Specification Testing for Multivariate Time Series Volatility Models

Volatility models have been playing an important role in economics and finance. Using a multivariate generalized spectral approach, we propose a new class of generally applicable omnibus tests for univariate and multivariate volatility models. Both GARCH models and stochastic volatility models are covered. Our tests have a convenient asymptotic null N(0,1) distribution, and can detect a wide range of misspecifications for volatility dynamics. Distinct from the existing tests for volatility models, our tests are robust to higher order time-varying moments of unknown form (e.g., time-varying skewness and kurtosis). Our tests check a large number of lags and are therefore expected to be powerful against neglected volatility dynamics that occurs at higher order lags or display long memory properties. Despite using a large number of lags, our tests do not suffer much from loss of a large number of degrees of freedom, because our approach naturally discounts higher order lags, which is consistent with the stylized fact that economic or financial markets are more affected by the recent past events than by the remote past events. No specific estimation method is required, and parameter estimation uncertainty has no impact on the limit distribution of the test statistics. Moreover, there is no need to formulate an alternative volatility model, and only estimated standardized residuals are needed to implement our tests. We do not have to calculate tedious score functions or derivatives of volatility models with respect to estimated parameters, which are model-specific and are required in some existing popular tests for volatility models. We examine the finite sample performance of the proposed tests. An empirical application to some popular GARCH models for stock returns illustrates our approachGeneralized spectral derivative, Kernel, Multivariate generalized spectrum, Multivariate GARCH models, Nonlinear volatility dynamics, Robustness, Specification testing, Stochastic Volatility Model, Time-varying higher order moments of unknown form.

Towards Efficient Maximum Likelihood Estimation of LPV-SS Models

How to efficiently identify multiple-input multiple-output (MIMO) linear parameter-varying (LPV) discrete-time state-space (SS) models with affine dependence on the scheduling variable still remains an open question, as identification methods proposed in the literature suffer heavily from the curse of dimensionality and/or depend on over-restrictive approximations of the measured signal behaviors. However, obtaining an SS model of the targeted system is crucial for many LPV control synthesis methods, as these synthesis tools are almost exclusively formulated for the aforementioned representation of the system dynamics. Therefore, in this paper, we tackle the problem by combining state-of-the-art LPV input-output (IO) identification methods with an LPV-IO to LPV-SS realization scheme and a maximum likelihood refinement step. The resulting modular LPV-SS identification approach achieves statical efficiency with a relatively low computational load. The method contains the following three steps: 1) estimation of the Markov coefficient sequence of the underlying system using correlation analysis or Bayesian impulse response estimation, then 2) LPV-SS realization of the estimated coefficients by using a basis reduced Ho-Kalman method, and 3) refinement of the LPV-SS model estimate from a maximum-likelihood point of view by a gradient-based or an expectation-maximization optimization methodology. The effectiveness of the full identification scheme is demonstrated by a Monte Carlo study where our proposed method is compared to existing schemes for identifying a MIMO LPV system

Nonlinearities and cyclical behavior: the role of chartists and fundamentalists

We develop a behavioral exchange rate model with chartists and fundamentalists to study cyclical behavior in foreign exchange markets. Within our model, the market impact of fundamentalists depends on the strength of their belief in fundamental analysis. Estimation of a STAR GARCH model shows that the more the exchange rate deviates from its fundamental value, the more fundamentalists leave the market. In contrast to previous findings, our paper indicates that due to the nonlinear presence of fundamentalists, market stability decreases with increasing misalignments. A stabilization policy such as central bank interventions may help to deflate bubbles

A Random Force is a Force, of Course, of Coarse: Decomposing Complex Enzyme Kinetics with Surrogate Models

The temporal autocorrelation (AC) function associated with monitoring order parameters characterizing conformational fluctuations of an enzyme is analyzed using a collection of surrogate models. The surrogates considered are phenomenological stochastic differential equation (SDE) models. It is demonstrated how an ensemble of such surrogate models, each surrogate being calibrated from a single trajectory, indirectly contains information about unresolved conformational degrees of freedom. This ensemble can be used to construct complex temporal ACs associated with a "non-Markovian" process. The ensemble of surrogates approach allows researchers to consider models more flexible than a mixture of exponentials to describe relaxation times and at the same time gain physical information about the system. The relevance of this type of analysis to matching single-molecule experiments to computer simulations and how more complex stochastic processes can emerge from a mixture of simpler processes is also discussed. The ideas are illustrated on a toy SDE model and on molecular dynamics simulations of the enzyme dihydrofolate reductase.Comment: 11 pages / 6 figure

Dynamic Spatial Autoregressive Models with Autoregressive and Heteroskedastic Disturbances

We propose a new class of models specifically tailored for spatio-temporal data analysis. To this end, we generalize the spatial autoregressive model with autoregressive and heteroskedastic disturbances, i.e. SARAR(1,1), by exploiting the recent advancements in Score Driven (SD) models typically used in time series econometrics. In particular, we allow for time-varying spatial autoregressive coefficients as well as time-varying regressor coefficients and cross-sectional standard deviations. We report an extensive Monte Carlo simulation study in order to investigate the finite sample properties of the Maximum Likelihood estimator for the new class of models as well as its flexibility in explaining several dynamic spatial dependence processes. The new proposed class of models are found to be economically preferred by rational investors through an application in portfolio optimization.Comment: 33 pages, 5 figure