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Joint Econometrics and Statistics Seminar Series Lent term 2013-14

The Departments of Statistics and Economics jointly organize these workshops throughout the year.

During Michaelmas term, they take place on Friday mornings at 12pm in NAB 2.16. In Lent term they will be held in the Leverhulme Library (COL 6.15)  All are very welcome to attend and refreshments are provided.

For information regarding the Michaelmas term series see here|. Please contact Dr. Marcia Schafgans| and Dr. Matteo Barigozzi| for further information.

joint stats and econometrics

17 January 2014

Clement de Chaisemartin (University of Warwick)

Title:  Defying the Late Identification of local treatment effects when the instrument violates monotonicity

Abstract:  The instrumental variable method relies on a strong  no-defiers condition, which requires that the instrument affect every subject's treatment decision in the same direction. This paper shows that  no-defiers  can be replaced by a weaker  compliers-defiers condition, which requires that a subgroup of compliers have the same size and the same distribution of potential outcomes as de fiers. This condition is necessary and sufficient for IV to capture causal effects for the remaining part of compliers. In many applications,  compliers-defiers  is a very weak condition. For instance, in Angrist & Evans (1998), 94% of DGPs compatible with the data satisfy  compliers-defiers , while 0% satisfy  no-defiers.

31 January 2014

Alexei Onatski (University of Cambridge)

Title: Signal detection in high dimension

Abstract:  This paper applies Le Cam’s asymptotic theory of statistical experiments to the signal detection problem in high-dimension. We consider the problem of testing the null hypothesis of sphericity of a high-dimensional covariance matrix against an alternative of (unspecified) multiple symmetry-breaking directions (multispiked alternatives). Simple analytical expressions for the Gaussian asymptotic power envelope and the asymptotic powers of previously proposed tests are derived. Those asymptotic powers remain valid for non-Gaussian data satisfying mild moment restrictions. They appear to lie very substantially below the Gaussian power envelope, at least for small values of the number of symmetry-breaking directions. In contrast, the asymptotic power of Gaussian likelihood ratio tests based on the eigenvalues of the sample covariance matrix are shown to be very close to the envelope. Although based on Gaussian likelihoods, those tests remain valid under non-Gaussian densities satisfying mild moment conditions. The results of this paper extend to the case of multispiked alternatives and possibly non-Gaussian densities the findings of an earlier study (Onatski, Moreira and Hallin 2013a) of the single-spiked case. The methods we are using here, however, are entirely new, as the Laplace approximation methods considered in the single-spiked context do not extend to the multispiked case.

joint paper with Marc Hallin and Marcelo Moreira.

14 February 2014

John Aston (University of Cambridge)

Title:  Detecting and Assessing Change Points using HMMs

Abstract:  Hidden Markov Models (HMMs) are routinely used to detect change points in time series, by associating changes in underlying hidden states with change points. In this talk, we will review recent work on not only detecting but also assessing uncertainty in changes found using HMMs. We will show that change point distributions can be found in a variety of settings including mean and variance changes. It will also be seen that, using approximations and data transforms, a variety of more complex scenarios can be investigated including changes in the autocovariance structure. The methods will be illustrated with examples from Brain Imaging and Oceanography, amongst others.

 21 February 2014

Menelaos Karanasos (Brunel University)

Title:  A unifed theory for time varying models: foundations with applications in the presence of breaks and heteroscedasticity (and some results on Companion and Hessenberg matrices)

Abstract:  The paper develops an integrated approach to examine the dynamics of stochastic time series processes with time dependent coefficients. We provide the closed form of the general solution for 'time varying' models which is a long standing research topic. This enable us to characterize these models by deriving, first, its multistep ahead predictor, second, the first two unconditional moments, and third, its covariance structure. In addition, capitalizing on the connection between linear difference equations and the product of companion matrices, we employ our general methodology to obtain an explicit formula for the latter. We also apply our techniques to obtain results on Hessenberg matrices.

To illustrate the practical significance of our results we consider autoregressive moving average models with multiple abrupt breaks and also apply our unified approach to a variety of processes such as i) periodic, cyclical and smooth transition autoregressive moving average models, ii) time varying generalized autoregressive conditional heteroscedasticity specifications, and iii) generalized random coefficients autoregressive models.

Joint with: A. Paraskevopoulos and S. Dafnos

28 February 2014

Weining Wang (Humboldt University of Berlin)

Title:  Hidden Markov structures for dynamic copulae

Abstract: Understanding the time series dynamics of a multivariate dimensional dependency structure is a challenging task. A multivariate covariance driven Gaussian or mixed normal time varying models are limited in capturing important  data features such as heavy tails, asymmetry, and nonlinear dependencies. This research aims at tackling this problem by proposing and analysing a hidden Markov model (HMM) for hierarchical Archimedean copulae (HAC). The HAC constitute a wide class of models for multivariate dimensional dependencies, and HMM is a statistical technique for describing regime switching dynamics. HMM applied to HAC flexibly models multivariate dimensional non-Gaussian time series. We apply the expectation maximization (EM) algorithm for parameter estimation. Consistency results for both parameters and HAC structures are established in an HMM framework. The model is calibrated to exchange rate data with a VaR application. This example is motivated by a local adaptive analysis that yields a time varying HAC model. We compare the forecasting performance with other classical dynamic models. In another, second, application we model a rainfall process. This task is of particular theoretical and practical interest because of the specific structure and required untypical treatment of precipitation data.

7 March 2014

Soumen Lahiri (North Carolina State University)

Title: Rates of convergence of the Adaptive LASSO estimators to the Oracle distribution and higher order refinements by the bootstrap

Abstract:  Zou ( 2006; J. Amer.  Statist.  Assoc.) proposed the ALASSO method for simultaneous variable selection and estimation of the non‐zero regression parameters, and established its oracle property. In this talk, we provide a precise description of the rate of convergence of the ALASSO estimators of the non‐zero components to the oracle distribution.  It is shown that the rate critically depends on the choices of the penalty parameter and the  initial  estimator,  and that  confidence intervals (CIs) based on the oracle limit law have poor coverage accuracy. As an alternative, we consider the residual bootstrap method for the ALASSO estimators  and  show that a naive application of the bootstrap, although consistent, may result in a very slow rate of approximation, with or without studentization. We construct a suitably bias‐adjusted and studentized pivotal version of the ALASSO estimator and show that the bootstrap applied to this modified pivot achieves second‐order correctness, even when the dimension of the non‐zero regression parameters is unbounded. Results from a moderately large simulation study show marked improvement in coverage accuracy for the bootstrap CIs over the oracle based CIs in finite samples.

10 March 2014

Martina Mincheva (Princeton University)
**CHANGE OF TIME AND DAY**  16.30-17.30

Title:  Covariance estimation - big data challenges and financial applications

Abstract:  High-dimensional settings have recently become one of the major focuses of statistical research, driven by applications in finance and genetics. In a data rich environment, the number of parameters can diverge at a rate faster than that of the sample size.
My focus is on creating consistent covariance and precision matrix estimators. I propose the POET (Principal Orthogonal complEments
Thresholding) estimator which deals with the big data challenge by establishing low-dimensional patterns, namely a low-rank component and a sparse component. I demonstrate its performance in a real-data setup for risk management and portfolio allocation.

14 March 2014

Federico Martellosio (University of Surrey)

Title:  Properties of the Maximum Likelihood Estimator in Spatial Autoregressive Models

Abstract:  The (quasi-) maximum likelihood estimator (MLE) for the autoregressive parameter in a spatial autoregressive model cannot in general be written explicitly in terms of the data. The only known properties of the estimator have hitherto been its first-order asymptotic properties (Lee, 2004, Econometrica), derived under specific assumptions on the evolution of the spatial weights matrix involved. In this paper we show that the exact cumulative distribution function of the estimator can, under mild assumptions, be written down explicitly. A number of immediate consequences of the main result are discussed, and several examples of theoretical and practical interest are analyzed in detail.The examples are of interest in their own right, but also serve to illustrate some unexpected features of the distribution of the MLE. In particular, we show that the distribution of the MLE may not be supported on the entire parameter space, and may be nonanalytic at some points in its support.