large price movements on one day are followed by similarly large movements on successive…
Time series foundation models (FMs) have emerged as a popular paradigm for zero-shot multi-domain forecasting. These models are trained on numerous diverse datasets and claim to be effective forecasters across multiple different time series…
This paper considers how a formal mathematically-based model can be used in support of evolutionary software development, and in particular how such a model can be kept consistent with the implementation as it changes to meet new…
We develop methodology allowing to simulate a stationary functional time series defined by means of its spectral density operators. Our framework is general, in that it encompasses any such stationary functional time series, whether linear…
A characteristic feature of functional data is the presence of phase variability in addition to amplitude variability. Existing functional regression methods do not handle time variability in an explicit and efficient way. In this paper we…
We seek to narrow the gap between parametric and nonparametric modelling of stationary time series processes. The approach is inspired by recent advances in focused inference and model selection techniques. The paper generalises and extends…
In this paper we first study the fixed-time stabilizability of discrete-time switched linear control systems. Using a geometric approach, we derive conditions under which such systems can be stabilized within a prescribed number of steps,…
This article presents an empirical validation of the functional multidimensional scaling model, a novel approach that improves the smoothness of time-varying dissimilarities in a low-dimensional space, embedding a modified Adam stochastic…
We develop a generalized stability framework for stochastic discrete-time systems, where the generality pertains to the ways in which the distribution of the state energy can be characterized. We use tools from finance and operations…
Tracking the build-up of financial vulnerabilities is a key component of financial stability policy. Due to the complexity of the financial system, this task is daunting, and there have been several proposals on how to manage this goal. One…
The rapid advancement of models based on artificial intelligence demands innovative monitoring techniques which can operate in real time with low computational costs. In machine learning, especially if we consider artificial neural networks…
The ability to model continuous change in Reiter's temporal situation calculus action theories has attracted a lot of interest. In this paper, we propose a new development of his approach, which is directly inspired by hybrid systems in…
We define a class of functions which have a known decay rate coupled with a periodic fluctuation. We identify conditions on the kernel of a linear summation convolution Volterra equation which give the equivalence of the kernel lying in…
This paper introduces a novel quantile approach to harness the high-frequency information and improve the daily conditional quantile estimation. Specifically, we model the conditional standard deviation as a realized GARCH model and employ…
A method for an evaluation of the error between an unknown parameter and its estimator is developed. Its application enables us to preserve the asymptotic power of a constructed test. Testing problems in AR(1) and ARCH models are studied…