Granger Causality of Gaussian Signals from Binary or Non-uniformly Quantized Measurements

Abstract

This paper studies the assessment of Granger causality between jointly Gaussian sig -nals from binary/non-uniformly quantized measurements. A necessary and sufficient condition is proposed for Granger causality inference under binary quantization. Furthermore, sufficient conditions are introduced to infer Granger causality between jointly Gaussian signals through non-uniformly quantized measurements. No assumptions are made on the identifiability of the jointly Gaussian random processes through the quantized observations.