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1.
    
This paper investigates inference and volatility forecasting using a Markov switching heteroscedastic model with a fat‐tailed error distribution to analyze asymmetric effects on both the conditional mean and conditional volatility of financial time series. The motivation for extending the Markov switching GARCH model, previously developed to capture mean asymmetry, is that the switching variable, assumed to be a first‐order Markov process, is unobserved. The proposed model extends this work to incorporate Markov switching in the mean and variance simultaneously. Parameter estimation and inference are performed in a Bayesian framework via a Markov chain Monte Carlo scheme. We compare competing models using Bayesian forecasting in a comparative value‐at‐risk study. The proposed methods are illustrated using both simulations and eight international stock market return series. The results generally favor the proposed double Markov switching GARCH model with an exogenous variable. Copyright © 2008 John Wiley & Sons, Ltd.  相似文献   

2.
    
This paper examined the forecasting performance of disaggregated data with spatial dependency and applied it to forecasting electricity demand in Japan. We compared the performance of the spatial autoregressive ARMA (SAR‐ARMA) model with that of the vector autoregressive (VAR) model from a Bayesian perspective. With regard to the log marginal likelihood and log predictive density, the VAR(1) model performed better than the SAR‐ARMA( 1,1) model. In the case of electricity demand in Japan, we can conclude that the VAR model with contemporaneous aggregation had better forecasting performance than the SAR‐ARMA model. Copyright © 2011 John Wiley & Sons, Ltd.  相似文献   

3.
    
Value‐at‐risk (VaR) forecasting via a computational Bayesian framework is considered. A range of parametric models is compared, including standard, threshold nonlinear and Markov switching generalized autoregressive conditional heteroskedasticity (GARCH) specifications, plus standard and nonlinear stochastic volatility models, most considering four error probability distributions: Gaussian, Student‐t, skewed‐t and generalized error distribution. Adaptive Markov chain Monte Carlo methods are employed in estimation and forecasting. A portfolio of four Asia–Pacific stock markets is considered. Two forecasting periods are evaluated in light of the recent global financial crisis. Results reveal that: (i) GARCH models outperformed stochastic volatility models in almost all cases; (ii) asymmetric volatility models were clearly favoured pre crisis, while at the 1% level during and post crisis, for a 1‐day horizon, models with skewed‐t errors ranked best, while integrated GARCH models were favoured at the 5% level; (iii) all models forecast VaR less accurately and anti‐conservatively post crisis. Copyright © 2011 John Wiley & Sons, Ltd.  相似文献   

4.
    
We consider a Bayesian model averaging approach for the purpose of forecasting Swedish consumer price index inflation using a large set of potential indicators, comprising some 80 quarterly time series covering a wide spectrum of Swedish economic activity. The paper demonstrates how to efficiently and systematically evaluate (almost) all possible models that these indicators in combination can give rise to. The results, in terms of out‐of‐sample performance, suggest that Bayesian model averaging is a useful alternative to other forecasting procedures, in particular recognizing the flexibility by which new information can be incorporated. Copyright © 2004 John Wiley & Sons, Ltd.  相似文献   

5.
Whitlock and Queen (1998) developed a dynamic graphical model for forecasting traffic flows at a number of sites at a busy traffic junction in Kent, UK. Some of the data collection sites at this junction have been faulty over the data collection period and so there are missing series in the multivariate problem. Here we adapt the model developed in Whitlock and Queen ( 1998 ) to accommodate these missing data. Markov chain Monte Carlo methods are used to provide forecasts of the missing series, which in turn are used to produce forecasts for some of the other series. The methods are used on part of the network and shown to be very promising. Copyright © 2000 John Wiley & Sons, Ltd.  相似文献   

6.
    
Testing the validity of value‐at‐risk (VaR) forecasts, or backtesting, is an integral part of modern market risk management and regulation. This is often done by applying independence and coverage tests developed by Christoffersen (International Economic Review, 1998; 39(4), 841–862) to so‐called hit‐sequences derived from VaR forecasts and realized losses. However, as pointed out in the literature, these aforementioned tests suffer from low rejection frequencies, or (empirical) power when applied to hit‐sequences derived from simulations matching empirical stylized characteristics of return data. One key observation of the studies is that higher‐order dependence in the hit‐sequences may cause the observed lower power performance. We propose to generalize the backtest framework for VaR forecasts, by extending the original first‐order dependence of Christoffersen to allow for a higher‐ or kth‐order dependence. We provide closed‐form expressions for the tests as well as asymptotic theory. Not only do the generalized tests have power against kth‐order dependence by definition, but also included simulations indicate improved power performance when replicating the aforementioned studies. Further, included simulations show much improved size properties of one of the suggested tests. Copyright © 2017 John Wiley & Sons, Ltd.  相似文献   

7.
    
The paper derives the scalar special case of the well‐known BEKK multivariate GARCH model using a multivariate extension of the random coefficient autoregressive (RCA) model. This representation establishes the relevant structural and asymptotic properties of the scalar BEKK model using the theoretical results available in the literature for general multivariate GARCH. Sufficient conditions for the (direct) DCC model to be consistent with a scalar BEKK representation are established. Moreover, an indirect DCC model that is consistent with the scalar BEKK representation is obtained, and is compared with the direct DCC model using an empirical example. The paper shows, within an asset allocation and risk measurement framework, that the two models are similar in terms of providing parameter estimates and forecasting value‐at‐risk thresholds for equally weighted and minimum variance portfolios. Copyright © 2008 John Wiley & Sons, Ltd.  相似文献   

8.
    
Reliable correlation forecasts are of paramount importance in modern risk management systems. A plethora of correlation forecasting models have been proposed in the open literature, yet their impact on the accuracy of value‐at‐risk calculations has not been explicitly investigated. In this paper, traditional and modern correlation forecasting techniques are compared using standard statistical and risk management loss functions. Three portfolios consisting of stocks, bonds and currencies are considered. We find that GARCH models can better account for the correlation's dynamic structure in the stock and bond portfolios. On the other hand, simpler specifications such as the historical mean model or simple moving average models are better suited for the currency portfolio. Copyright © 2007 John Wiley & Sons, Ltd.  相似文献   

9.
    
This paper compares daily exchange rate value at risk estimates derived from econometric models with those implied by the prices of traded options. Univariate and multivariate GARCH models are employed in parallel with the simple historical and exponentially weighted moving average methods. Overall, we find that during periods of stability, the implied model tends to overestimate value at risk, hence over‐allocating capital. However, during turbulent periods, it is less responsive than the GARCH‐type models, resulting in an under‐allocation of capital and a greater number of failures. Hence our main conclusion, which has important implications for risk management, is that market expectations of future volatility and correlation, as determined from the prices of traded options, may not be optimal tools for determining value at risk. Therefore, alternative models for estimating volatility should be sought. Copyright © 2004 John Wiley & Sons, Ltd.  相似文献   

10.
The paper deals with unobserved components in ARIMA models with GARCH errors, in the context of an actual application, namely seasonal adjustment of the monthly Spanish money supply series. The series shows clear evidence of (moderate) non-linearity, which does not disappear with simple outlier correction. The GARCH structure explains reasonably well the non-linearity, and this explanation is robust with respect to the GARCH specification. We look at the time variation of the standard error of the adjusted series estimator and show how it can be measured. Next, we look at the implications this variation has on short-term monetary control. The non-linearity seems to have a small effect in practice. It is further seen that the conditional variance of the GARCH process may, in turn, be decomposed into components. In fact, the conditional variance of the money supply series is the sum of a weak linear trend, a strong non-linear seasonal component, and a moderate non-linear irregular component. This information has policy implications: for example, there are periods in the year when policy can be more assertive because information is more precise. Finally, looking at the non-linear components of the money supply it is seen how linear combinations of non-linear series can produce series that behave linearly.  相似文献   

11.
    
In examining stochastic models for commodity prices, central questions often revolve around time‐varying trend, stochastic convenience yield and volatility, and mean reversion. This paper seeks to assess and compare alternative approaches to modelling these effects, with focus on forecast performance. Three specifications are considered: (i) random‐walk models with GARCH and normal or Student‐t innovations; (ii) Poisson‐based jump‐diffusion models with GARCH and normal or Student‐t innovations; and (iii) mean‐reverting models that allow for uncertainty in equilibrium price. Our empirical application makes use of aluminium spot and futures price series at daily and weekly frequencies. Results show: (i) models with stochastic convenience yield outperform all other competing models, and for all forecast horizons; (ii) the use of futures prices does not always yield lower forecast error values compared to the use of spot prices; and (iii) within the class of (G)ARCH random‐walk models, no model uniformly dominates the other. Copyright © 2008 John Wiley & Sons, Ltd.  相似文献   

12.
    
This article develops a new method for detrending time series. It is shown how, in a Bayesian framework, a generalized version of the Hodrick–Prescott filter is obtained by specifying prior densities on the signal‐to‐noise ratio (q) in the underlying unobserved components model. This helps ensure an appropriate degree of smoothness in the estimated trend while allowing for uncertainty in q. The article discusses the important issue of prior elicitation for time series recorded at different frequencies. By combining prior expectations with the likelihood, the Bayesian approach permits detrending in a way that is more consistent with the properties of the series. The method is illustrated with some quarterly and annual US macroeconomic series. Copyright © 2006 John Wiley & Sons, Ltd.  相似文献   

13.
    
We propose in this paper a threshold nonlinearity test for financial time series. Our approach adopts reversible‐jump Markov chain Monte Carlo methods to calculate the posterior probabilities of two competitive models, namely GARCH and threshold GARCH models. Posterior evidence favouring the threshold GARCH model indicates threshold nonlinearity or volatility asymmetry. Simulation experiments demonstrate that our method works very well in distinguishing GARCH and threshold GARCH models. Sensitivity analysis shows that our method is robust to misspecification in error distribution. In the application to 10 market indexes, clear evidence of threshold nonlinearity is discovered and thus supporting volatility asymmetry. Copyright © 2005 John Wiley & Sons, Ltd.  相似文献   

14.
    
We analyze multicategory purchases of households by means of heterogeneous multivariate probit models that relate to partitions formed from a total of 25 product categories. We investigate both prior and post hoc partitions. We search model structures by a stochastic algorithm and estimate models by Markov chain Monte Carlo simulation. The best model in terms of cross‐validated log‐likelihood refers to a post hoc partition with two groups; the second‐best model considers all categories as one group. Among prior partitions with at least two category groups a five‐group model performs best. Effects on average basket value differ for the model with five prior category groups from those for the best‐performing model in 40% and 24% of the investigated categories for features and displays, respectively. In addition, the model with five prior category groups also underestimates total sales revenue across all categories by about 28%. Copyright © 2016 John Wiley & Sons, Ltd.  相似文献   

15.
    
This paper proposes a parsimonious threshold stochastic volatility (SV) model for financial asset returns. Instead of imposing a threshold value on the dynamics of the latent volatility process of the SV model, we assume that the innovation of the mean equation follows a threshold distribution in which the mean innovation switches between two regimes. In our model, the threshold is treated as an unknown parameter. We show that the proposed threshold SV model can not only capture the time‐varying volatility of returns, but can also accommodate the asymmetric shape of conditional distribution of the returns. Parameter estimation is carried out by using Markov chain Monte Carlo methods. For model selection and volatility forecast, an auxiliary particle filter technique is employed to approximate the filter and prediction distributions of the returns. Several experiments are conducted to assess the robustness of the proposed model and estimation methods. In the empirical study, we apply our threshold SV model to three return time series. The empirical analysis results show that the threshold parameter has a non‐zero value and the mean innovations belong to two separately distinct regimes. We also find that the model with an unknown threshold parameter value consistently outperforms the model with a known threshold parameter value. Copyright © 2016 John Wiley & Sons, Ltd.  相似文献   

16.
    
This research incorporates realized volatility and overnight information into risk models, wherein the overnight return often contributes significantly to the total return volatility. Extending a semiparametric regression model based on asymmetric Laplace distribution, we propose a family of RES-CAViaR-oc models by adding overnight return and realized measures as a nowcasting technique for simultaneously forecasting Value-at-Risk (VaR) and expected shortfall (ES). We utilize Bayesian methods to estimate unknown parameters and forecast VaR and ES jointly for the proposed model family. We also conduct extensive backtests based on joint elicitability of the pair of VaR and ES during the out-of-sample period. Our empirical study on four international stock indices confirms that overnight return and realized volatility are vital in tail risk forecasting.  相似文献   

17.
    
This study investigates the forecasting performance of the GARCH(1,1) model by adding an effective covariate. Based on the assumption that many volatility predictors are available to help forecast the volatility of a target variable, this study shows how to construct a covariate from these predictors and plug it into the GARCH(1,1) model. This study presents a method of building a covariate such that the covariate contains the maximum possible amount of predictor information of the predictors for forecasting volatility. The loading of the covariate constructed by the proposed method is simply the eigenvector of a matrix. The proposed method enjoys the advantages of easy implementation and interpretation. Simulations and empirical analysis verify that the proposed method performs better than other methods for forecasting the volatility, and the results are quite robust to model misspecification. Specifically, the proposed method reduces the mean square error of the GARCH(1,1) model by 30% for forecasting the volatility of S&P 500 Index. The proposed method is also useful in improving the volatility forecasting of several GARCH‐family models and for forecasting the value‐at‐risk. Copyright © 2013 John Wiley & Sons, Ltd.  相似文献   

18.
    
The variance of a portfolio can be forecast using a single index model or the covariance matrix of the portfolio. Using univariate and multivariate conditional volatility models, this paper evaluates the performance of the single index and portfolio models in forecasting value‐at‐risk (VaR) thresholds of a portfolio. Likelihood ratio tests of unconditional coverage, independence and conditional coverage of the VaR forecasts suggest that the single‐index model leads to excessive and often serially dependent violations, while the portfolio model leads to too few violations. The single‐index model also leads to lower daily Basel Accord capital charges. The univariate models which display correct conditional coverage lead to higher capital charges than models which lead to too many violations. Overall, the Basel Accord penalties appear to be too lenient and favour models which have too many violations. Copyright © 2008 John Wiley & Sons, Ltd.  相似文献   

19.
    
A new clustered correlation multivariate generalized autoregressive conditional heteroskedasticity (CC‐MGARCH) model that allows conditional correlations to form clusters is proposed. This model generalizes the time‐varying correlation structure of Tse and Tsui (2002, Journal of Business and Economic Statistics 20 : 351–361) by classifying the correlations among the series into groups. To estimate the proposed model, Markov chain Monte Carlo methods are adopted. Two efficient sampling schemes for drawing discrete indicators are also developed. Simulations show that these efficient sampling schemes can lead to substantial savings in computation time in Monte Carlo procedures involving discrete indicators. Empirical examples using stock market and exchange rate data are presented in which two‐cluster and three‐cluster models are selected using posterior probabilities. This implies that the conditional correlation equation is likely to be governed by more than one set of decaying parameters. Copyright © 2011 John Wiley & Sons, Ltd.  相似文献   

20.
    
Focusing on the interdependence of product categories we analyze multicategory buying decisions of households by a finite mixture of multivariate Tobit‐2 models with two response variables: purchase incidence and expenditure. Mixture components can be interpreted as household segments. Correlations for purchases of different categories turn out to be much more important than correlations among expenditures as well as correlations among purchases and expenditures of different categories. About 18% of all pairwise purchase correlations are significant. We compare the best‐performing large‐scale model with 28 categories to four small‐scale models each with seven categories. In our empirical study the large‐scale model clearly attains a better forecasting performance. The small‐scale models provide several biased correlations and miss about 50% of the significant correlations which the large scale model detects. Copyright © 2013 John Wiley & Sons, Ltd.  相似文献   

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