Tseng, Neng FangNeng FangTsengYING-CHAO HUNGNakano, JunjiJunjiNakano2023-09-212023-09-212023-01-0101439782https://scholars.lib.ntu.edu.tw/handle/123456789/635579Granger causality is a classical and important technique for measuring predictability from one group of time series to another by incorporating information of the variables described by a full vector autoregressive (VAR) process. However, in some applications economic forecasts need to be made based on information provided merely by a portion of variates (e.g., removal of a listed stock due to halting, suspension or delisting). This requires a new formulation of forecast based on an embedded subprocess of VAR, whose theoretical properties are often difficult to obtain. To avoid the issue of identifying the VAR subprocess, we propose a computation-based approach so that sophisticated predictions can be made by utilizing a reduced variable information set estimated from sampled data. Such estimated information set allows us to develop a suitable statistical hypothesis testing procedure for characterizing all designated Granger causal relationships, as well as a useful graphical tool for presenting the causal structure over the prediction horizon. Finally, simulated data and a real example from the stock markets are used to illustrate the proposed method.Gaussian white noise | modified Wald test | multivariate delta method | reduced information set | subprocess | Vector autoregression[SDGs]SDG8journal article10.1111/jtsa.127202-s2.0-85169679276https://api.elsevier.com/content/abstract/scopus_id/85169679276