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«Recent Advances and Trends in Time Series Analysis: Nonlinear Time Series, High Dimensional Inference and Beyond Sunday, April 27 - Friday May 2, ...»

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Recent Advances and Trends in Time Series Analysis: Nonlinear Time

Series, High Dimensional Inference and Beyond

Sunday, April 27 - Friday May 2, 2014

MEALS

*Breakfast (Bu↵et): 7:00–9:30 am, Sally Borden Building, Monday–Friday

*Lunch (Bu↵et): 11:30 am–1:30 pm, Sally Borden Building, Monday–Friday

*Dinner (Bu↵et): 5:30–7:30 pm, Sally Borden Building, Sunday–Thursday

Co↵ee Breaks: As per daily schedule, in the foyer of the TransCanada Pipeline Pavilion (TCPL)

*Please remember to scan your meal card at the host/hostess station in the dining room for each meal.

MEETING ROOMS

All lectures will be held in the lecture theater in the TransCanada Pipelines Pavilion (TCPL). An LCD projector, a laptop, a document camera, and blackboards are available for presentations.

SCHEDULE

Titles of the talks and abstracts can be found below the schedule.

Sunday 16:00 Check-in begins (Front Desk - Professional Development Centre - open 24 hours) 17:30–19:30 Bu↵et Dinner, Sally Borden Building 20:00 Informal gathering in 2nd floor lounge, Corbett Hall Beverages and a small assortment of snacks are available on a cash honor system.

Monday 7:00–8:45 Breakfast 8:45–9:00 Introduction and Welcome by BIRS Station Manager, TCPL 9:00 Lectures 09:00-09:30 Peter Robinson 09:30-10:00 Liudas Giraitis 10:00-10:30 Co↵ee Break, TCPL 10:30 Lectures 10:30-11:00 Ejaz Ahmed 10:30-11:00 Daniel Pena 11:30–13:00 Lunch 13:00–14:00 Guided Tour of The Ban↵ Centre; meet in the 2nd floor lounge, Corbett Hall 14:00 Group Photo; meet in foyer of TCPL (photograph will be taken outdoors so a jacket might be required).

14:30 Lectures 14:30-15:00 Rainer Dahlhaus 15:00-15:30 Co↵ee Break, TCPL 15:30 Lectures 15:30-16:00 Piotr Kokoszka 16:00-16:30 Eniuce Menezes 16:30-17:00 David Sto↵er 17:30–19:30 Dinner 1 Tuesday 7:00–9:00 Breakfast 9:00 Lectures 09:00-09:30 Murad Taqqu 09:30-10:00 Vladas Pipiras 10:00-10:30 Co↵ee Break, TCPL 10:30 Lectures 10:30-11:00 Gail Ivano↵ 11:00-11:30 Jens-Peter Kreiss 11:30–13:30 Lunch 13:30 Lectures 13:30-14:00 Francois Roue↵ 14:00-14:30 Nozer Singpurwalla 14:30-15:00 Mohsen Pourahmadi 15:00-15:30 Co↵ee Break, TCPL 15:30 Lectures 15:30-16:00 Zhengyan Lin 16:00-16:30 Bojan Basrak 16:30-17:00 Robert Lund 17:30–19:30 Dinner Wednesday 7:00–9:00 Breakfast 9:00 Lectures 09:00-09:30 Thomas Mikosch 09:30-10:00 Timothy McMurry 10:00-10:30 Co↵ee Break, TCPL 10:30 Lectures 10:30-11:00 Herold Dehling 11:00-11:30 Michael Baron 11:30–13:30 Lunch Free Afternoon 17:30–19:30 Dinner

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** 5-day workshop participants are welcome to use BIRS facilities (BIRS Co↵ee Lounge, TCPL and Reading Room) until 3 pm on Friday, although participants are still required to checkout of the guest rooms by 12 noon. **

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Speaker: Ejaz Ahmed (Brock University/University of Windsor, Canada) Title: Big Data, Big Bias, Small Surprise Abstract: In high-dimensional statistics settings where number of variables is greater than observations, or when number of variables are increasing with the sample size, many penalized regularization strategies were studied for simultaneous variable selection and post-estimation. However, a model may have sparse signals as well as with a number predictors with weak signals. In this scenario variable selection methods may not distinguish predictors with weak signals and sparse signals. The prediction based on a selected submodel may not be preferable in such cases. For this reason, we propose a high-dimensional shrinkage estimation strategy to improve the prediction performance of a submodel. Such a high-dimensional shrinkage estimator (HDSE) is constructed by shrinking a ridge estimator in the direction of a candidate submodel. We demonstrate that the proposed HDSE performs uniformly better than the ridge estimator.

Interestingly, it improves the prediction performance of given candidate submodel generated from most existing variable selection methods. The relative performance of the proposed HDSE strategy is appraised by both simulation studies and the real data analysis.

Speaker: Michael Baron (University of Texas at Dallas, US) Title: Bayesian and asymptotically pointwise optimal change-point detection in multivariate time series Abstract: Bayesian multichannel change-point detection problem is studied for simultaneously observed time series, where each component can experience a sudden change in distribution. The loss function penalizes for false alarms and detection delays, and the penalty increases with each missed change-point.

Asymptotically pointwise optimal (APO) rules are obtained, translating the classical concept of Bickel and Yahav to the sequential change-point detection. These APO rules are attractive because of their simple analytic form, direct computation, and weak assumptions. Extensions for the case of nuisance parameters are rather straightforward.

The new methods are applied in environmental science, finance, and energy disaggregation. In epidemiology, APO rules are constructed for the early detection of unusual patterns, epidemics, and pre-epidemic trends. Epidemic models often involve nuisance parameters, time-dependence, nonstationarity, and rather complex prior distributions. Proposed APO rules can operate under these conditions, achieving asymptotic optimality.





Speaker: Bojan Basrak (University of Zagreb, Croatia) Title: On heavy tailed time series and functional limit theorems Abstract: It is well known that stationary distribution of some standard (nonlinear) time series models, like GARCH for instance, exhibits regularly varying tails. Typically, the regular variation property extends to all finite dimensional distributions of such processes. This fact, together with some natural restrictions on dependence within the series, allows one to describe the asymptotic behavior of extremes and partial sums for such models. We discuss this type of results in detail, and show how can use them to obtain new functional limit theorems for various time series models. The choice of topology used in those theorems turns out to be important.

Speaker: Gemai Chen (University of Calgary, Canada)Title: Dependent Extremes

4 Abstract: The literature on extreme values is rich when the extremes are independent or asymptotically independent. When the extremes are dependent, not much experience is available, especially for finite sample data analysis. This talk reports some results obtained in studying finite sample dependent extremes.

Speaker: Rainer Dahlhaus (Heidelberg University, Germany) Title: Local polynomial fits for locally stationary processes Abstract: We develop the concept of local polynomial fits for parameter curves for locally stationary processes. We derive the asymptotic properties of these estimates and discuss how the bandwidth can be chosen. We also discuss local polynomial spectral estimates.

Speaker: Herold Dehling ((Ruhr-Universit¨t Bochum, Germany) a Title: Robust Change-Point Tests for Time Series Abstract: We present recent developments on robust change-point tests for time series, both in the short-range as well as in the long-range dependent case. Given the data X1,..., Xn, we test the hypothesis of a level shift at an unknown point in time. Our tests are based on common two-sample tests, such as the Wilcoxon test and the Hodges-Lehmann test. Specifically, we study the test statisP Pn tics max1kn 1 k Xi ) : 1  i  k j  n}. We j=k+1 1{Xi Xj }, and max1kn 1 median{(Xj i=1 derive the asymptotic distribution of these test statistics, and more generally of two-sample U-processes and U-quantiles of dependent data, both under the hypothesis as well as under local alternatives. (Joint work with Roland Fried (Dortmund), Murad Taqqu (Boston), Aeneas Rooch, Martin Wendler (Bochum).)

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Speaker: Piotr Fry´lewicz (London School of Economics, UK) z Title: Modelling multivariate financial returns using changepoint-induced multiscale bases Abstract: Low-frequency financial returns can be modelled as centered around piecewise-constant trend functions which change at certain points in time. We propose a new stochastic time series framework which captures this feature. The main ingredient of our model is a hierarchically-ordered oscillatory basis of simple piecewise-constant functions. It di↵ers from the Fourier-like bases traditionally used in time series analysis in that it is determined by change-points, and hence needs to be estimated from the data before it can be used. The resulting model enables easy simulation and provides interpretable decomposition of non-stationarity into short- and long-term components. The model permits consistent estimation of the multiscale change-point-induced basis via binary segmentation (or other methods), which results in a variable-span moving-average estimator of the current trend, and allows for short-term forecasting of the average return (joint work with Anna Louise Schroeder).

Speaker: Liudas Giraitis (Queen Mary University of London, UK) Title: Autoregressive conditional duration and FIGARCH models: origins of long memory Abstract: Although properties of ARCH(1) model are well investigated, existence of long memory FIGARCH and IARCH solution was not established in the literature. These two popular ARCH type models which are widely used in applied literature, were causing theoretical controversy because of suspicion that other solutions besides the trivial zero one, do not exist. Since ARCH models with non-zero intercept have a unique stationary solution and exclude long memory, existence of finite variance FIGARCH and IARCH models and, thus, possibility of long memory in ARCH setting was doubtful. The present paper solves this controversy by showing that FIGARCH and IARCH equations have a non-trivial covariance stationary solution, and that such solution exhibits long memory. Existence and uniqueness of stationary Integrated AR(1) processes is also discussed, and long memory as inherited their feature is established.

Summarizing, we show that covariance stationary IARCH, FIEGARCH and IAR(1) processes exist, their class is wide, and they do not have short memory (joint work with D Surgailis and A Skarnulis).

Speaker: Edit Gombay (University of Alberta, Canada) Title: Change Detection for Time Series Following Generalized Linear Models Abstract: The models considered are of great practical importance as they are used in measuring health care performance, in following financial markets, analysing industrial processes, and in climate studies. We survey recent theoretical developments concerning logistic and other regression models that allow AR(p)type dependence structure together with the presence of covariates. Conditions are set for the Maximum Partial Likelihood Estimators existence and its convergence to the true value. We can prove that this convergence is at the optimal rate. The performance of the score vector of the partial likelihood function is analysed. We can use it for change detection and in sequential monitoring. Its usefulness will be demonstrated on data from clinical studies.

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Speaker: Piotr Kokoszka (Colorado State University, US) Title: Functional framework for high frequency financial data with focus on regression and predictability of intraday price curves Abstract: The talk will introduce the concept of a functional time series and focus on two specific statistical problems for such series, both motivated by intraday price curves. We explain how intraday price curves can be transformed to form an approximately stationary functional time series. We consider a contemporaneous regression of such transformed daily curves on risk factors, which may be daily functions as well. We then present a significance test designed to determine if the shape of an intraday price curve can be predicted from the past shapes of such curves.

Speaker: Jens-Peter Kreiss (Technical University of Braunschweig, Germany) Title: Baxter’s inequality and sieve bootstrap for random fields Abstract: The concept of autoregressive sieve bootstrap for time series is extended to random fields.

Given a finite data sample of rectangular shape, the procedure fits a finite-order autoregressive model to the sample using Yule-Walker-type estimators. The residuals of this fit are resampled, which allows for construction of a bootstrap sample in order to approximate the distribution of the statistic of interest. The distinctive feature of the sieve bootstrap is that the order of the AR fit is chosen depending on the sample size; in particular, it increases to infinity as the sample Size tends to infinity, but at a much slower rate. A general check criterion is presented which allows for a large class of statistics to determine whether the proposed bootstrap procedure works or not. This work depends largely on two general results for random fields which may be of interest of its own: The first one is a one-sided autoregressive representation of the underlying spatial process with summable autoregressive coe cients (which goes back to the early work of Whittle), while the other one is a kind of Baxters inequality for random fields. This is a joint work with Marco Meyer and Carsten Jentsch.

Speaker: Reg Kulperger (University of Western Ontario, Canada) Title: GARCH in mean process: estimation and asymptotics

Abstract:

Speaker: Zhengyan Lin (Zhejiang University, China) Title: On weak convergence of stochastic processes to stochastic integrals Abstract: Weak convergence of various general functionals of partial sums of dependent random variables (statistics) to stochastic integrals now plays an important role in the modern probability theory and statistics theory. In this talk, we introduce the weak convergence of various general functionals of partial sums of causal processes to stochastic integrals driven by both the Brownian motion and Levy-stable process.



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