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-STS345A the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

Asymptotic Theory for Clustered Samples

We provide a complete asymptotic distribution theory for clustered data with a large number of independent groups, generalizing the classic laws of large numbers, uniform laws, central limit theory, and clustered covariance matrix estimation. Our theory allows for clustered observations with heterogeneous and unbounded cluster sizes. Our conditions cleanly nest the classical results for i.n.i.d. observations, in the sense that our conditions specialize to the classical conditions under independent sampling. We use this theory to develop a full asymptotic distribution theory for estimation based on linear least-squares, 2SLS, nonlinear MLE, and nonlinear GMM

Non-Parametric Data Dependent Bootstrap for Conditional Moment Model

A new non-parametric bootstrap is introduced for dependent data. The bootstrap is based on a weighted empirical-likelihood estimate of the one-step-ahead conditional distribution, imposing the conditional moment restrictions implied by the model. This is the first dependent-data bootstrap procedure which imposes conditional moment restrictions on a bootstrap distribution. The method can be applied to form confidence intervals and p-values from hypothesis tests in Generalized Method of Moments estimation The bootstrap method is illustrated with an application to autoregressive models with martingale difference errors.

Asymptotic Moments of Autoregressive Estimates with a Near Unit Root and Minimax Risk

This moments of the asymptotic distribution of the least-squares estimator of the local-to-unity autoregressive model are computed using computationally simple integration. These calculations show that conventional simulation estimation of moments can be substantially inaccurate unless thesimulationsamplesizeisverylarge. Wealsoexploretheminimaxefficiency of autoregressive coefficient estimation, and numerically show that a simple Stein shrinkage estimator has minimax risk which is uniformly better than least squares, even though the estimation dimension is just one

Estimation and Inference in Models of Cointegration: A Simulation Study

This paper studies the finite sample distributions of estimators of the cointegrating vector of linear regression models with I(1) variables. Attention is concentrated on the least squares (OLS) and instrumental variables (IV) methods analyzed in other recent work (Phillips and Hansen (1988)). The general preference of OLS to IV techniques suggested by asymptotic theory is reinforced by our simulations. An exception arises for cases of low signal to noise, where spurious IV techniques (so named for their use of instruments that are structurally unrelated to the model) outperform uncorrected least squares. We verify the presence of a small sample estimation bias and show that the Park-Phillips bias correction does reduce the magnitude of this problem. We also find that there is substantial distributional divergence of t-statistics from the normal, unless the Phillips-Hansen endogeneity correction is used. Finally, we apply these methods to aggregate consumption and income data. Our empirical results indicate that the endogeneity and serial dependence connections are important and lead to intuitively plausible changes in the estimated coefficients

Statistical Inference in Instrumental Variables Regression with I(1) Processes

This paper studies the asymptotic properties of instrumental variable (IV) estimates of multivariate cointegrating regressions. The framework of study is based on earlier work by Phillips and Durlauf (1986) and Park and Phillips (1988, 1989). In particular, the results in these papers are extended to allow for IV regressions that accommodate deterministic and stochastic regressors as well as quite general deterministic processes in the data generating mechanism. It is found that IV regressions are consistent even when the instruments are stochastically independent of the regressors. This phenomenon, which contrasts with traditional theory for stationary time series, is a beneficial artifact of spurious regression theory whereby stochastic trends in the instruments ensure their relevance asymptotically. Problems of inference are also addressed and some promising new theoretical results are reported. These involve a class of Wald tests which are modified by semiparametric corrections for serial correlation and for endogeneity. The resulting test statistics which we term fully modified Wald tests have limiting chi-squared distributions, thereby removing the obstacles to inference in cointegrated systems that were presented by the nuisance parameter dependencies in earlier work. Interestingly, IV methods themselves are insufficient to achieve this end and an endogeneity correction is still generally required, again in contrast to traditional theory. Our results therefore provide strong support for the conclusion reached by Hendry (1986) that there is no free lunch in estimating cointegrated systems. Some simulation results are reported which seek to explore the sampling behavior of our suggested procedures. These simulations compare our fully modified (semiparametric) methods with the parametric error correction methodology that has been extensively used in recent empirical research and with conventional least squares regression. Both the fully modified and error correction methods work well in finite samples and the sampling performance of each procedure confirms the relevance of asymptotic distribution theory, as distinct from superconsistency results, in discriminating between different statistical methods

Uncovering the Relationship between Real Interest Rates and Economic Growth

We analyze long-span data on real interest rates and productivity growth with the focus on estimating their long-run correlation. The evidence points to a moderately negative correlation, meaning that real interest rates are mildly countercyclical, although the estimates are not precise. Our best estimate of the long-run correlation is -0.20. The implications for long-term projections are as follows. A negative correlation implies that long-run costs due to a period of low interest rates will tend to be slightly offset by a period of high productivity growth. Conversely, long-run benefits during a period of high interest rates will be offset by low productivity growth. This implication is consistent with the question raised in the project solicitation concerning why the trust fund stochastic simulations tend to show less long-run variability than do the alternative assumption projections. We also examine the implications for the variability of long-term projections of trust fund accumulation. As expected, we find that a negative correlation reduces the variability in the stochastic intervals. However, our simplified calculations suggest that the effect is modest.Social Security Administrationhttp://deepblue.lib.umich.edu/bitstream/2027.42/102614/1/wp303.pd

Forchhammeria and Stixis (Brassicales): Stem and Wood Anatomical Diversity, Ecological and Phylogenetic Significance

Qualitative and quantitative data are given for wood anatomy of six of the 11 recognized species of Forchhammeria (Mexico, Central America, West Indies), a genus formerly placed in Capparaceae. Though still in Brassicales, the genus has been excluded, along with several other genera, from the major recognized families of that order on the basis of molecular data. Liquid-preserved material of several species permitted detailed histological accounts of the successive cambia and their development in the stems of Forchhammeria. Successive cambia have a curious distribution in Brassicales that may represent homoplasies. Most wood features of the genus do not appear highly xeromorphic, but presence of tracheids as a wood background tissue and abundance of starch and perhaps water storage in ray parenchyma and conjunctive tissue can be cited as mechanisms likely to resist embolism formation. Forchhammeria retains green leaves throughout the dry season. Forchhammeria tamaulipana, known only from Tamaulipas State, Mexico, the single species of a new subgenus, Pauciflora, is newly described. Its embryos have nearly equal cotyledons and germinate epigeously, whereas all remaining species of the genus are pseudomonocotylous and hypogeous. These and other distinctive features of F. tamaulipana may prove significant in providing links to other brassicalean genera. The family name Stixaceae Doweld is now appropriate for Forchhammeria, Neothorelia, Stixis, and Tirani

Environmental Quality Management in a Region with External Development Pressures

The objective of this study was to examine the problems of managing residuals and environmental quality in a region facing potentially rapid growth as a consequence of externally made development decisions. The research adapted and applied the residuals environmental management concept which recognizes the need for an integration of physical methods, implementation incentives and institutional arrangements in controlling air, water and solid residuals. The area selected for study, the Uintah Basin in Southeastern utah, has the potential for extensive energy resource and mineral development and could experience a large population influx and accelerated economic growth as a result. in the face of a wide range of possible resource developments, the study used an alternative futures approach, in which combinations of exogenous events leading to different types and levels of economic activities and employment inpacts were identified. Economic and land use simulation models were applied to project the effects of the futures on the basin. Materials balances were then drawn up for major polluting activities to determine the residuals that would be produced and discharged to the environment if there were not controls. An environmental impact and management model, structured as al inear programming model, was used to evaluate environmental management strategies. The model incorporated various production processes and residuals treatment methods. Air and water quality simulation models were applied to assess environmental impacts and generate model constraints. Several dimesnsions of environmental management strategies were analyzed including alternative production processes, waste treatment methods, and various implementation incentives such as effluent charges, effluent standards and effects of legal restructions. This report was submitted in fulfillment of Contract No. R-803203 by the Utah Water Research Laboratory, Utah State University under the sponsorship of the U.S. Environmental Protection Agency. This report covers the period July 22, 1974 to january 31, 1977, and was completed as of February 21, 1977

Status of Exosphaeroma amplicauda (Stimpson, 1857), E-aphrodita (Boone, 1923) and description of three new species (Crustacea, Isopoda, Sphaeromatidae) from the north-eastern Pacific

Exosphaeroma amplicauda (Stimpson, 1857) from the west coast of North America is reviewed and redescribed and revealed to be a group of closely related species. A neotype is designated and the species redescribed based on the neotype and topotypic specimens. Exosphaeroma amplicauda is known only from the coast of California, at Marin, Sonoma and San Mateo Counties. E. aphrodita (Boone, 1923), type locality La Jolla, California and previously considered nomen dubium is taken out of synonymy and re-validated. A further three species: E. paydenae sp. n., E. russellhansoni sp. n., and E. pentcheffi sp. n. are described herein. Sphaeroma octonctum Richardson, 1899 is placed into junior synonymy with Exosphaeroma amplicauda. A key to the Pacific West Coast Exosphaeroma is provided