Denial constraints are vital in data quality management, but traditional mining algorithms struggle with time series data. To address this, we introduce a novel data quality rule, threshold Denial Constraints ($t$DCs), which enables predicate scaling in numerical contexts. We formalize the inference system for$t$DCs and demonstrate the monotonicity and abruptness of threshold predicates. To efficiently mine$t$DCs, we design the tDCDiscover algorithm, which leverages batch computation of differences and thresholds to significantly reduce the time required for acquiring homologous predicate evidence, achieving a 50% -66% decrease. Additionally, we introduce an evidence matrix to store evidence, lowering the complexity of evidence matching from$O(m)$to$O(1)$. We propose two pruning strategies: triviality pruning and prediction coverage pruning, to effectively decrease the search paths to one-fifth of their original number and eliminating at least 90% of unnecessary paths. We theoretically prove that tDCDiscover ensures minimal, valid, and complete results. Experimental results on eight real-world datasets demonstrate that, compared to the current state-of-the-art denial constraint mining techniques, tDCDiscover achieves more than double the efficiency when processing high-dimensional time series data. In downstream data cleaning tasks, tDCDiscover improves error detection precision by an average of 40% and repair accuracy by 18%, further offering advantages in time series data quality management.