This paper presents theoretical results in the formulation and estimation of multivariate gen- eralized ARCH models within simultaneous equations systems. A new parameterization of the multivariate ARCH process is proposed and equivalence relations are discussed for the various ARCH parameterizations. Constraints suffcient to guarantee the positive deffniteness of the con- ditional covariance matrices are developed, and necessary and suffcient conditions for covariance stationarity are presented. Identifcation and maximum likelihood estimation of the parameters in the simultaneous equations context are also covered.

https://www.jstor.org/stable/pdfplus/3532933.pdf

Multivariate Simultaneous Generalized ARCH

ARCH modeling in finance: A review of the theory and empirical evidence

A multivariate time series model with time varying conditional variances and covariances but with constant conditional correlations is proposed. In a multivariate regression framework, the model is readily interpreted as an extension of the seemingly unrelated regression (SUR) model allowing for heteroskedasticity. Each of the conditional variances are parameterized as a univariate generalized autoregressive conditional heteroskedastic (GARCH) process. The descriptive validity of the model is illustrated for a set of 5 nominal European-US dollar exchange rates following the inception of the European Monetary System (EMS). EMS results are compared to estimates obtained for the same model using data over the pre-EMS period, July 1973 to March 1979. When compared to the pre-EMS free float period, the comovements between the currencies are found to be significantly higher over the later period.

Modelling the Coherence in Short-run Nominal Exchange Rates: A Multivariate Generalized ARCH Model.

We study the properties of the quasi-maximum likelihood estimator (QMLE) and related test statistics in dynamic models that jointly parameterize conditional means and conditional covariances, when a normal log-likelihood os maximized but the assumption of normality is violated. Because the score of the normal log-likelihood has the martingale difference property when the forst two conditional moments are correctly specified, the QMLE is generally Consistent and has a limiting normal destribution. We provide easily computable formulas for asymptotic standard errors that are valid under nonnormality. Further, we show how robust LM tests for the adequacy of the jointly parameterized mean and variance can be computed from simple auxiliary regressions. An appealing feature of these robyst inference procedures is that only first derivatives of the conditional mean and variance functions are needed. A monte Carlo study indicates that the asymptotic results carry over to finite samples. Estimation of several AR a...

/pdf/quasi-maximum-likelihood-estimation-and-inference-in-dynamic-437k6nnyca.pdf

Quasi-maximum likelihood estimation and inference in dynamic models with time-varying covariances

A voluminous literature has emerged for modeling the temporal dependencies in financial market volatility using ARCH and stochastic volatility models. While most of these studies have documented highly significant in-sample parameter estimates and pronounced intertemporal volatility persistence, traditional ex-post forecast evaluation criteria suggest that the models provide seemingly poor volatility forecasts. Contrary to this contention, we show that volatility models produce strikingly accurate interdaily forecasts for the latent volatility factor that would be of interest in most financial applications. New methods for improved ex-post interdaily volatility measurements based on high-frequency intradaily data are also discussed.

https://faculty.washington.edu/ezivot/econ589//////AndersenBollerslevIER1998.pdf

Answering the skeptics: yes, standard volatility models do provide accurate forecasts*

This paper models different components of the return distribution which are assumed to be directed by a latent news process. The conditional variance of returns is a combination of jumps and smoothly changing components. This mixture captures occasional large changes in price, due to the impact of news innovations such as earnings surprises, as well as smoother changes in prices which can result from liquidity trading or strategic trading as information disseminates. Unlike typical SV-jump models, previous realizations of both jump and normal innovations can feedback asymmetrically into expected volatility. This is a new source of asymmetry (in addition to good versus bad news) that improves forecasts of volatility particularly after large moves such as the '87 crash. A heterogeneous Poisson process governs the likelihood of jumps and is summarized by a time-varying conditional intensity parameter. The model is applied to returns from individual companies and three indices. We provide empirical evidence of the impact and feedback effects of jump versus normal return innovations, contemporaneous and lagged leverage effects, the time-series dynamics of jump clustering, and the importance of modeling the dynamics of jumps around high volatility episodes.

News Arrival, Jump Dynamics and Volatility Components for Individual Stock Returns

This paper models dierent components of the return distribution which are assumed to be directed by a latent news process. The conditional variance of returns is a combination of jumps and smoothly changing components. This mixture captures occasional large changes in price, due to the impact of news innovations such as earnings surprises, as well as smoother changes in prices which can result from liquidity trading or strategic trading as information disseminates. Unlike typical SV-jump models, previous realizations of both jump and normal innovations can feedback asymmetrically into expected volatility. This is a new source of asymmetry (in addition to good versus bad news) that improves forecasts of volatility particularly after large moves such as the ’87 crash. A heterogeneous Poisson process governs the likelihood of jumps and is summarized by a timevarying conditional intensity parameter. The model is applied to returns from individual companies and three indices. We provide empirical evidence of the impact and feedback eects of jump versus normal return innovations, contemporaneous and lagged leverage eects, the time-series dynamics of jump clustering, and the importance of modeling the dynamics of jumps around high volatility

News Arrival, Jump Dynamics and Volatility Components for Individual Stock Returns ⁄

This article uses a Markov-switching model that incorporates duration dependence to capture nonlinear structure in both the conditional mean and the conditional variance of stock returns. The model sorts returns into a high-return stable state and a low-return volatile state. We label these as bull and bear markets, respectively. The filter identifies all major stock-market downturns in over 160 years of monthly data. Bull markets have a declining hazard functions although the best market gains come at the start of a bull market. Volatility increases with duration in bear markets. Allowing volatility to vary with duration captures volatility clustering.

Identifying Bull and Bear Markets in Stock Returns

Hamilton's nonlinear Markovian filter is extended to allow state transitions to be duration dependent. Restrictions are imposed on the state transition matrix associated with a τ-order Markov system such that the corresponding first-order conditional transition probabilities are functions of both the inferred current state and also the number of periods the process has been in that state. High-order structure is parsimoniously summarized by the inferred duration variable. Applied to U.S. postwar real GNP growth rates, we obtain evidence in support of nonlinearity, asymmetry between recessions and expansions, and duration dependence for recessions but not for expansions.

/pdf/duration-dependent-transitions-in-a-markov-model-of-u-s-gnp-3avnvlurfo.pdf

Duration-Dependent Transitions in a Markov Model of U.S. GNP Growth

Many finance questions require a full characterization of the distribution of returns. We propose a bivariate model of returns and realized volatility (RV), and explore which features of that time-series model contribute to superior density forecasts over horizons of 1 to 60 days out of sample. This term structure of density forecasts is used to investigate the importance of: the intraday information embodied in the daily RV estimates; the functional form for log(RV) dynamics; the timing of information availability; and the assumed distributions of both return and log(RV) innovations. We find that a joint model of returns and volatility that features two components for log(RV) provides a good fit to S&P 500 and IBM data, and is a significant improvement over an EGARCH model estimated from daily returns.

/pdf/do-high-frequency-measures-of-volatility-improve-forecasts-3laiwmmrjq.pdf

Thomas H. McCurdy

Papers

News Arrival, Jump Dynamics and Volatility Components for Individual Stock Returns

News Arrival, Jump Dynamics and Volatility Components for Individual Stock Returns ⁄

Identifying Bull and Bear Markets in Stock Returns

Duration-Dependent Transitions in a Markov Model of U.S. GNP Growth

Do High-Frequency Measures of Volatility Improve Forecasts of Return Distributions?