| Abstract |
We develop a unified finite-time theory for the ordinary least squares estimation of possibly unstable and even slightly explosive vector autoregressive models under linear restrictions, with the applicable region π(π΄)β€1+ππ, where π(π΄) is the spectral radius of the transition matrix π΄ in the VAR(1) representation, π is the time horizon and π>0 is a universal constant. The linear restriction framework encompasses various existing models such as banded/network vector autoregressive models. We show that the restrictions reduce the error bounds via not only the reduced dimensionality but also a scale factor resembling the asymptotic covariance matrix of the estimator in the fixed-dimensional setup: as long as the model is correctly specified, this scale factor is decreasing in the number of restrictions. It is revealed that the phase transition from slow to fast error rate regimes is determined by the smallest singular value of π΄, a measure of the least excitable mode of the system. The minimax lower bounds are derived across different regimes. The developed non-asymptotic theory not only bridges the theoretical gap between stable and unstable regimes but precisely characterizes the effect of restrictions and its interplay with model parameters. Simulations support our theoretical results. |
| About the speaker |
Dr. Yao Zheng is an assistant professor in the Department of Statistics at the University of Connecticut. She obtained both of her PhD and BSc from the University of Hong Kong in 2017 and 2013 respectively. Dr. Zhengβs research area covers Time series analysis, High dimensional statistics and Econometrics. She aims to develop novel methods and theory to address the new statistical and computational challenges posed by the data in the high dimensionality and complex temporal structure. She is elected as a member of the International Statistical Institute (ISI) since 2022.
For more information about her research, please visit her website: https://yaozheng-stat.github.io/
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