A tutorial will take place in a hybrid mode on the 7th of August 2026 in the Building Tokokan (Fukakusa campus of Ryukoku University, 67 Tsukamoto-cho, Fukakusa, Fushimi-ku, Kyoto 612-8577, Japan), Room 104.

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Accurate inference in time series and network data: Learning from small samples

Prof. Elvezio Ronchetti, University of Geneva, Switzerland.
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Description:

Standard first-order asymptotic approximations of p-values and coverages of confidence intervals can be inaccurate, especially in small samples or when extreme tail probabilities are required. The goal of this tutorial is to provide approximations of distributions of estimators and test statistics that lead to accurate inference in time series and network data models. Specifically, in the first part we present the basic ideas and tools of small sample asymptotics approximations in a general framework. They are based on the concept of Legendre transformation and can be interpreted in the framework of optimal transportation. In the second part we show how to derive and implement these methods in time series models via the frequency domain approach. The results are compared to various forms of bootstrap for short and long range dependence, and for Gaussian and non Gaussian processes. Finally, in the third part we turn to spatial panel data model, with fixed effects, time-varying covariates, and spatially correlated errors. We remark that we can cast the methodology into the framework of the statistical analysis of random fields on a network graph, where the underlying, known, network graph describes the spatial structure. The new techniques provide accurate approximations of tail areas and p-values, which feature relative error of order $O(1/(n(T-1)))$ with n being the cross-sectional dimension and T the time-series dimension. An empirical application to the investment-saving relationship in OECD (Organisation for Economic Co-operation and De- velopment) countries shows the advantages of using the new techniques compared to standard first-order asymptotics. .