A Multivariate GARCH Model with Time-Varying Correlations

In this paper we propose a new multivariate GARCH model with time-varying correlations. We adopt the vech representation based on the conditional variances and the conditional correlations. While each conditional-variance term is assumed to follow a univariate GARCH formulation, the conditional-correlation matrix is postulated to follow an autoregressive moving average type of analogue. By imposing some suitable restrictions on the conditional-correlation-matrix equation, we manage to construct a MGARCH model in which the conditional-correlation matrix is guaranteed to be positive definite during the optimisation. Thus, our new model retains the intuition and interpretation of the univariate GARCH model and yet satisfies the positive-definite condition as found in the constant-correlation and BEKK models. We report some Monte Carlo results on the finite-sample distributions of the QMLE of the varying-correlation MGARCH model. The new model is applied to some real data sets. It is found that extending the constant-correlation model to allow for time-varying correlations provides some interesting time histories that are not available in a constant-correlation model.

On the indoor beamformer design with reverberation

Beamforming remains to be an important technique for signal enhancement. For applications in open space, the transfer function describing waves propagation has an explicit expression, which can be employed for beamformer design. However, the function becomes very complex in an indoor environment due to the effects of reverberation. In this paper, this problem is discussed. A method based on the image source method (ISM) is applied to model the room impulse responses (RIRs), which will act as the transfer function between source and sensor. The indoor beamformer design problem is formulated as a minimax optimization problem. We propose and study several optimization models based on the -norm to design the beamformer. We found that it is advantageous to separate early and late reverberations in the design process and better designs can be achieved. Several numerical experiments are presented using both simulated data and real recordings to evaluate the proposed methods

On the sparse beamformer design

In designing acoustic broadband beamformers, the complexity can grow significantly when the number of microphones and the filter length increase. It is advantageous if many of the filter coefficients are zeroes so that the implementation can be executed with less computation. Moreover, the size of the array can also be pruned to reduce complexity. These problems are addressed in this paper. A suitable optimization model is proposed. Both array pruning and filter thinning can be solved together as a two-stage optimization problem to yield the final sparse designs. Numerical results show that the complexity of the designed beamformers can be reduced significantly with minimal effect on performance

A New Hybrid Descent Method with Application to the Optimal Design of Finite Precision FIR Filters

In this paper, the problem of the optimal design of discrete coefficient FIR filters is considered. A novelhybrid descent method, consisting of a simulated annealing algorithm and a gradient-based method, isproposed. The simulated annealing algorithm operates on the space of orthogonal matrices and is used tolocate descent points for previously converged local minima. The gradient-based method is derived fromconverting the discrete problem to a continuous problem via the Stiefel manifold, where convergence canbe guaranteed. To demonstrate the effectiveness of the proposed hybrid descent method, several numericalexamples show that better discrete filter designs can be sought via this hybrid descent method

House Market in Chinese Cities: Dynamic Modeling, In0 Sample Fitting and Out-of- Sample Forecasting

This paper attempts to contribute in several ways. Theoretically, it proposes simple models of house price dynamics and construction dynamics, all based on the maximization problems of forward-looking agents, which may carry independent interests. Simplified versions of the model implications are estimated with the data from four major cities in China. Both price and construction dynamics exhibit strong persistence in all cities. Significant heterogeneity across cities is found. Our models out-perform widely used alternatives in in-sample-fitting for all cities, although similar success is only limited to highly developed cities in out-of-sample forecasting. Policy implications and future research directions are also discussed.