Related papers: Nonlinear GARCH model and 1/f noise
Gravitational clustering is an intrinsically non-linear process that generates significant non-Gaussian signatures in the density field. We consider how these affect power spectrum determinations from galaxy and weak-lensing surveys.…
There exist very few results on mixing for non-stationary processes. However, mixing is often required in statistical inference for non-stationary processes such as time-varying ARCH (tvARCH) models. In this paper, bounds for the mixing…
GARCH is one of the most prominent nonlinear time series models, both widely applied and thoroughly studied. Recently, it has been shown that the COGARCH model (which was introduced a few years ago by Kl\"{u}ppelberg, Lindner and Maller)…
Simple analytically solvable models are proposed exhibiting 1/f spectrum in wide range of frequency. The signals of the models consist of pulses (point process) which interevent times fluctuate about some average value, obeying an…
This chapter presents specific aspects of Gaussian process modeling in the presence of complex noise. Starting from the standard homoscedastic model, various generalizations from the literature are presented: input varying noise variance,…
In this study, we develop a unified volatility modeling framework that embeds GARCH dynamics directly within recurrent neural networks. We propose two interpretable hybrid architectures, GARCH-GRU and GARCH-LSTM, that integrate the…
SVR-GARCH model tends to "backward eavesdrop" when forecasting the financial time series volatility in which case it tends to simply produce the prediction by deviating the previous volatility. Though the SVR-GARCH model has achieved good…
We propose a new model for nonstationary integer-valued time series which is particularly suitable for data with a strong trend. In contrast to popular Poisson-INGARCH models, but in line with classical GARCH models, we propose to pick the…
The probability density function (PDF) of the roughness, i.e., of the temporal variance, of 1/f^alpha noise signals is studied. Our starting point is the generalization of the model of Gaussian, time-periodic, 1/f noise, discussed in our…
Stock market indices are volatile by nature, and sudden shocks are known to affect volatility patterns. The autoregressive conditional heteroskedasticity (ARCH) and generalized ARCH (GARCH) models neglect structural breaks triggered by…
Noise power spectra in spatially extended dynamical systems are investigated, using as a model the Complex Ginzburg-Landau equation with a stochastic term. Analytical and numerical investigations show that the temporal noise spectra are of…
Estimating conditional quantiles of financial time series is essential for risk management and many other applications in finance. It is well-known that financial time series display conditional heteroscedasticity. Among the large number of…
A wideband Gaussian Noise Model of the nonlinear noise power spectral density is developed for a single semiconductor optical amplifier as described by the Agrawal model. A simple, interpretable closed-form expression is obtained for the…
We propose an artificial market model based on deterministic agents. The agents modify their ask/bid price depending on past price changes. The temporal development of market price fluctuations is calculated numerically. A probability…
In an asset return series there is a conditional asymmetric dependence between current return and past volatility depending on the current return's sign. To take into account the conditional asymmetry, we introduce new models for asset…
We are interested in proposing approximations of a sequence of probability measures in the convex order by finitely supported probability measures still in the convex order. We propose to alternate transitions according to a martingale…
We examine the efficiency of the Asymmetric Power ARCH (APARCH) model in the case where the residuals follow the standardized Pearson type IV distribution. The model is tested with a variety of loss functions and the efficiency is examined…
This paper introduces a unified approach for modeling high-frequency financial data that can accommodate both the continuous-time jump-diffusion and discrete-time realized GARCH model by embedding the discrete realized GARCH structure in…
Complex dynamical systems which are governed by anomalous diffusion often can be described by Langevin equations driven by L\'evy stable noise. In this article we generalize nonlinear stochastic differential equations driven by Gaussian…
We assess the advantage of combining univariate and multivariate portfolio risk forecasts with the aid of forecast reconciliation techniques. In our analyzes, we assume knowledge of portfolio weights, a standard for portfolio risk…