GARCH model

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Pair Trading in Tehran Stock Exchange based on Smooth Transition GARCH Model

Pair Trading in Tehran Stock Exchange based on Smooth Transition GARCH Model

First, we implement smooth transition GARCH model with the second-order logistic function on the return spread for the in-sample period using equations 4 and 5. For optimizing the parameters, we consider a sample size of 2,000 for simulating the data using MCMC model. In order to implement this model, we use Metropolis-Hastings method and consider the burn-in sample of 1,000 and a total sample of 50,000 iterations. We only take the second half of each iteration (Martin, A. D., Quinn, K. M., & Park, J. H., 2011).

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Modelling financial time series with SEMIFAR GARCH model

Modelling financial time series with SEMIFAR GARCH model

This paper extends the SEMIFAR model to a SEMIFAR-GARCH model, so that conditional heteroskedasticity in financial time series can also be modelled by the SEMIFAR model. A semiparametric estimation procedure is proposed. Asymptotic results on the SEMIFAR model are extended to the current proposal. It is shown in particular that the same asymptotic results obtained in Beran and Feng (2001) for the SEMIFAR model with i.i.d. normal innovations hold for the SEMIFAR-GARCH model under the much weaker condition that the GARCH innovation process has finite fourth moments. These theoretical results and the important property that the estimates of the FARIMA and GARCH parameter vectors are independent of each other, allow us to apply the data-driven SEMIFAR algorithms to estimate the trend and the FARIMA parameters in the SEMIFAR-GARCH model. It is proposed to estimate the GARCH parameter from the approximated GARCH innovations calculated by inverting the final residuals. Data examples show that the proposed algorithm works well. Further extensions of the SEMIFAR model are also possible. For instance, a seasonal component can also be introduced into the mean function to model daily periodicity in high-frequency financial data.
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A Multiplicative Seasonal ARIMA/GARCH Model in EVN Traffic Prediction

A Multiplicative Seasonal ARIMA/GARCH Model in EVN Traffic Prediction

In the next step, the heteroscedasticity test is implemented and it shows that our traffic data contains volatility periods. Thus, we can proceed to build GARCH model based on the multiplicative seasonal ARIMA model that we achieved. Following the steps mentioned above, GARCH (1, 1) assuming GED formulates which has the smallest measure of forecast error, i.e. MAE and RMSE, should be chosen as the one with the most accurate fit of the time series model. MAE indicates that the average difference between the forecast and the observed value of the model is 0.080042, while RMSE and MAPE are 0.131390 and 276.0843, respectively.
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Stock Volatility Modelling with Augmented GARCH Model with Jumps

Stock Volatility Modelling with Augmented GARCH Model with Jumps

Based on empirical evidences for some of FTSE100 companies, this paper examines two GARCH models with jumps to evaluate the impact of news flow intensity on stock volatility. First it will be considered the well-known GARCH model with jumps proposed in [1]. Then we will introduce the GARCH-Jumps model augmented with news intensity and obtain some empirical results. The main assumption of the model is that jump intensity might change over time and that jump intensity depends linearly on the number of news. It is not clear whether news adds any value to a jump-GARCH model. However, the comparison of the values of log likelihood shows that the GARCH-Jumps model augmented with news intensity performs slightly better than ”pure” GARCH or the GARCH model with Jumps. We
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GARCH model with cross sectional volatility; GARCHX models

GARCH model with cross sectional volatility; GARCHX models

We call our model GARCHX models since the constant in GARCH models is replaced by an extra term, i.e., the lagged cross-sectional market volatility, and thus the GARCHX model does not need additional parameters. Note that the cross-sectional market volatility is lagged to make the GARCHX mode conditional. The GARCHX model is simple, but includes information on some important factors, especially the market factor, via the cross-sectional volatility. Our model is a special case of the multivariate Factor-GARCH model of Engle, Ng, and Rothchild (1990) in the sense that only one factor, i.e., the market factor is included. Note that the main problem in the multivariate GARCH models is that the number of parameters to be estimated grows very fast and we need to impose some restrictions to make the conditional covariance matrix positive definite. Several methods have been suggested to solve these problems; see chapter 12, Campbell, Lo, and MacKinlay (1997).
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Examination of garch model for determinants of infosys stock returns

Examination of garch model for determinants of infosys stock returns

The research on asset volatility in financial market is the such as capital assets pricing, financial derivatives pricing, and financial risk measurement. The premise of quantitative financial analysis is to accurately measure and predict asset quality. Therefore, the measurement are a hotspot of research all the time. To measure and predict asset volatility accurately, Bollerslev built a generalised ARCH (GARCH) model based on the ARCH model. Then, GARCH model was extended. The GARCH process is often preferred by financial professionals because it provides a more real-world context than other forms when trying to predict the prices and general process for a GARCH model involves three steps. The first is to estimate a
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A component GARCH model with time varying weights

A component GARCH model with time varying weights

In this paper we propose a modification of the standard GARCH model, which allows time varying persistence in the volatility dynamics. Namely, a lower degree of persistence is assigned to extreme returns taking place in highly volatile periods rather than to shocks of lower magnitude occurring in tranquil periods. However, the model structure could be easily modified to account for more general situations in which variations in the volatility persistence originate from different sources such as, for example, leverage effects and intraday or intraweek seasonal effects in volatility. It is important to note that, on an observational ground, our model is able to reproduce most of the stylized features for which RS-GARCH model have been designed but, at the same time, it is still characterized by tractable inference procedures.
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Theory and inference for a Markov switching GARCH model

Theory and inference for a Markov switching GARCH model

term u t is i.i.d. with zero mean and unit variance. In order to ensure easily the positivity of the conditional variance we impose the restrictions ω > 0, α ≥ 0 and β ≥ 0. For simplicity, we assume that µ t is constant. The sum α + β measures the persistence of a shock to the conditional variance in equation (2). When a GARCH model is estimated using daily or higher frequency data, the estimate of this sum tends to be close to one, indicating that the volatility process is highly persistent and the second moment of the return process may not exist. However it was argued that the high persistence may artificially result from regime shifts in the GARCH parameters over time, see Diebold (1986), Lamoureux and Lastrapes (1990), and Mikosch and Starica (2004), among others.
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An Asymmetric Block Dynamic Conditional Correlation Multivariate GARCH Model

An Asymmetric Block Dynamic Conditional Correlation Multivariate GARCH Model

By now, the GARCH model of Bollerslev (1986) has been extended to several classes of multivariate GARCH models (see Bauwens, Laurent and Rombouts (2006)). GARCH itself has come a long way since Robert Engle’s (1982) pioneering paper on the ARCH. Multivariate GARCH (MGARCH) research focuses on ways of simplifying the variance- covariance matrix where the number of parameters to be estimated explodes for higher dimensions making estimation costly and computationally intractable. The approaches to simplify the estimation of the parameters of the variance-covariance matrix are now well- developed although suggestions have been made to come up with models that account for economic theory as a basis for simplifying this matrix, Diebold (2004).
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Using Emotional Markers' Frequencies in Stock Market ARMAX GARCH Model

Using Emotional Markers' Frequencies in Stock Market ARMAX GARCH Model

Abstract. We analyze the possibility of improving the prediction of stock market indicators by adding information about public mood ex- pressed in Twitter posts. To estimate public mood, we analysed frequen- cies of 175 emotional markers - words, emoticons, acronyms and ab- breviations - in more than two billion tweets collected via Twitter API over a period from 13.02.2013 to 22.04.2015. We explored the Granger causality relations between stock market returns of S&P500, DJIA, Ap- ple, Google, Facebook, Pfizer and Exxon Mobil and emotional markers frequencies. We found that 17 emotional markers out of 175 are Granger causes of changes in returns without reverse effect. These frequencies were tested by Bayes Information Criteria to determine whether they provide additional information to the baseline ARMAX-GARCH model. We found Twitter data can provide additional information and managed to improve prediction as compared to a model based solely on emotional markers.
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GARCH Model with Jumps: Testing the Impact of News Intensity on Stock Volatility

GARCH Model with Jumps: Testing the Impact of News Intensity on Stock Volatility

In the papers [11] and [12] authors analyze the impact of extraneous sources of information (viz. news and trade volume) on stock volatility by considering some augmented Generalized Autoregressive Conditional Heteroscedasticity (GARCH) models. Following the study of [13], it was supposed that trading volume can be considered as a pro- portional proxy for information arrivals to the market. Also it was considered the daily number of press releases on a stock (news intensity) as an alternative explanatory variable in the basic equation of GARCH model.

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Performance of Markov Switching GARCH Model Forecasting Inflation Uncertainty

Performance of Markov Switching GARCH Model Forecasting Inflation Uncertainty

This paper seeks to uncover the non-linear characteristics of uncertainty underlying the US inflation rates over the period 1971-2015 within a regime-switching framework. Accordingly, we employ two variants of a Markov regime-switching GARCH model, one with normally distributed errors (MS-GARCH-N) and another with t-distributed errors (MS-GARCH-t), and compare their relative in-sample as well as out-of-sample performances with those of their standard single-regime counterparts. Consistent with the findings in existing studies, both of our regime-switching models are successful in identifying the year 1984 as the breakpoint in inflation volatility. Among other interesting results is a new finding that the process of switching to the low volatility regime started around April, 1979 and continued until mid 1983. This time frame is matched with the period of aggressive monetary policy changes implemented by the then Fed chairman Paul Volcker. As regards the performance in forecasting uncertainty, for shorter horizons spanning 1 to 5 months, MS-GARCH-N forecasts are found to outperform all other models whereas for 8 to 12-month ahead forecasts MS-GARCH-t appears superior.
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Modelling of crude oil prices using hybrid arima-garch model

Modelling of crude oil prices using hybrid arima-garch model

This study explores the potential of hybrid ARIMA-GARCH model in handling volatile data. The price of crude oil data will be used for this purpose. This report consists of five chapters. Chapter 1 presents the research framework. It starts with the introduction of time series and followed by the statement of problem, the objectives of the study, the scope of the study and the significance of the study.

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Fourier  type estimation of the power garch model with stable  paretian innovations

Fourier type estimation of the power garch model with stable paretian innovations

We propose an estimation method for the so–called power GARCH model with stable Paretian (SP) innovations. The method is based on the integrated weighted squared distance between the characteristic function of the SP distribution and an empirical counterpart computed from the GARCH residuals. Under fairly standard conditions the estimator was shown to be consistent. Its asymptotic distribution however proved non–standard and in fact splits into two parts: One regular Gaussian distribution cor- responding to the parameters of the SP law, while the other part of the distribution corresponding to the GARCH parameters is singular and in particular it is concen- trated on a hyperplane. For the regular Gaussian part it was possible to even optimize the choice of the weight function so that the estimators of the SP parameters attain minimum variance.
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Forecasting conditional volatility on the RIN market using MS GARCH model

Forecasting conditional volatility on the RIN market using MS GARCH model

discussed in the paper by M. Paolella and L. Taschini [1.32] and authors suggest two ways. The first way is to do only the unconditional analysis of the tails of the data, in other words, to avoid the zeros-problem, because the zeros are in the centre. The second one is a conditional analysis using mixed-normal and mixed- stable GARCH models. In this paper we don’t compare results of estimation using MS ARMA-GARCH-M and mixed GARCH model. We just consider results of regime switching GARCH model and a model from the previous paper [1.19] where we excluded zeros and estimated ARMA-t-GARCH model as O. Sabbaghi and N. Sabbaghi [1.35].
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The Log-GARCH Model via ARMA Representations

The Log-GARCH Model via ARMA Representations

The log-GARCH model provides a flexible framework for the modelling of economic uncertainty, financial volatility and other positively valued variables. Its exponen- tial specification ensures fitted volatilities are positive, allows for flexible dynamics, simplifies inference when parameters are equal to zero under the null, and the log- transform makes the model robust to jumps or outliers. An additional advantage is that the model admits ARMA-like representations. This means log-GARCH mod- els can readily be estimated by means of widely available software, and enables a vast range of well-known time-series results and methods. This chapter provides an overview of the log-GARCH model and its ARMA representation(s), and of how estimation can be implemented in practice. After the introduction, we delineate the univariate log-GARCH model with volatility asymmetry (“leverage”), and show how its (nonlinear) ARMA representation is obtained. Next, stationary covariates (“X”) are added, before a first-order specification with asymmetry is illustrated em- pirically. Then we turn our attention to multivariate log-GARCH-X models. We start by presenting the multivariate specification in its general form, but quickly turn our focus to specifications that can be estimated equation-by-equation – even in the presence of Dynamic Conditional Correlations (DCCs) of unknown form. Next, a multivariate non-stationary log-GARCH-X model is formulated, in which the X-covariates can be both stationary and/or nonstationary. A common critique directed towards the log-GARCH model is that its ARCH terms may not exist in the presence of inliers. An own Section is devoted to how this can be handled in prac- tice. Next, the generalisation of log-GARCH models to logarithmic Multiplicative Error Models (MEMs) is made explicit. Finally, the chapter concludes.
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Asymptotic Theory for a Vector ARMA-GARCH Model,

Asymptotic Theory for a Vector ARMA-GARCH Model,

consistency of the QMLE was obtained under only the second-order moment condi- tion. Unlike Weiss (1986) and Pantula (1989) for the univariate case, the asymptotic normality of the QMLE for the vector ARCH model requires only the second-order moment of the unconditional errors, and the finite fourth-order moment of the condi- tional errors. The asymptotic normality of the QMLE for the vector ARMA-ARCH model was proved using the fourth-order moment, which is an extension of Weiss (1986) and Pantula (1989). For the general vector ARMA-GARCH model, the asymptotic normality of the QMLE requires the assumption that the sixth-order moment exists. Whether this result will hold under some weaker moment condi- tions remains to be proved.
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A Multivariate Generalized Orthogonal Factor GARCH Model

A Multivariate Generalized Orthogonal Factor GARCH Model

GARCH model. Our model is related to the factor GARCH model of Engle et al. (1990), but it is more parsimonious and easier to estimate. Gaussian maximum likeli- hood (ML) estimates can be straightforwardly obtained and likelihood functions based on other distributions, such as the (multivariate) t distribution, can also be readily formulated. This is illustrated by the empirical application of the paper where, in- stead of the commonly used t distribution, a mixture of normal distributions is more appropriate and, therefore, applied. Interestingly, some parameters of the conditional covariance matrix, which are not identi fi able in the Gaussian model, become identi fi - able in a model based on a mixture of normal distributions. In practice the fi rst step of applying any factor GARCH model consists of selecting the unknown number of conditionally heteroskedastic common factors. In order to facilitate this selection two tests are developed in the paper.
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Theory and inference for a Markov switching Garch model.

Theory and inference for a Markov switching Garch model.

term u t is i.i.d. with zero mean and unit variance. In order to ensure easily the positivity of the conditional variance we impose the restrictions ω > 0, α ≥ 0 and β ≥ 0. For simplicity, we assume that µ t is constant. The sum α + β measures the persistence of a shock to the conditional variance in equation (2). When a GARCH model is estimated using daily or higher frequency data, the estimate of this sum tends to be close to one, indicating that the volatility process is highly persistent and the second moment of the return process may not exist. However it was argued that the high persistence may artificially result from regime shifts in the GARCH parameters over time, see Diebold (1986), Lamoureux and Lastrapes (1990), and Mikosch and Starica (2004), among others.
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Composite Likelihood for Bilinear  GARCH Model

Composite Likelihood for Bilinear GARCH Model

In this study, we focus on the class of BL-GARCH models, which is initially introduced by Storti & Vitale [1] in order to handle leverage effects and volatility clustering. First we illustrate some properties of BL-GARCH (1, 2) model, like the positivity, stationarity and marginal distribution; then we study the statistical inference, apply the composite likelihood on panel of BL-GARCH (1, 2) model, and study the asymptotic behavior of the estimators, like the consistency property and the asymptotic normality.

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