Related papers: A Functional Version of the ARCH Model
Interest in functional time series has spiked in the recent past with papers covering both methodology and applications being published at a much increased pace. This article contributes to the research in this area by proposing a new…
We combine geometric data analysis and stochastic modeling to describe the collective dynamics of complex systems. As an example we apply this approach to financial data and focus on the non-stationarity of the market correlation structure.…
A multi-factor extension of the Hobson and Rogers (HR) model, incorporating a quadratic variance function (QHR model), is proposed and analysed. The QHR model allows for greater flexibility in defining the moving average filter while…
The functional linear model is an important extension of the classical regression model allowing for scalar responses to be modeled as functions of stochastic processes. Yet, despite the usefulness and popularity of the functional linear…
As high-dimensional and high-frequency data are being collected on a large scale, the development of new statistical models is being pushed forward. Functional data analysis provides the required statistical methods to deal with large-scale…
This note develops a stochastic model of asset volatility. The volatility obeys a continuous-time autoregressive equation. Conditions under which the process is asymptotically stationary and possesses long memory are characterised.…
The proposed model is aimed to reveal important patterns in the behavior of a simplified financial system. The patterns could be detected as regular cycles consisting of debt bubbles and crises. Financial cycles have a well defined…
Financial data are as a rule asymmetric, although most econometric models are symmetric. This applies also to continuous-time models for high-frequency and irregularly spaced data. We discuss some asymmetric versions of the continuous-time…
This paper proposes a forecast-centric adaptive learning model that engages with the past studies on the order book and high-frequency data, with applications to hypothesis testing. In line with the past literature, we produce brackets of…
To support the adoption of active disturbance rejection control (ADRC) in industrial practice, this article aims at improving both understanding and implementation of ADRC using traditional means, in particular via transfer functions and a…
Models for financial risk often assume that underlying asset returns are stationary. However, there is strong evidence that multivariate financial time series entail changes not only in their within-series dependence structure, but also in…
Periodicity is a common feature of time series. For finite-dimensional data, periodic autoregressive moving average (ARMA) models have been extensively studied. In functional time series analysis, AR models have been extended to incorporate…
We present functional forms allowing a broader range of analytic solutions to common economic equilibrium problems. These can increase the realism of pen-and-paper solutions or speed large-scale numerical solutions as computational…
This paper introduces a multivariate spatiotemporal autoregressive conditional heteroscedasticity (ARCH) model based on a vec-representation. The model includes instantaneous spatial autoregressive spill-over effects in the conditional…
This paper studies a regression model with functional dependent and explanatory variables, both of which exhibit nonstationary dynamics. The model assumes that the nonstationary stochastic trends of the dependent variable are explained by…
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…
This study aims to widen the sphere of pratical applicability of the HAC model combined with the ARMA-APARCH volatility forecast model and the extreme values theory. A sequential process of modeling of the VaR of a portfolio based on the…
The HGARCH model allows long-memory impact in volatilities. A new HGARCH model with time-varying amplitude is considered in this paper. We show the stability of the model as well. A score test is introduced to check the time-varying…
This work is devoted to functional ARMA$(p, q)$ processes and approximating vector models based on functional PCA in the context of prediction. After deriving sufficient conditions for the existence of a stationary solution to both the…
An approach is presented for making predictions about functional time series. The method is applied to data coming from periodically correlated processes and electricity demand, obtaining accurate point forecasts and narrow prediction bands…