Traditional instrumental variable approaches assume uniform instrument relevance across all observations, an assumption frequently violated in time series applications due to structural breaks, regime changes, and evolving economic relationships. This paper develops a comprehensive framework for identifying, estimating, and conducting inference on local average treatment effects when the strength of the instrument varies over time. We introduce the concept of π-LATE, which represents treatment effects for the subset of observations where instruments remain relevant, and demonstrate methods for individually identifying compliers in time series data. Through extensive simulation studies and an empirical application to monetary policy transmission, we demonstrate that focusing on strongly identified subsamples can substantially improve estimation precision while maintaining a valid causal interpretation. Our survey of recent publications in leading economics journals reveals that weak identification affects 75% of time series specifications, yet strong identification often exists in large subsamples, suggesting the widespread applicability of our methods.