scholarly journals Functional ARCH and GARCH Models: A Yule-Walker Approach

2020 ◽  
Author(s):  
Sebastian Kühnert
Keyword(s):  
Financial Time Series ◽  
Sufficient Conditions ◽  
Stationary Solutions ◽  
Garch Models ◽  
Estimation Errors ◽  
Linear Processes ◽  
Financial Time ◽  
Finite Dimensional ◽  
Arch Processes ◽  
Finite Moments

Conditional heteroskedastic financial time series are commonly modelled by (G)ARCH processes. ARCH(1) and GARCH were recently established in C[0,1] and L^2[0,1]. This article provides sufficient conditions for the existence of strictly stationary solutions, weak dependence and finite moments of (G)ARCH processes for any order in C[0,1] and L^p[0,1]. It deduces explicit asymptotic upper bounds of estimation errors for the shift term, the complete (G)ARCH operators and the projections of ARCH operators on finite-dimensional subspaces. The operator estimaton is based on Yule-Walker equations, and estimating the GARCH operators also involves a result estimating operators in invertible linear processes being valid beyond the scope of (G)ARCH. Moreover, our results regarding (G)ARCH can be transferred to functional AR(MA).

scholarly journals Functional ARCH and GARCH Models: A Yule-Walker Approach

2020 ◽  
Author(s):  
Sebastian Kühnert
Keyword(s):  
Financial Time Series ◽  
Sufficient Conditions ◽  
Dimensional Subspace ◽  
Stationary Solutions ◽  
Finite Dimensional Subspace ◽  
Estimation Errors ◽  
Linear Processes ◽  
Finite Dimensional ◽  
Garch Processes ◽  
Asymptotic Upper Bound

Conditional heteroskedastic financial time series are commonly modelled by ARCH and GARCH. ARCH(1) and GARCH processes were recently extended to the function spaces C[0,1] and L2[0,1], their probabilistic features were studied and their parameters were estimated. The projections of the operators on finite-dimensional subspace were estimated, as were the complete operators in GARCH(1,1). An explicit asymptotic upper bound of the estimation errors was stated in ARCH(1). This article provides sufficient conditions for the existence of strictly stationary solutions, weak dependence and finite moments of ARCH and GARCH processes in various Lp[0,1] spaces, C[0,1] and other spaces. In L2[0,1] we deduce explicit asymptotic upper bounds of the estimation errors for the shift term and the complete operators in ARCH and GARCH and for the projections of the operators on a finite-dimensional subspace in ARCH. The operator estimaton is based on Yule-Walker equations. The estimation of the GARCH operators also involves a result concerning the estimation of the operators in invertible, linear processes which is valid beyond the scope of ARCH and GARCH. Through minor modifications, all results in this article regarding functional ARCH and GARCH can be transferred to functional ARMA.

scholarly journals Functional ARCH and GARCH Models: A Yule-Walker Approach

2019 ◽  
Author(s):  
Sebastian Kühnert
Keyword(s):  
Financial Time Series ◽  
Sufficient Conditions ◽  
Dimensional Subspace ◽  
Stationary Solutions ◽  
Finite Dimensional Subspace ◽  
Estimation Errors ◽  
Linear Processes ◽  
Finite Dimensional ◽  
Garch Processes ◽  
Asymptotic Upper Bound

Conditional heteroskedastic financial time series are commonly modelled by ARCH and GARCH. ARCH(1) and GARCH processes were recently extended to the function spaces C[0,1] and L2[0,1], their probabilistic features were studied and their parameters were estimated. The projections of the operators on finite-dimensional subspace were estimated, as were the complete operators in GARCH(1,1). An explicit asymptotic upper bound for the estimation errors was stated in ARCH(1). This article provides sufficient conditions for the existence of strictly stationary solutions, weak dependence and finite moments of ARCH and GARCH processes in various Lp[0,1] spaces, C[0,1] and other spaces. In L2[0,1] we deduce explicit asymptotic upper bounds of the estimation errors for the shift term and the complete operators in ARCH and GARCH and for the projections of the operators on a finite-dimensional subspace in ARCH. The operator estimaton is based on Yule-Walker equations. The estimation of the GARCH operators also involves a result concerning the estimation of the operators in invertible, linear processes which is valid beyond the scope of ARCH and GARCH. Through minor modifications, all results in this article regarding functional ARCH and GARCH can be transferred to functional ARMA.

scholarly journals Functional ARCH and GARCH Models: A Yule-Walker Approach

2020 ◽  
Author(s):  
Sebastian Kühnert
Keyword(s):  
Financial Time Series ◽  
Sufficient Conditions ◽  
Dimensional Subspace ◽  
Stationary Solutions ◽  
Finite Dimensional Subspace ◽  
Estimation Errors ◽  
Linear Processes ◽  
Finite Dimensional ◽  
Garch Processes ◽  
Asymptotic Upper Bound

Conditional heteroskedastic financial time series are commonly modelled by ARCH and GARCH. ARCH(1) and GARCH processes were recently extended to the function spaces C[0,1] and L2[0,1], their probabilistic features were studied and their parameters were estimated. The projections of the operators on finite-dimensional subspace were estimated, as were the complete operators in GARCH(1,1). An explicit asymptotic upper bound of the estimation errors was stated in ARCH(1). This article provides sufficient conditions for the existence of strictly stationary solutions, weak dependence and finite moments of ARCH and GARCH processes in various Lp[0,1] spaces, C[0,1] and other spaces. In L2[0,1] we deduce explicit asymptotic upper bounds of the estimation errors for the shift term and the complete operators in ARCH and GARCH and for the projections of the operators on a finite-dimensional subspace in ARCH. The operator estimaton is based on Yule-Walker equations. The estimation of the GARCH operators also involves a result concerning the estimation of the operators in invertible, linear processes which is valid beyond the scope of ARCH and GARCH. Through minor modifications, all results in this article regarding functional ARCH and GARCH can be transferred to functional ARMA.

Financial Data Mining Using Flexible ICA-GARCH Models

2010 ◽  
pp. 255-272
Author(s):  
Philip L.H. Yu ◽  
Edmond H.C. Wu ◽  
W.K. Li
Keyword(s):  
Data Mining ◽  
Time Series ◽  
Risk Management ◽  
Independent Component Analysis ◽  
Value At Risk ◽  
Financial Time Series ◽  
Multivariate Time Series ◽  
Independent Component ◽  
Garch Models ◽  
Financial Time

As a data mining technique, independent component analysis (ICA) is used to separate mixed data signals into statistically independent sources. In this chapter, we apply ICA for modeling multivariate volatility of financial asset returns which is a useful tool in portfolio selection and risk management. In the finance literature, the generalized autoregressive conditional heteroscedasticity (GARCH) model and its variants such as EGARCH and GJR-GARCH models have become popular standard tools to model the volatility processes of financial time series. Although univariate GARCH models are successful in modeling volatilities of financial time series, the problem of modeling multivariate time series has always been challenging. Recently, Wu, Yu, & Li (2006) suggested using independent component analysis (ICA) to decompose multivariate time series into statistically independent time series components and then separately modeled the independent components by univariate GARCH models. In this chapter, we extend this class of ICA-GARCH models to allow more flexible univariate GARCH-type models. We also apply the proposed models to compute the value-at-risk (VaR) for risk management applications. Backtesting and out-of-sample tests suggest that the ICA-GARCH models have a clear cut advantage over some other approaches in value-at-risk estimation.

scholarly journals ON THE STATIONARITY OF DYNAMIC CONDITIONAL CORRELATION MODELS

2016 ◽  
Vol 33 (3) ◽  
pp. 636-663 ◽  
Author(s):  
Jean-David Fermanian ◽  
Hassan Malongo
Keyword(s):  
Markov Chains ◽  
Sufficient Conditions ◽  
Stationary Solutions ◽  
Garch Models ◽  
Conditional Correlation ◽  
Dynamic Conditional Correlation ◽  
Correlation Models

We provide conditions for the existence and the uniqueness of strictly stationary solutions of the usual Dynamic Conditional Correlation GARCH models (DCC-GARCH). The proof is based on Tweedie’s (1988) criteria, after having rewritten DCC-GARCH models as nonlinear Markov chains. We also study the existence of their moments and discuss the tightness of our sufficient conditions.

scholarly journals Use GARCH Models to Build a Econometric Model to Predict Average Daily Closing Prices of the Iraqi Stock Exchange for the Period 2013-2016

Webology ◽  
2021 ◽  
Vol 18 (Special Issue 04) ◽  
pp. 385-400
Author(s):  
Dr. Abed Ali Hamad ◽  
Dr. Ahmad Hussein Battal
Keyword(s):  
Stock Prices ◽  
Econometric Model ◽  
Stock Exchange ◽  
Financial Time Series ◽  
Information Criterion ◽  
Garch Models ◽  
Financial Time ◽  
Egarch Model ◽  
Schwarz Criterion ◽  
Statistical Criteria

This research aims to build a standard model for the analysis and prediction of the average daily closing price fluctuations for companies registered in the Iraq Stock Exchange for the period 07/01/2013 to 30/06/2016, using the conditional generalized Heteroscedasticity Generalized Autoregressive (GARCH) models. As these models deal with the fluctuations that occur in the financial time series. The results of the analysis showed that the best model for predicting the volatility of average closing prices in the Iraq Stock Exchange is the EGARCH model (3,1), depending on the statistical criteria used in the preference between the models (Akaike Information Criterion, Schwarz Criterion), and these models can provide information for investors in order to reduce the risk resulting from fluctuations in stock prices in the Iraqi financial market.

scholarly journals Estimating and Forecasting Volatility of Financial Time Series in Pakistan with GARCH-type Models

2007 ◽  
Vol 12 (2) ◽  
pp. 115-149
Author(s):  
G.R. Pasha ◽  
Tahira Qasim ◽  
Muhammad Aslam
Keyword(s):  
Time Series ◽  
Stock Exchange ◽  
Financial Time Series ◽  
Garch Models ◽  
Financial Time ◽  
Daily Data ◽  
Asymmetric Garch ◽  
Gjr Model ◽  
Forecasting Volatility ◽  
Tail Distributions

In this paper we compare the performance of different GARCH models such as GARCH, EGARCH, GJR and APARCH models, to characterize and forecast financial time series volatility in Pakistan. The comparison is carried out by comparing symmetric and asymmetric GARCH models with normal and fat-tailed distributions for the innovations, over short and long forecast horizons. The forecasts are evaluated according to a set of statistical loss functions. Daily data on the Karachi Stock Exchange (KSE) 100 index are analyzed. The empirical results demonstrate that the use of asymmetry in the GARCH models and the assumption of fat-tail distributions for the innovations improve the volatility forecasts. Overall, EGARCH fits the best while the GJR model, with both normal and non-normal innovations, seems to provide superior forecasting ability over short and long horizons.

Sign in / Sign up

Export Citation Format

Share Document