##### STATSCALE SEMINARS

##### CURRENT SEMINARS

29th January 2021

Speaker: Holger Dette (Ruhr-Universitaet Bochum)

Title: Testing relevant hypotheses in functional time series via self-normalization

Abstract: In this paper we develop methodology for testing relevant hypotheses in a tuning-free way. Our main focus is on functional time series, but extensions to other settings are also discussed. Instead of testing for exact equality, for example for the equality of two mean functions from two independent time series, we propose to test a {\it relevant} deviation under the null hypothesis. In the two sample problem this means that an $L^2$-distance between the two mean functions is smaller than a pre-specified threshold. For such hypotheses self-normalization, which was introduced by Shao (2010) and is commonly used to avoid the estimation of nuisance parameters, is not directly applicable. We develop new self-normalized procedures for testing relevant hypotheses and demonstrate the particular advantages of this approach in the the comparisons of eigenvalues and eigenfunctions.

Reference:

Holger Dette, Kevin Kokot and Stanislav Volgushev (2020). Journal of the Royal Statistical Society Series B, vol. 82, issue 3, 629-660

12th February 2021

Speaker: Matteo Barigozzi (Università di Bologna)

Title: Quasi Maximum Likelihood Estimation and Inference of Large Approximate Dynamic Factor Models via the EM algorithm

Abstract: This paper studies Quasi Maximum Likelihood estimation of dynamic factor models for large panels of time series. Specifically, we consider the case in which the autocorrelation of the factors is explicitly accounted for and therefore the model has a state-space form. Estimation of the factors and of their loadings is implemented by means of the Expectation Maximization (EM) algorithm, jointly with the Kalman smoother. We prove that, as both the dimension of the panel n and the sample size T diverge to infinity: (i) the estimated loadings are sqrt(T)-consistent and asymptotically normal if sqrt(T) /n → 0; (ii) the estimated factors are sqrt(n)-consistent and asymptotically normal if sqrt(n)/T → 0; (iii) the estimated common component is min(sqrt(T), sqrt(n))-consistent and asymptotically normal regardless of the relative rate of divergence of n and T . Although the model is estimated as if the idiosyncratic terms were cross-sectionally and serially uncorrelated, we show that these mis-specifications do not affect consistency. Moreover, the estimated loadings are asymptotically as efficient as those obtained with the Principal Components estimator, whereas numerical results show that the loss in efficiency of the estimated factors becomes negligible as n and T increase. We then propose robust estimators of the asymptotic covariances, which can be used to conduct inference on the loadings and to compute confidence intervals for the factors and common components. In a MonteCarlo simulation exercise and an analysis of US macroeconomic data, we study the performance of our estimators and we compare them with the traditional Principal Components approach.

26th February 2021

Speaker: Eric Kolaczyk (Boston University)

Title & Abstract to Follow

12th March 2021

Speaker: Sumanta Basu (Cornell University)

Title & Abstract to Follow

26th March 2021

Speaker: Hao Chen (UC David)

Title & Abstract to Follow

To register your interest in accessing the StatScale Seminars, contact Dr Hyeyoung Maeng

##### PREVIOUS SEMINARS

4th December 2020 - Priyanga Dilini Talagala (University of Moratuwa)

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9th October 2020 - Solt Kovacs (ETH Zurich)

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