TY - JOUR

T1 - Penalisation Methods in Fitting High‐Dimensional Cointegrated Vector Autoregressive Models

T2 - A Review

AU - Levakova, Marie

AU - Ditlevsen, Susanne

PY - 2024

Y1 - 2024

N2 - Cointegration has shown useful for modeling non-stationary data with long-run equilibrium relationships among variables, with applications in many fields such as econometrics, climate research and biology. However, the analyses of vector autoregressive models are becoming more difficult as data sets of higher dimensions are becoming available, in particular because the number of parameters is quadratic in the number of variables. This leads to lack of statistical robustness, and regularisation methods are paramount for obtaining valid estimates. In the last decade, many papers have appeared suggesting different penalisation approaches to the inference problem. Here, we make a comprehensive review of different penalisation methods adapted to the specific structure of vector cointegrated models suggested in the literature, with relevant references to software packages. The methods are evaluated and compared according to a range of error measures in a simulation study, considering combinations of low and high dimension of the system and small and large sample sizes.

AB - Cointegration has shown useful for modeling non-stationary data with long-run equilibrium relationships among variables, with applications in many fields such as econometrics, climate research and biology. However, the analyses of vector autoregressive models are becoming more difficult as data sets of higher dimensions are becoming available, in particular because the number of parameters is quadratic in the number of variables. This leads to lack of statistical robustness, and regularisation methods are paramount for obtaining valid estimates. In the last decade, many papers have appeared suggesting different penalisation approaches to the inference problem. Here, we make a comprehensive review of different penalisation methods adapted to the specific structure of vector cointegrated models suggested in the literature, with relevant references to software packages. The methods are evaluated and compared according to a range of error measures in a simulation study, considering combinations of low and high dimension of the system and small and large sample sizes.

U2 - 10.1111/insr.12553

DO - 10.1111/insr.12553

M3 - Review

JO - International Statistical Review

JF - International Statistical Review

SN - 0306-7734

ER -