Estimating SUR Tobit Model while errors are gaussian scale mixtures: with an application to high frequency financial data

This paper examines multivariate Tobit system with Scale mixture disturbances. Three estimation methods, namely Maximum Simulated Likelihood, Expectation Maximization Algorithm and Bayesian MCMC simulators, are proposed and compared via generated data experiments. The chief finding is that Bayesian approach outperforms others in terms of accuracy, speed and stability. The proposed model is also applied to a real data set and study the high frequency price and trading volume dynamics. The empirical results confirm the information contents of historical price, lending support to the usefulness of technical analysis. In addition, the scale mixture model is also extended to sample selection SUR Tobit and finite Gaussian regime mixtures.Tobit; Gaussian mixtures; Bayesian

Vector autoregression with varied frequency data

The Vector Autoregression (VAR) model has been extensively applied in macroeconomics. A typical VAR requires its component variables being sampled at a uniformed frequency, regardless of the fact that some macro data are available monthly and some are only quarterly. Practitioners invariably align variables to the same frequency either by aggregation or imputation, regardless of information loss or noises gain. We study a VAR model with varied frequency data in a Bayesian context. Lower frequency (aggregated) data are essentially a linear combination of higher frequency (disaggregated) data. The observed aggregated data impose linear constraints on the autocorrelation structure of the latent disaggregated data. The perception of a constrained multivariate normal distribution is crucial to our Gibbs sampler. Furthermore, the Markov property of the VAR series enables a block Gibbs sampler, which performs faster for evenly aggregated data. Lastly, our approach is applied to two classic structural VAR analyses, one with long-run and the other with short-run identification constraints. These applications demonstrate that it is both feasible and sensible to use data of different frequencies in a new VAR model, the one that keeps the branding of the economic ideas underlying the structural VAR model but only makes minimum modification from a technical perspective.Vector Autoregression; Bayesian; Temporal aggregation

Bayesian Portfolio Selection in a Markov Switching Gaussian Mixture Model

Departure from normality poses implementation barriers to the Markowitz mean-variance portfolio selection. When assets are affected by common and idiosyncratic shocks, the distribution of asset returns may exhibit Markov switching regimes and have a Gaussian mixture distribution conditional on each regime. The model is estimated in a Bayesian framework using the Gibbs sampler. An application to the global portfolio diversification is also discussed.Portfolio; Bayesian; Hidden Markov Model; Gaussian Mixture

Bayesian Portfolio Selection with Gaussian Mixture Returns

Markowitz portfolio selection is challenged by huge implementation barriers. This paper addresses the parameter uncertainty and deviation from normality in a Bayesian framework. The non-normal asset returns are modeled as finite Gaussian mixtures. Gibbs sampler is employed to obtain draws from the posterior predictive distribution of asset returns. Optimal portfolio weights are then constructed so as to maximize agents’ expected utility. Simple experiment suggests that our Bayesian portfolio selection procedure performs exceedingly well.portfolio selection; Gaussian mixtures; Bayesian

Essays on statistical inference with imperfectly observed data

Missing data is a common problem encountered by empirical researchers and practitioners. This dissertation is a collection of three essays on handling imperfectly observed economic data. The first essay addresses temporal aggregation where some high frequency data are missing but their sum or average are observed in the form of low frequency data. In a vector autoregression model with varied frequency data, the explicit form of the likelihood function and the posterior distribution of missing values are found without resorting to the recursive Kalman filter. The second essay further discusses data aggregation in a two-equation model in which the missing values are imputed by a regression. In two scenarios, the likelihood function is shown to be separable and the analytic maximum likelihood estimator can be obtained by two auxiliary regressions, which is advantageous to the conventional least squares imputation approach in terms of both efficiency and computability. The third essay concerns the finite-sample bias of estimators associated with the monotone instrumental variables, which is a useful assumption to partially identify the counterfactual outcomes. It is shown that a multi-level bootstrap procedure can reduce and gradually eliminate the bias. A simultaneous simulation strategy is also proposed to make multi-level bootstrap computationally feasible

Linear regression using both temporally aggregated and temporally disaggregated data: Revisited

This paper discusses regression models with aggregated covariate data. Reparameterized likelihood function is found to be separable when one endogenous variable corresponds to one instrument. In that case, the full-information maximum likelihood estimator has an analytic form, and thus outperforms the conventional imputed value two-step estimator in terms of both efficiency and computability. We also propose a competing Bayesian approach implemented by the Gibbs sampler, which is advantageous in more flexible settings where the likelihood does not have the separability property.Aggregated covariate; Maximum likelihood; Bayesian inference

Robust Intrinsic Ferromagnetism and Half Semiconductivity in Stable Two-Dimensional Single-Layer Chromium Trihalides

Two-dimensional (2D) intrinsic ferromagnetic (FM) semiconductors are crucial to develop low-dimensional spintronic devices. Using density functional theory, we show that single-layer chromium trihalides (SLCTs) (CrX$_3$,X=F, Cl, Br and I) constitute a series of stable 2D intrinsic FM semiconductors. A free-standing SLCT can be easily exfoliated from the bulk crystal, due to a low cleavage energy and a high in-plane stiffness. Electronic structure calculations using the HSE06 functional indicate that both bulk and single-layer CrX$_3$ are half semiconductors with indirect gaps and their valence bands and conduction bands are fully spin-polarized in the same spin direction. The energy gaps and absorption edges of CrBr$_3$ and CrI$_3$ are found to be in the visible frequency range, which implies possible opt-electronic applications. Furthermore, SLCTs are found to possess a large magnetic moment of 3$\mu_B$ per formula unit and a sizable magnetic anisotropy energy. The magnetic exchange constants of SLCTs are then extracted using the Heisenberg spin Hamiltonian and the microscopic origins of the various exchange interactions are analyzed. A competition between a near 90$^\circ$ FM superexchange and a direct antiferromagnetic (AFM) exchange results in a FM nearest-neighbour exchange interaction. The next and third nearest-neighbour exchange interactions are found to be FM and AFM respectively and this can be understood by the angle-dependent extended Cr-X-X-Cr superexchange interaction. Moreover, the Curie temperatures of SLCTs are also predicted using Monte Carlo simulations and the values can further increase by applying a biaxial tensile strain. The unique combination of robust intrinsic ferromagnetism, half semiconductivity and large magnetic anisotropy energies renders the SLCTs as promising candidates for next-generation semiconductor spintronic applications.Comment: 12 pages, 14 figures. published in J. Mater. Chem.