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Robust estimation for high-dimensional time series with heavy tails

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arxiv 2411.05217 v1 pith:CHPIYETE submitted 2024-11-07 math.ST stat.TH

Yu Wang , Guodong Li , Zhijie Xiao , Lihu Xu , Wenyang Zhang This is my paper
classification math.STstat.TH
keywords alphadataheavy-tailedhigh-dimensionalapplyclassicalestimationproblem
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abstract

We study in this paper the problem of least absolute deviation (LAD) regression for high-dimensional heavy-tailed time series which have finite $\alpha$-th moment with $\alpha \in (1,2]$. To handle the heavy-tailed dependent data, we propose a Catoni type truncated minimization problem framework and obtain an $\mathcal{O}\big( \big( (d_1+d_2) (d_1\land d_2) \log^2 n / n \big)^{(\alpha - 1)/\alpha} \big)$ order excess risk, where $d_1$ and $d_2$ are the dimensionality and $n$ is the number of samples. We apply our result to study the LAD regression on high-dimensional heavy-tailed vector autoregressive (VAR) process. Simulations for the VAR($p$) model show that our new estimator with truncation are essential because the risk of the classical LAD has a tendency to blow up. We further apply our estimation to the real data and find that ours fits the data better than the classical LAD.

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Cited by 3 Pith papers

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    Develops a joint Catoni-type framework that simultaneously estimates parameters and variance in heavy-tailed models via coupled equations, achieving oracle-matching non-asymptotic bounds under 2β-moment assumptions us...

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    A data-truncated regularized least squares estimator for high-dimensional BEKK-ARCH volatility models achieves non-asymptotic error bounds and minimax optimal rates under heavy tails, with consistent selection via rob...

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    A truncated, ℓ1-regularized least squares method on the VAR form of BEKK-ARCH estimates high-dimensional conditional covariance matrices at a near-optimal rate under heavy tails.

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