We consider n observations from the GARCH-type model: Z = UY, where U and Y are independent random variables. We aim to estimate density function Y where Y have a weighted distribution. We determine a sharp upper boun...We consider n observations from the GARCH-type model: Z = UY, where U and Y are independent random variables. We aim to estimate density function Y where Y have a weighted distribution. We determine a sharp upper bound of the associated mean integrated square error. We also make use of the measure of expected true evidence, so as to determine when model leads to a crisis and causes data to be lost.展开更多
Taking the price of grain in Guizhou Province as an example,by establishing GARCH model,I calculate VAR of logarithm return of grain price index,in order to conduct research on the variation law of price of the agricu...Taking the price of grain in Guizhou Province as an example,by establishing GARCH model,I calculate VAR of logarithm return of grain price index,in order to conduct research on the variation law of price of the agricultural products.The results show that VAR of grain in Guizhou has variation.After the year 2010,VAR value is gradually increasing,and the price variation risk of grain market tends to increase progressively.Based on the characteristics of grain price variation,a series of corresponding proposals are put forward to stabilize the grain price as follows:strengthen the agricultural infrastructure construction,and promote the agricultural overall production capacity;reinforce the market supervision on the circulation field of agricultural products,and maintain market order;improve regulation system of agricultural products,and stabilize the price of agricultural products;strengthen mobility regulation,and prevent a flood of speculative cash.展开更多
In this article a new approach for checking the adequacy of GARCH-type models in time series was proposed. The resulted tests involve weight functions, which provide them with the flexibility in choosing scores to enh...In this article a new approach for checking the adequacy of GARCH-type models in time series was proposed. The resulted tests involve weight functions, which provide them with the flexibility in choosing scores to enhance power performance. The choice of weight functions and the power properties of the tests are studied. For a large number of alternatives, asymptotically distribution-free maximin test is constructed. The tests are asymptotically chi-squared under the null hypothesis and easy to implement. Simulation results indicate that the tests perform well.展开更多
A statistical manifold of non-exponential type coming from a model for economics describing stock return process is constructed, with its geometric structure investigated and both Gaussian curvatures and mean curvatur...A statistical manifold of non-exponential type coming from a model for economics describing stock return process is constructed, with its geometric structure investigated and both Gaussian curvatures and mean curvatures of its curved exponential submanifolds deducted. A few graphs describing relevant scalar curvature, mean curvature and Gaussian curvature are also introduced.展开更多
The aim of this paper is to use the General Autoregressive Conditional Heteroscedastic (GARCH) type models for the estimation of volatility of the daily returns of the Kenyan stock market: that is Nairobi Securities E...The aim of this paper is to use the General Autoregressive Conditional Heteroscedastic (GARCH) type models for the estimation of volatility of the daily returns of the Kenyan stock market: that is Nairobi Securities Exchange (NSE). The conditional variance is estimated using the data from March 2013 to February 2016. We use both symmetric and asymmetric models to capture the most common features of the stock markets like leverage effect and volatility clustering. The results show that the volatility process is highly persistent, thus, giving evidence of the existence of risk premium for the NSE index return series. This in turn supports the positive correlation hypothesis: that is between volatility and expected stock returns. Another fact revealed by the results is that the asymmetric GARCH models provide better fit for NSE than the symmetric models. This proves the presence of leverage effect in the NSE return series.展开更多
The paper introduces a new simple semiparametric estimator of the conditional variance-covariance and correlation matrix (SP-DCC). While sharing a similar sequential approach to existing dynamic conditional correlatio...The paper introduces a new simple semiparametric estimator of the conditional variance-covariance and correlation matrix (SP-DCC). While sharing a similar sequential approach to existing dynamic conditional correlation (DCC) methods, SP-DCC has the advantage of not requiring the direct parameterization of the conditional covariance or correlation processes, therefore also avoiding any assumption on their long-run target. In the proposed framework, conditional variances are estimated by univariate GARCH models, for actual and suitably transformed series, in the first step;the latter are then nonlinearly combined in the second step, according to basic properties of the covariance and correlation operator, to yield nonparametric estimates of the various conditional covariances and correlations. Moreover, in contrast to available DCC methods, SP-DCC allows for straightforward estimation also for the non-symultaneous case, i.e. for the estimation of conditional cross-covariances and correlations, displaced at any time horizon of interest. A simple expost procedure to ensure well behaved conditional variance-covariance and correlation matrices, grounded on nonlinear shrinkage, is finally proposed. Due to its sequential implementation and scant computational burden, SP-DCC is very simple to apply and suitable for the modeling of vast sets of conditionally heteroskedastic time series.展开更多
This paper mainly talks about a popular approach of volatility of a GARCH-type model in R, while the disturbances are independent and have identical Student-t distribution. It uses the Metropolis-Hastings method to pe...This paper mainly talks about a popular approach of volatility of a GARCH-type model in R, while the disturbances are independent and have identical Student-t distribution. It uses the Metropolis-Hastings method to perform the computations and gives the programs in details in R.展开更多
A suitable statistical model has been explored for the investors as well as the researchers to resolve the future estimation of share volume by using daily stock volume data from Dhaka Stock Exchange （DSE）. The dail...A suitable statistical model has been explored for the investors as well as the researchers to resolve the future estimation of share volume by using daily stock volume data from Dhaka Stock Exchange （DSE）. The daily volume data from the June 1, 2004 to April 19, 2010 were retrieved from DSE website as a secondary data source. The Maximum Likelihood---Autoregressive Conditional Heteroskedasticity （ARCH） （Marquardt） method has been applied to construct the models for the stock volume data of DSE by using statistical package software E-Views of verson-5. First of all, an ＂Auto Regressive Integrated Moving Average （ARIMA） model＂ was fitted and observed that heteroscedastic volatilities were still present there. To eliminate this dilemma, ARCH class of volatility models has been used and finally the ARIMA with EGARCH model has been explored. Findings of this study have recognized that ARIMA with EGARCH model implies low mean square error, low mean absolute error, low bias proportion, and low variance proportion for share volume data with comparing to other models. Hence, the modelling concept established in this study would be a decisive study for the investors as well as the researchers.展开更多
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 B...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.展开更多
This paper examines the forecasting performance of different kinds of GARCH model （GRACH, EGARCH, TARCH and APARCH） under the Normal, Student-t and Generalized error distributional assumption. We compare the effect ...This paper examines the forecasting performance of different kinds of GARCH model （GRACH, EGARCH, TARCH and APARCH） under the Normal, Student-t and Generalized error distributional assumption. We compare the effect of different distributional assumption on the GARCH models. The data we analyze are the daily stocks indexes for Shenzhen Stock Exchange （SSE） in China from April 3^rd, 1991 to April 14^th, 2005. We find that improvements of the overall estimation are achieved when asymmetric GARCH models are used with student-t distribution and generalized error distribution. Moreover, it is found that TARCH and GARCH models give better forecasting performance than EGARCH and APARCH models. In forecasting performance, the model under normal distribution gives more accurate forecasting performance than non-normal densities and generalized error distributions clearly outperform the student-t densities in case of SSE.展开更多
This paper mainly through the comparison of GARCH-VaR China stock market board,small board and gem in the United States correspond to the three stock index volatility,volatility between stock indexes obtained U.S.stoc...This paper mainly through the comparison of GARCH-VaR China stock market board,small board and gem in the United States correspond to the three stock index volatility,volatility between stock indexes obtained U.S.stock market volatility risk multi-level market differences.As a suggestion and reference for investors,it can also provide reference for the supervision department of stock market risk.Based on the empirical research,analyzes the advantages and disadvantages of traditional risk measurement methods,and combined with GARCH model with high degree of complexity and the practice effect analysis,trying to find the objective measure stock model analysis.In the specific study of the volatility of the stock market,through the comparison of China’s three major plates and the market classification mechanism of mature U.S.stock market,combined with the objective situation of the market,draw conclusions and change expectations.From the empirical results,the U.S.stock market has recovered after the financial crisis,and its performance on risk volatility is better than China’s three major plates.From the comparison of the stock market in the same country,the small and medium-sized plates tend to have greater risks,while the risks of the main board and the gem have the characteristics of low average value but frequent fluctuations.展开更多
The financial market is the core of national economic development,and stocks play an important role in the financial market.Analyzing stock prices has become the focus of investors,analysts,and people in related field...The financial market is the core of national economic development,and stocks play an important role in the financial market.Analyzing stock prices has become the focus of investors,analysts,and people in related fields.This paper evaluates the volatility of Apple Inc.(AAPL)returns using five generalized autoregressive conditional heteroskedasticity(GARCH)models:sGARCH with constant mean,GARCH with sstd,GJR-GARCH,AR(1)GJR-GARCH,and GJR-GARCH in mean.The distribution of AAPL’s closing price and earnings data was analyzed,and skewed student t-distribution(sstd)and normal distribution(norm)were used to further compare the data distribution of the five models and capture the shape,skewness,and loglikelihood in Model 4-AR(1)GJR-GARCH.Through further analysis,the results showed that Model 4,AR(1)GJR-GARCH,is the optimal model to describe the volatility of the return series of AAPL.The analysis of the research process is both,a process of exploration and reflection.By analyzing the stock price of AAPL,we reflect on the shortcomings of previous analysis methods,clarify the purpose of the experiment,and identify the optimal analysis model.展开更多
Since the establishment of financial models for risk prediction,the measurement of volatility at risky market has improved,and its significance has also grown.For high-frequency financial data,the degree of investment...Since the establishment of financial models for risk prediction,the measurement of volatility at risky market has improved,and its significance has also grown.For high-frequency financial data,the degree of investment risk,which has always been the focus of attention,is measured by the variance of residual sequence obtained following model regression.By integrating the long short-term memory(LSTM)model with multiple generalized autoregressive conditional heteroscedasticity(GARCH)models,a new hybrid LSTM model is used to predict stock price volatility.In this paper,three GARCH models are used,and the model that can best fit the data is determined.展开更多
文摘We consider n observations from the GARCH-type model: Z = UY, where U and Y are independent random variables. We aim to estimate density function Y where Y have a weighted distribution. We determine a sharp upper bound of the associated mean integrated square error. We also make use of the measure of expected true evidence, so as to determine when model leads to a crisis and causes data to be lost.
基金Supported by Guizhou Provincial Science and Technology Department Soft Science United Funds Research Program(2010LKC2005)
文摘Taking the price of grain in Guizhou Province as an example,by establishing GARCH model,I calculate VAR of logarithm return of grain price index,in order to conduct research on the variation law of price of the agricultural products.The results show that VAR of grain in Guizhou has variation.After the year 2010,VAR value is gradually increasing,and the price variation risk of grain market tends to increase progressively.Based on the characteristics of grain price variation,a series of corresponding proposals are put forward to stabilize the grain price as follows:strengthen the agricultural infrastructure construction,and promote the agricultural overall production capacity;reinforce the market supervision on the circulation field of agricultural products,and maintain market order;improve regulation system of agricultural products,and stabilize the price of agricultural products;strengthen mobility regulation,and prevent a flood of speculative cash.
基金supported by a grant from the Research Grants Council of Hong Kong.Jianhong Wu was also supported by a grant from Humanities & Social Sciences in Chinese University (07JJD790154)the Youth Talent Foundation of Zhejiang GongShang University (Q09-12)
文摘In this article a new approach for checking the adequacy of GARCH-type models in time series was proposed. The resulted tests involve weight functions, which provide them with the flexibility in choosing scores to enhance power performance. The choice of weight functions and the power properties of the tests are studied. For a large number of alternatives, asymptotically distribution-free maximin test is constructed. The tests are asymptotically chi-squared under the null hypothesis and easy to implement. Simulation results indicate that the tests perform well.
基金Sponsored by the National Natural Science Foundation of China(10871218)
文摘A statistical manifold of non-exponential type coming from a model for economics describing stock return process is constructed, with its geometric structure investigated and both Gaussian curvatures and mean curvatures of its curved exponential submanifolds deducted. A few graphs describing relevant scalar curvature, mean curvature and Gaussian curvature are also introduced.
文摘The aim of this paper is to use the General Autoregressive Conditional Heteroscedastic (GARCH) type models for the estimation of volatility of the daily returns of the Kenyan stock market: that is Nairobi Securities Exchange (NSE). The conditional variance is estimated using the data from March 2013 to February 2016. We use both symmetric and asymmetric models to capture the most common features of the stock markets like leverage effect and volatility clustering. The results show that the volatility process is highly persistent, thus, giving evidence of the existence of risk premium for the NSE index return series. This in turn supports the positive correlation hypothesis: that is between volatility and expected stock returns. Another fact revealed by the results is that the asymmetric GARCH models provide better fit for NSE than the symmetric models. This proves the presence of leverage effect in the NSE return series.
文摘The paper introduces a new simple semiparametric estimator of the conditional variance-covariance and correlation matrix (SP-DCC). While sharing a similar sequential approach to existing dynamic conditional correlation (DCC) methods, SP-DCC has the advantage of not requiring the direct parameterization of the conditional covariance or correlation processes, therefore also avoiding any assumption on their long-run target. In the proposed framework, conditional variances are estimated by univariate GARCH models, for actual and suitably transformed series, in the first step;the latter are then nonlinearly combined in the second step, according to basic properties of the covariance and correlation operator, to yield nonparametric estimates of the various conditional covariances and correlations. Moreover, in contrast to available DCC methods, SP-DCC allows for straightforward estimation also for the non-symultaneous case, i.e. for the estimation of conditional cross-covariances and correlations, displaced at any time horizon of interest. A simple expost procedure to ensure well behaved conditional variance-covariance and correlation matrices, grounded on nonlinear shrinkage, is finally proposed. Due to its sequential implementation and scant computational burden, SP-DCC is very simple to apply and suitable for the modeling of vast sets of conditionally heteroskedastic time series.
文摘This paper mainly talks about a popular approach of volatility of a GARCH-type model in R, while the disturbances are independent and have identical Student-t distribution. It uses the Metropolis-Hastings method to perform the computations and gives the programs in details in R.
文摘A suitable statistical model has been explored for the investors as well as the researchers to resolve the future estimation of share volume by using daily stock volume data from Dhaka Stock Exchange （DSE）. The daily volume data from the June 1, 2004 to April 19, 2010 were retrieved from DSE website as a secondary data source. The Maximum Likelihood---Autoregressive Conditional Heteroskedasticity （ARCH） （Marquardt） method has been applied to construct the models for the stock volume data of DSE by using statistical package software E-Views of verson-5. First of all, an ＂Auto Regressive Integrated Moving Average （ARIMA） model＂ was fitted and observed that heteroscedastic volatilities were still present there. To eliminate this dilemma, ARCH class of volatility models has been used and finally the ARIMA with EGARCH model has been explored. Findings of this study have recognized that ARIMA with EGARCH model implies low mean square error, low mean absolute error, low bias proportion, and low variance proportion for share volume data with comparing to other models. Hence, the modelling concept established in this study would be a decisive study for the investors as well as the researchers.
文摘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.
文摘This paper examines the forecasting performance of different kinds of GARCH model （GRACH, EGARCH, TARCH and APARCH） under the Normal, Student-t and Generalized error distributional assumption. We compare the effect of different distributional assumption on the GARCH models. The data we analyze are the daily stocks indexes for Shenzhen Stock Exchange （SSE） in China from April 3^rd, 1991 to April 14^th, 2005. We find that improvements of the overall estimation are achieved when asymmetric GARCH models are used with student-t distribution and generalized error distribution. Moreover, it is found that TARCH and GARCH models give better forecasting performance than EGARCH and APARCH models. In forecasting performance, the model under normal distribution gives more accurate forecasting performance than non-normal densities and generalized error distributions clearly outperform the student-t densities in case of SSE.
文摘This paper mainly through the comparison of GARCH-VaR China stock market board,small board and gem in the United States correspond to the three stock index volatility,volatility between stock indexes obtained U.S.stock market volatility risk multi-level market differences.As a suggestion and reference for investors,it can also provide reference for the supervision department of stock market risk.Based on the empirical research,analyzes the advantages and disadvantages of traditional risk measurement methods,and combined with GARCH model with high degree of complexity and the practice effect analysis,trying to find the objective measure stock model analysis.In the specific study of the volatility of the stock market,through the comparison of China’s three major plates and the market classification mechanism of mature U.S.stock market,combined with the objective situation of the market,draw conclusions and change expectations.From the empirical results,the U.S.stock market has recovered after the financial crisis,and its performance on risk volatility is better than China’s three major plates.From the comparison of the stock market in the same country,the small and medium-sized plates tend to have greater risks,while the risks of the main board and the gem have the characteristics of low average value but frequent fluctuations.
文摘The financial market is the core of national economic development,and stocks play an important role in the financial market.Analyzing stock prices has become the focus of investors,analysts,and people in related fields.This paper evaluates the volatility of Apple Inc.(AAPL)returns using five generalized autoregressive conditional heteroskedasticity(GARCH)models:sGARCH with constant mean,GARCH with sstd,GJR-GARCH,AR(1)GJR-GARCH,and GJR-GARCH in mean.The distribution of AAPL’s closing price and earnings data was analyzed,and skewed student t-distribution(sstd)and normal distribution(norm)were used to further compare the data distribution of the five models and capture the shape,skewness,and loglikelihood in Model 4-AR(1)GJR-GARCH.Through further analysis,the results showed that Model 4,AR(1)GJR-GARCH,is the optimal model to describe the volatility of the return series of AAPL.The analysis of the research process is both,a process of exploration and reflection.By analyzing the stock price of AAPL,we reflect on the shortcomings of previous analysis methods,clarify the purpose of the experiment,and identify the optimal analysis model.
文摘Since the establishment of financial models for risk prediction,the measurement of volatility at risky market has improved,and its significance has also grown.For high-frequency financial data,the degree of investment risk,which has always been the focus of attention,is measured by the variance of residual sequence obtained following model regression.By integrating the long short-term memory(LSTM)model with multiple generalized autoregressive conditional heteroscedasticity(GARCH)models,a new hybrid LSTM model is used to predict stock price volatility.In this paper,three GARCH models are used,and the model that can best fit the data is determined.
