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 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
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 agr...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
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
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
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
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
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 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.
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.
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.
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.
