ARCH model Research Papers - Academia.edu (original) (raw)

This paper examines both the benefits of choosing an internationally diversified portfolio and the evolution of the portfolio risk in the context of the current global financial crisis. The portfolio is comprised of three benchmark... more

This paper examines both the benefits of choosing an internationally diversified portfolio and the evolution of the portfolio risk in the context of the current global financial crisis. The portfolio is comprised of three benchmark indexes from Romania, UK and USA. Study results show that on the background of a global economic climate eroded strongly by the effects of the current financial crisis, international diversification does not reduce risk. Moreover, using ARCH and GARCH models shows that the evolution of portfolio volatility is influenced by the effects of the current global financial crisis.

Volatility in the stock return is an integral part of stock market with the alternating bull and bear phases. In the bullish market, the share prices soar high and in the bearish market share prices fall down and these ups and downs... more

Volatility in the stock return is an integral part of stock market with the alternating bull and bear phases. In the bullish market, the share prices soar high and in the bearish market share prices fall down and these ups and downs determine the return and volatility of the stock market. Volatility is a symptom of a highly liquid stock market. Volatility of returns in financial markets can be a major stumbling block for attracting investment. In this study, we use the Generalized Autoregressive Conditional Heteroskedasticity (GARCH) model to model volatility. The analysis was done using a time series data for the period 1st January 2008 to I0th April 2012 on 18 banks in India and empirical findings revealed that all banks stock return series reports an evidence of time varying volatility which exhibits clustering and high persistence.

We review the past 25 years of time series research that has been published in journals managed by the International Institute of Forecasters (Journal of Forecasting 1982 International Journal of Forecasting 1985. During this period, over... more

We review the past 25 years of time series research that has been published in journals managed by the International Institute of Forecasters (Journal of Forecasting 1982 International Journal of Forecasting 1985. During this period, over one third of all papers published in these journals concerned time series forecasting. We also review highly influential works on time series forecasting that have been published elsewhere during this period. Enormous progress has been made in many areas, but we find that there are a large number of topics in need of further development. We conclude with comments on possible future research directions in this field.

This paper provides a review of some recent theoretical results for time series models with GARCH errors, and is directed towards practitioners. Starting with the simple ARCH model and proceeding to the GARCH model, some results for... more

This paper provides a review of some recent theoretical results for time series models with GARCH errors, and is directed towards practitioners. Starting with the simple ARCH model and proceeding to the GARCH model, some results for stationary and nonstationary ARMA-GARCH are summarized. Various new ARCH-type models, including double threshold ARCH and GARCH, ARFIMA-GARCH, CHARMA and vector ARMA-GARCH, are also reviewed.

This paper extends the conventional Bayesian mixture of normals model by permitting state probabilities to depend on observed covariates. The dependence is captured by a simple multinomial probit model. A conventional and rapidly mixing... more

This paper extends the conventional Bayesian mixture of normals model by permitting state probabilities to depend on observed covariates. The dependence is captured by a simple multinomial probit model. A conventional and rapidly mixing MCMC algorithm provides access to the posterior distribution at modest computational cost. This model is competitive with existing econometric models, as documented in the paper's illustrations. The first illustration studies quantiles of the distribution of earnings of men conditional on age and education, and shows that smoothly mixing regressions are an attractive alternative to non-Baeysian quantile regression. The second illustration models serial dependence in the S&P 500 return, and shows that the model compares favorably with ARCH models using out of sample likelihood criteria.

This paper investigates several strategies for consistently estimating the so-called Hurst parameter H responsible for the long-memory correlations in a linear class of ARCH time series, known as LARCH models, as well as in the... more

This paper investigates several strategies for consistently estimating the so-called Hurst parameter H responsible for the long-memory correlations in a linear class of ARCH time series, known as LARCH models, as well as in the continuous-time Gaussian stochastic process named fractional Brownian motion (fBm). A LARCH model's parameter is estimated using a conditional maximum likelihood method, which is proved to be consistent, to allow model validation via a portmanteau theorem, and to have good stability properties. A local Whittle estimator is also discussed. By constructing the LARCH and fBm processes on a common probability space, and showing the convergence of various partial sums of the former to the latter in L 2 , the article is able to propose a specially designed conditional maximum likelihood method for estimating the fBm's Hurst parameter. In keeping with the popular nancial interpretation of ARCH models, all estimators are based only on observation of the \returns" of the model, not on their \volatilities".

The purpose of this report is to describe deployment of the Relay NBS Thoracic Stent Graft with the Plus Delivery System (Bolton Medical, Sunrise, FL) in a flexible resin arch model with a 15-mm radius curve as well as our preliminary... more

The purpose of this report is to describe deployment of the Relay NBS Thoracic Stent Graft with the Plus Delivery System (Bolton Medical, Sunrise, FL) in a flexible resin arch model with a 15-mm radius curve as well as our preliminary clinical results. The Relay NBS graft with the Plus Delivery System was evaluated by way of bench testing, which was performed with stent grafts with diameters ranging from 24 to 46 mm and lengths ranging from 100 to 250 mm in flexible resin arch models with a 15-mm arch radius of curvature. The deployment sequence was analyzed. The Relay NBS graft with the Plus Delivery System was deployed in two patients, respectively, having a 6.5-cm penetrating aortic ulcer of the proximal third of the descending thoracic aorta and a DeBakey type-I aortic dissection with chronic false lumen dilatation after surgery due to an entry site at the distal thoracic aorta. Bench tests showed proper conformation and apposition of the Relay NBS graft with the Plus Delivery System in the flexible resin model. This stent graft was deployed successfully into the two patients with a correct orientation of the first stent and without early or late complications. The Relay NBS graft with the Plus Delivery System ensures an optimal conformation and apposition of the first stent in the aortic arch with a small radius of curvature.

Preservation of architectural heritage is considered a fundamental issue in the cultural life of modern societies. In addition to their historical interest, monuments significantly contribute to the economy of cities and countries by... more

Preservation of architectural heritage is considered a fundamental issue in the cultural life of modern societies. In addition to their historical interest, monuments significantly contribute to the economy of cities and countries by providing key attractions. In this context, structural damage identification at an early stage plays an important role for heritage preservation.

This paper proposes spectral and asymmetric-volatility based methods for cluster analysis of stock returns. Using the information about both the periodogram of the squared returns and the estimated parameters in the TARCH equation, we... more

This paper proposes spectral and asymmetric-volatility based methods for cluster analysis of stock returns. Using the information about both the periodogram of the squared returns and the estimated parameters in the TARCH equation, we compute a distance matrix for the stock returns. Clusters are formed by looking to the hierarchical structure tree (or dendrogram) and the computed principal coordinates. We

It is well-known that financial data sets exhibit conditional heteroskedasticity. GARCH type models are often used to model this phenomenon. Since the distribution of the rescaled innovations is generally far from a normal distribution, a... more

It is well-known that financial data sets exhibit conditional heteroskedasticity. GARCH type models are often used to model this phenomenon. Since the distribution of the rescaled innovations is generally far from a normal distribution, a semiparametric approach is advisable. Several publications observed that adaptive estimation of the Euclidean parameters is not possible in the usual parametrization when the distribution of the rescaled innovations is the unknown nuisance parameter. However, there exists a reparametrization such that the efficient score functions in the parametric model of the autoregression parameters are orthogonal to the tangent space generated by the nuisance parameter, thus suggesting that adaptive estimation of the autoregression parameters is possible. Indeed, we construct adaptive and hence efficient estimators in a general GARCH in mean type context including integrated GARCH models.

Hétéroscedasticité, activité de marché, volatilité, causalité, modèles de durées

Resumo: Este trabalho objetiva mensurar a volatilidade dos preços futuros do açúcar negociados na BM&F, bem como verificar quais entre os modelos univariados propostos apresenta melhor desempenho preditivo para o preço da commodity em... more

Resumo: Este trabalho objetiva mensurar a volatilidade dos preços futuros do açúcar negociados na BM&F, bem como verificar quais entre os modelos univariados propostos apresenta melhor desempenho preditivo para o preço da commodity em questão. Para tanto se utilizam modelos de análise de volatilidade do tipo ARCH e modelos univariados de previsão aplicados a séries temporais, entre os quais os modelos ARIMA e SARIMA. Os resultados empíricos sugerem não haver presença de assimetria entre choques positivos e negativos e indicam a persistência na volatilidade dos preços do açúcar, implicando que os choques de volatilidade se dissiparão lentamente ao longo do tempo, podendo gerar perdas econômicas. Quanto aos modelos de previsão, o modelo ARIMA apresentou os menores valores para os critérios Akaike e Schwarz e para a soma dos quadrados dos resíduos. Porém o modelo SARIMA apresentou melhor ajuste teórico à série de preços do açúcar, bem como para o erro quadrado médio de previsão (EQM) ex-post. Palavras-chaves: preços do açúcar, modelos de previsão e volatilidade.

Most high-frequency asset returns exhibit seasonal volatility patterns. This article proposes a new class of models featuring periodicity in conditional heteroscedasticity explicitly designed to capture the repetitive seasonal time... more

Most high-frequency asset returns exhibit seasonal volatility patterns. This article proposes a new class of models featuring periodicity in conditional heteroscedasticity explicitly designed to capture the repetitive seasonal time variation in the second-order moments. ...

The financial crisis of 2007-2009 has questioned the provisions of Basel II agreement on capital adequacy requirements and the appropriateness of VaR measurement. This paper reconsiders the use of Value-at-Risk as a measure for potential... more

The financial crisis of 2007-2009 has questioned the provisions of Basel II agreement on capital adequacy requirements and the appropriateness of VaR measurement. This paper reconsiders the use of Value-at-Risk as a measure for potential risk of economic losses in financial markets by estimating VaR for daily stock returns with the application of various parametric univariate models that belong to the class of ARCH models which are based on the skewed Student distribution. We use daily data for three groups of stock market indices, namely Developed, Southeast Asia and Latin America. The data covers the period 1987-2009. We conduct our analysis with the adoption of the methodology suggested by Giot and Laurent (2003). Therefore, we estimate an APARCH model based on the skewed Student distribution to fully take into account the fat left and right tails of the returns distribution. The main finding of our analysis is that the skewed Student APARCH improves considerably the forecasts of one-day-ahead VaR for long and short trading positions. Additionally, we evaluate the performance of each model with the calculation of Kupie"s (1995) Likelihood Ratio test on the empirical failure test. Moreover, for the case of the skewed Student APARCH model we compute the expected shortfall and the average multiple of tail event to risk measure. These two measures help us to further assess the information we obtained from the estimation of the empirical failure rates.

The ARCH type of models is a notorious family of models proven to be suitable for predicting financial returns. Their notoriety flourished after Bollerslev (1986) developed the econometric Generalized ARCH model (GARCH). This paper... more

The ARCH type of models is a notorious family of models proven to be suitable for predicting financial returns. Their notoriety flourished after Bollerslev (1986) developed the econometric Generalized ARCH model (GARCH). This paper provides a presentation of the main characteristics of the modeling of financial returns with the objective to calibrate an EGARCH (Exponential GARCH) model for the logarithmic

We consider a model Yt=sigmatetatY\_t=\sigma\_t\eta\_tYt=sigmatetat in which (sigmat)(\sigma\_t)(sigmat) is not independent of the noise process (etat)(\eta\_t)(etat), but sigmat\sigma\_tsigmat is independent of etat\eta\_tetat for each ttt. We assume that (sigmat)(\sigma\_t)(sigmat) is stationary and we propose an... more

We consider a model Yt=sigmatetatY\_t=\sigma\_t\eta\_tYt=sigmatetat in which (sigmat)(\sigma\_t)(sigmat) is not independent of the noise process (etat)(\eta\_t)(etat), but sigmat\sigma\_tsigmat is independent of etat\eta\_tetat for each ttt. We assume that (sigmat)(\sigma\_t)(sigmat) is stationary and we propose an adaptive estimator of the density of ln(sigma2t)\ln(\sigma^2\_t)ln(sigma2t) based on the observations YtY\_tYt. Under various dependence structures, the rates of this nonparametric estimator coincide with the

2961 1. Introduction 2961 1.1. Definitions 2961 1.2. Empirical regularities of asset returns 2963 1.3. Univariate parametric models 2967 1.4. ARCH in mean models 2972 1.5. Nonparametric and semiparametric methods 2972 2. Inference... more

2961 1. Introduction 2961 1.1. Definitions 2961 1.2. Empirical regularities of asset returns 2963 1.3. Univariate parametric models 2967 1.4. ARCH in mean models 2972 1.5. Nonparametric and semiparametric methods 2972 2. Inference procedures 2974 2.1. Testing for ARCH 2974 2.2. Maximum likelihood methods 2977 2.3. Quasi-maximum likelihood methods 2983 2.4. Specification checks 2984

The performance of an ARCH model selection algorithm based on the standardized prediction error criterion (SPEC) is evaluated. The evaluation of the algorithm is performed by comparing different volatility forecasts in option pricing... more

The performance of an ARCH model selection algorithm based on the standardized prediction error criterion (SPEC) is evaluated. The evaluation of the algorithm is performed by comparing different volatility forecasts in option pricing through the simulation of an options market. Traders employing the SPEC model selection algorithm use the model with the lowest sum of squared standardized one-step-ahead prediction errors for obtaining their volatility forecast. The cumulative profits of the participants in pricing one-day index straddle options always using variance forecasts obtained by GARCH, EGARCH and TARCH models are compared to those made by the participants using variance forecasts obtained by models suggested by the SPEC algorithm. The straddles are priced on the Standard and Poor 500 (S & P 500) index. It is concluded that traders, who base their selection of an ARCH model on the SPEC algorithm, achieve higher profits than those, who use only a single ARCH model. Moreover, the SPEC algorithm is compared with other criteria of model selection that measure the ability of the ARCH models to forecast the realized intra-day volatility. In this case too, the SPEC algorithm users achieve the highest returns. Thus, the SPEC model selection method appears to be a useful tool in selecting the appropriate model for estimating future volatility in pricing derivatives.

This paper presents the R package AdMit which provides task of tuning a sam- pling algorithm. The relevance of the package is shown in two examples. The rst aims at illustrating in detail the use of the functions provided by the package... more

This paper presents the R package AdMit which provides task of tuning a sam- pling algorithm. The relevance of the package is shown in two examples. The rst aims at illustrating in detail the use of the functions provided by the package in a bivariate bimodal distribution. The second shows the relevance of the adaptive mixture procedure through the Bayesian

This paper proposes volatility and spectral based methods for cluster analysis of stock returns. Using the information about both the estimated parameters in the threshold GARCH (or TGARCH) equation and the periodogram of the squared... more

This paper proposes volatility and spectral based methods for cluster analysis of stock returns. Using the information about both the estimated parameters in the threshold GARCH (or TGARCH) equation and the periodogram of the squared returns, we compute a distance matrix for the stock returns. Clusters are formed by looking to the hierarchical structure tree (or dendrogram) and the computed principal coordinates. We employ these techniques to investigate the similarities and dissimilarities between the "bluechip" stocks used to compute the Dow Jones Industrial Average (DJIA) index.

Building models for high dimensional portfolios is important in risk management and asset allocation. Here we propose a novel and fast way of estimating models of time-varying covariances that overcome an undiagnosed incidental parameter... more

Building models for high dimensional portfolios is important in risk management and asset allocation. Here we propose a novel and fast way of estimating models of time-varying covariances that overcome an undiagnosed incidental parameter problem which has troubled existing methods when applied to hundreds or even thousands of assets. Indeed we can handle the case where the cross-sectional dimension is larger than the time series one. The theory of this new strategy is developed in some detail, allowing formal hypothesis testing to be carried out on these models. Simulations are used to explore the performance of this inference strategy while empirical examples are reported which show the strength of this method. The out of sample hedging performance of various models estimated using this method are compared.

Building models for high dimensional portfolios is important in risk management and asset allocation. Here we propose a novel and fast way of estimating models of time-varying covariances that overcome an undiagnosed incidental parameter... more

Building models for high dimensional portfolios is important in risk management and asset allocation. Here we propose a novel and fast way of estimating models of time-varying covariances that overcome an undiagnosed incidental parameter problem which has troubled existing methods when applied to hundreds or even thousands of assets. Indeed we can handle the case where the cross-sectional dimension is larger than the time series one. The theory of this new strategy is developed in some detail, allowing formal hypothesis testing to be carried out on these models. Simulations are used to explore the performance of this inference strategy while empirical examples are reported which show the strength of this method. The out of sample hedging performance of various models estimated using this method are compared.

Although volatility clustering has a long history as a salient empirical regularity characterizing high-frequency speculative prices, it was not until recently that applied researchers in finance have recognized the importance of... more

Although volatility clustering has a long history as a salient empirical regularity characterizing high-frequency speculative prices, it was not until recently that applied researchers in finance have recognized the importance of explicitly modeling time-varying second-order moments. Instrumental in most of these empirical studies has been the Autoregressive Conditional Heteroskedasticity (ARCH) model introduced by Engle (1982). This paper contains an overview of some of the developments in the formulation of ARCH models and a survey of the numerous empirical applications using financial data. Several suggestions for future research, including the implementation and tests of competing asset pricing theories, market microstructure models, information transmission mechanisms, dynamic hedging strategies, and the pricing of derivative assets, are also discussed.

The volatility clustering frequently observed in financial/economic time series is often ascribed to GARCH and/or stochastic volatility models. This paper demonstrates the usefulness of reconceptualizing the usual definition of... more

The volatility clustering frequently observed in financial/economic time series is often ascribed to GARCH and/or stochastic volatility models. This paper demonstrates the usefulness of reconceptualizing the usual definition of conditional heteroscedasticity as the (h = 1) special case of h-step-ahead conditional heteroscedasticity, where the conditional volatility in period t depends on observable variables up through period t-h. Here it is shown that, for h > 1, h-stepahead conditional heteroscedasticity arises-necessarily and endogenously-from nonlinear serial dependence in a time series; whereas one-step-ahead conditional heteroscedasticity (i.e., h = 1) requires multiple and heterogeneously-skedastic innovation terms. Consequently, the best response to observed volatility clustering may often be to model the nonlinear serial dependence which is likely causing it, rather than 'tacking on' an ad hoc volatility model. Even where such nonlinear modeling is infeasible-or where volatility is quantified using, say, a model-free implied volatility measure rather than squared returns-these results suggest a reconsideration of the usefulness of lag-one terms in volatility models. An application to observed daily stock returns is given.

The uctuation of a bilateral exchange rate in a target zone is often chosen as part of oÆcial agreements between two or more countries (such as in the European Monetary System { EMS) or of informal unilateral monetary policy packages a... more

The uctuation of a bilateral exchange rate in a target zone is often chosen as part of oÆcial agreements between two or more countries (such as in the European Monetary System { EMS) or of informal unilateral monetary policy packages a country adopts for itself. The defendability of such a regime in the face of asymmetric shocks is always an issue. In this paper, we examine a long period in the life of the EMS and we argue that the increase in volatility in the interest rates could help identifying periods of possible impending crisis for the exchange rates. Our framework provides a way to put to test the quality of the reaction by monetary authorities and to relate perceived weakness to subsequent episodes of realignment in the central parity. We examine ten years of Italian Lira one month Eurodeposit daily between 1983 and 1993 addressing three empirical questions: 1. Is interest rate volatility a measure of the perceived degree of vulnerability of the institutional agreements and...

We compare density forecasts of the S&P 500 index from 1991 to 2004, obtained from option prices and daily and 5-min index returns. Risk-neutral densities are given by using option prices to estimate diffusion and jump-diffusion processes... more

We compare density forecasts of the S&P 500 index from 1991 to 2004, obtained from option prices and daily and 5-min index returns. Risk-neutral densities are given by using option prices to estimate diffusion and jump-diffusion processes which incorporate stochastic volatility. Three transformations are then used to obtain real-world densities. These densities are compared with historical densities defined by ARCH models. For horizons of two and four weeks the best forecasts are obtained from risk-transformations of the risk-neutral densities, while the historical forecasts are superior for the one-day horizon; our ranking criterion is the out-of-sample likelihood of observed index levels. Mixtures of the real-world and historical densities have higher likelihoods than both components for short forecast horizons.

As it is possible to model both linear and nonlinear structures in time series by using Artificial Neural Network (ANN), it is suitable to apply this method to the chaotic series having nonlinear component. Therefore, in this study, we... more

As it is possible to model both linear and nonlinear structures in time series by using Artificial Neural Network (ANN), it is suitable to apply this method to the chaotic series having nonlinear component. Therefore, in this study, we propose to employ ANN method for high volatility ...

We study the activity, i.e., the number of transactions per unit time, of financial markets. Using the diffusion entropy technique we show that the autocorrelation of the activity is caused by the presence of peaks whose time distances... more

We study the activity, i.e., the number of transactions per unit time, of financial markets. Using the diffusion entropy technique we show that the autocorrelation of the activity is caused by the presence of peaks whose time distances are distributed following an asymptotic power law which ultimately recovers the Poissonian behavior. We discuss these results in comparison with ARCH models, stochastic volatility models and multi-agent models showing that ARCH and stochastic volatility models better describe the observed experimental evidences.

v. 2, n. 3, art. 9, p. 509-530, Set./Dez. 2008 www.anpad.org.br/rac-e 510 R R R RESUMO ESUMO ESUMO ESUMO O presente trabalho tem como objetivo apresentar e testar uma modificação no tradicional modelo de Multifatores de Fama e French... more

v. 2, n. 3, art. 9, p. 509-530, Set./Dez. 2008 www.anpad.org.br/rac-e 510 R R R RESUMO ESUMO ESUMO ESUMO O presente trabalho tem como objetivo apresentar e testar uma modificação no tradicional modelo de Multifatores de Fama e French (1996), a partir das necessidades de adaptação para o caso brasileiro. Este modelo leva em consideração duas anomalias que devem ser acrescentadas ao Modelo CAPM, que são o tamanho e o índice book-to-market. Aqui fizemos uma aplicação aos resultados apresentados por 205 ações negociadas na BOVESPA, e também realizamos uma modificação no modelo original, a partir da verificação de problemas de pressupostos que necessitariam de correções. Incorporamos então parâmetros dos Modelos ARCH e GARCH. Os resultados encontrados demonstram que os modelos auto-regressivos heterocedásticos podem ser utilizados para a melhoria do modelo original de Fama e French (1996), quando aplicados ao mercado brasileiro. As conclusões do trabalho também indicam que essas modificações no modelo apresentam resultados estatisticamente significativos, na maioria dos casos, corroborando o que foi sugerido pelos testes realizados. Palavras-chave: modelo de Fama e French; mercados emergentes, BOVESPA, modelo ARCH, eficiência de mercado.

In this paper we conduct a close examination of the relationship between return shocks and conditional volatility. We do so in a framework where the impact of return shocks on conditional volatility is specified as a general function and... more

In this paper we conduct a close examination of the relationship between return shocks and conditional volatility. We do so in a framework where the impact of return shocks on conditional volatility is specified as a general function and estimated nonparametrically using implied volatility data -the Market Volatility Index (VIX). This setup can provide a good description of the impact of return shocks on conditional volatility, and it appears that the news impact curves implied by the VIX data are useful in selecting ARCH specifications at the weekly frequency. We find that the Exponential ARCH model of Nelson [Econometrica 59 (1991) 347] is capable of capturing most of the asymmetric effect, when return shocks are relatively small. For large negative shocks, our nonparametric function points to larger increases in conditional volatility than those predicted by a standard EGARCH. Our empirical analysis further demonstrates that an EGARCH model with separate coefficients for large and small negative shocks is better able to capture the asymmetric effect. D 2002 Elsevier Science B.V. All rights reserved. JEL classification: G10; C14 Keywords: Asymmetric volatility; News impact curve 0927-5398/02/$ -see front matter D 2002 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 7 -5 3 9 8 ( 0 1 ) 0 0 0 5 7 -3

A number of ARCH models are considered in the framework of evaluating the performance of a method for model selection based on a standardized prediction error criterion (SPEC). According to this method, the ARCH model with the lowest sum... more

A number of ARCH models are considered in the framework of evaluating the performance of a method for model selection based on a standardized prediction error criterion (SPEC). According to this method, the ARCH model with the lowest sum of squared standardized forecasting errors is selected for predicting future volatility. A number of statistical criteria, that measure the distance between predicted and inter-day realized volatility, are used to examine the performance of a model to predict future volatility, for forecasting horizons ranging from one day to 100 days ahead. The results reveal that the SPEC model selection procedure has a satisfactory performance in picking that model that generates 'better' volatility predictions. A comparison of the SPEC algorithm with a set of other model evaluation criteria yields similar findings. It appears, therefore, that it can be regarded as a tool in guiding the choice of the appropriate model for predicting future volatility, with applications in evaluating portfolios, managing financial risk and creating speculative strategies with options.

The seminal study by initiated a stream of papers testing for the cross-sectional relation between return and risk. The debate whether beta is a valid measure of risk has been reanimated by and subsequent studies. Rather than focusing on... more

The seminal study by initiated a stream of papers testing for the cross-sectional relation between return and risk. The debate whether beta is a valid measure of risk has been reanimated by and subsequent studies. Rather than focusing on exogenous variables that have a larger explanatory power than an asset's beta in cross sectional tests, we assume the matrix of variances-covariances to follow a time varying ARCH process. Using monthly data from the UK market from February 1975 to December 1996, we compare the cross sectional return-risk relations obtained with an unconditional specification for assets' betas to those obtained when the estimated betas are based on an ARCH model. We also investigate the Pettengill, approach, which allows a negative cross sectional return-risk relation in periods in which the market portfolio yields a negative return relative to the risk free rate. These tests are also carried out on samples pertaining to a specific month and on samples from which a particular month is removed. Our results suggest that CAPM holds better in downward moving markets than in upward moving markets hence beta is a more appropriate measure of risk in bear markets.

Motivated by studying asymptotic properties of the maximum likelihood estimator (MLE) in stochastic volatility (SV) models, in this paper we investigate likelihood estimation in state space models. We first prove, under some regularity... more

Motivated by studying asymptotic properties of the maximum likelihood estimator (MLE) in stochastic volatility (SV) models, in this paper we investigate likelihood estimation in state space models. We first prove, under some regularity conditions, there is a consistent sequence of roots of the likelihood equation that is asymptotically normal with the inverse of the Fisher information as its variance. With an extra assumption that the likelihood equation has a unique root for each n, then there is a consistent sequence of estimators of the unknown parameters. If, in addition, the supremum of the log likelihood function is integrable, the MLE exists and is strongly consistent. Edgeworth expansion of the approximate solution of likelihood equation is also established. Several examples, including Markov switching models, ARMA models, (G)ARCH models and stochastic volatility (SV) models, are given for illustration.

Reçu le 13 novembre 1998, accepté après révision le 13 avril 2000) Résumé. Nous étudions une classe de modèles ARCH dont les paramètres dépendent d'une chaîne de Markov non observée. Nous donnons des conditions nécessaires et suffisantes... more

Reçu le 13 novembre 1998, accepté après révision le 13 avril 2000) Résumé. Nous étudions une classe de modèles ARCH dont les paramètres dépendent d'une chaîne de Markov non observée. Nous donnons des conditions nécessaires et suffisantes de stationnarité. Nous étudions ensuite la convergence de l'estimateur du maximum de vraisemblance et le problème de l'identification du nombre d'états de la chaîne.

Asymptotic properties of the quasi-maximum likelihood estimator (QMLE) for non-linear ARCH(q) models -including for example Asymmetric Power ARCH and log-ARCH -are derived. Strong consistency is established under the assumptions that the... more

Asymptotic properties of the quasi-maximum likelihood estimator (QMLE) for non-linear ARCH(q) models -including for example Asymmetric Power ARCH and log-ARCH -are derived. Strong consistency is established under the assumptions that the ARCH process is geometrically ergodic, the conditional variance function has a …nite logmoment, and …nite second moment of the rescaled error. Asymptotic normality of the estimator is established under the additional assumption that certain ratios involving the conditional variance function are suitably bounded, and that the rescaled errors have little more than fourth moment. We verify our general conditions, including identi…cation, for a wide range of leading speci…c ARCH models.

We argue a source of time-varying term premium (TVTP) in Japanese government bond market, and show that it is interest rate smoothing that causes empirical failures of expectation theory of term structure of interest rates. We estimate a... more

We argue a source of time-varying term premium (TVTP) in Japanese government bond market, and show that it is interest rate smoothing that causes empirical failures of expectation theory of term structure of interest rates. We estimate a regime switching ARCH model where an interest rate smoothing regime can be identified. Based on a model of time-inconsistency by Missale and Blanchard (1994), we further focus on a role of debt maturity in TVTP, which is an alternative to an ARCH process.

In this paper we test for Generalized AutoRegressive Conditional Heteroskedasticity GARCH in daily data on 22 exchange rates and 13 stock market indices using the standard Lagrange Multiplier LM test for GARCH and a LM test that is... more

In this paper we test for Generalized AutoRegressive Conditional Heteroskedasticity GARCH in daily data on 22 exchange rates and 13 stock market indices using the standard Lagrange Multiplier LM test for GARCH and a LM test that is resistant to patches of additive outliers. The data span two samples of 5 years ranging from 1986 to 1995. Using asymptotic arguments and Monte Carlo simulations, in which w e evaluate our empirical method, we show that patches of outliers can have signi cant e ects on test outcomes. Our main empirical result is that we nd spurious GARCH in about 40 of the cases, while in many other cases we nd evidence of GARCH even though such sequences of extraordinary observations seem to be present.

We evaluate the performance of an extensive family of ARCH models in modelling daily Valueat-Risk (VaR) of perfectly diversified portfolios in five stock indices, using a number of distributional assumptions and sample sizes. We find,... more

We evaluate the performance of an extensive family of ARCH models in modelling daily Valueat-Risk (VaR) of perfectly diversified portfolios in five stock indices, using a number of distributional assumptions and sample sizes. We find, first, that leptokurtic distributions are able to produce better one-step-ahead VaR forecasts; second, the choice of sample size is important for the accuracy of the forecast, whereas the specification of the conditional mean is indifferent. Finally, the ARCH structure producing the most accurate forecasts is different for every portfolio and specific to each equity index.