Multivariate volatility models

Correlations between asset returns are important in many financial applications. In recent years, multivariate volatility models have been used to describe the time-varying feature of the correlations. However, the curse of dimensionality quickly becomes an issue as the number of correlations is $k(k-1)/2$ for $k$ assets. In this paper, we review some of the commonly used models for multivariate volatility and propose a simple approach that is parsimonious and satisfies the positive definite constraints of the time-varying correlation matrix. Real examples are used to demonstrate the proposed model.Comment: Published at http://dx.doi.org/10.1214/074921706000001058 in the IMS Lecture Notes Monograph Series (http://www.imstat.org/publications/lecnotes.htm) by the Institute of Mathematical Statistics (http://www.imstat.org

Sample selection and preservation techniques for the Mars sample return mission

It is proposed that a miniaturized electron spin resonance (ESR) spectrometer be developed as an effective, nondestructivew sample selection and characterization instrument for the Mars Rover Sample Return mission. The ESR instrument can meet rover science payload requirements and yet has the capability and versatility to perform the following in situ Martian sample analyses: (1) detection of active oxygen species, and characterization of Martian surface chemistry and photocatalytic oxidation processes; (2) determination of paramagnetic Fe(3+) in clay silicate minerals, Mn(2+) in carbonates, and ferromagnetic centers of magnetite, maghemite and hematite; (3) search for organic compounds in the form of free radicals in subsoil, and detection of Martian fossil organic matter likely to be associated with carbonate and other sedimentary deposits. The proposed instrument is further detailed

High-dimensional Linear Regression for Dependent Data with Applications to Nowcasting

Recent research has focused on $\ell_1$ penalized least squares (Lasso) estimators for high-dimensional linear regressions in which the number of covariates $p$ is considerably larger than the sample size $n$. However, few studies have examined the properties of the estimators when the errors and/or the covariates are serially dependent. In this study, we investigate the theoretical properties of the Lasso estimator for a linear regression with a random design and weak sparsity under serially dependent and/or nonsubGaussian errors and covariates. In contrast to the traditional case, in which the errors are independent and identically distributed and have finite exponential moments, we show that $p$ can be at most a power of $n$ if the errors have only finite polynomial moments. In addition, the rate of convergence becomes slower owing to the serial dependence in the errors and the covariates. We also consider the sign consistency of the model selection using the Lasso estimator when there are serial correlations in the errors or the covariates, or both. Adopting the framework of a functional dependence measure, we describe how the rates of convergence and the selection consistency of the estimators depend on the dependence measures and moment conditions of the errors and the covariates. Simulation results show that a Lasso regression can be significantly more powerful than a mixed-frequency data sampling regression (MIDAS) and a Dantzig selector in the presence of irrelevant variables. We apply the results obtained for the Lasso method to nowcasting with mixed-frequency data, in which serially correlated errors and a large number of covariates are common. The empirical results show that the Lasso procedure outperforms the MIDAS regression and the autoregressive model with exogenous variables in terms of both forecasting and nowcasting

Estimating Long Memory Time-Series-Cross-Section Data

This paper extends the MD (multiple differenced) methodology of Tsay (2006) to estimate a class of time-series-cross-section (TSCS) models consisting of stationary or nonstationary long memory regressors and errors, while allowing for correlations and heteroskedasticities in both cross-section and time dimensions. Interestingly, the regression coefficients of these models still can be easily tested with the MD-based approach using the critical values from the standard normal distribution. Under various combinations of long memory processes and cross-section dimensions, the finite sample performance of the MD-based method is promising even though the time span is only 20. We then apply this method to reexamine the data of Hicks and Swank (1992). The testing results are more in line with the findings in Beck and Katz (1995) whereby the evidence for positive voter turnout effects in Hicks and Swank (1992) is no more highly statistically significant when the number of differencing is greater than or equal to 1.

Discussion of "Feature Matching in Time Series Modeling" by Y. Xia and H. Tong

Discussion of "Feature Matching in Time Series Modeling" by Y. Xia and H. Tong [arXiv:1104.3073]Comment: Published in at http://dx.doi.org/10.1214/11-STS345B the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

A Generalized ARFIMA Process with Markov-Switching Fractional Differencing Parameter

We propose a general class of Markov-switching-ARFIMA processes in order to combine strands of long memory and Markov-switching literature. Although the coverage of this class of models is broad, we show that these models can be easily estimated with the DLV algorithm proposed. This algorithm combines the Durbin-Levinson and Viterbi procedures. A Monte Carlo experiment reveals that the finite sample performance of the proposed algorithm for a simple mixture model of Markov-switching mean and ARFIMA(1, d, 1) process is satisfactory. We apply the Markov-switching-ARFIMA models to the U.S. real interest rates, the Nile river level, and the U.S. unemployment rates, respectively. The results are all highly consistent with the conjectures made or empirical results found in the literature. Particularly, we confirm the conjecture in Beran and Terrin (1996) that the observations 1 to about 100 of the Nile river data seem to be more independent than the subsequent observations, and the value of differencing parameter is lower for the first 100 observations than for the subsequent data.Markov chain; ARFIMA process; Viterbi algorithm; Long memory.