Chronic inflation in Iran results from the complex interaction of exchange rate shocks, liquidity growth, and fiscal dominance. Yet the literature cannot distinguish the activation horizons of these factors, impeding policy design. We disentangle causality horizons and identify when transmission channels activate. Using 1990–2023 data, we decompose the series via maximal overlap discrete wavelet transform (MODWT) into short-run (<2 years), medium-run (2–4 years), and long-run (>4 years) horizons, and then apply a rolling-window Granger causality test. Combining these methods allows tracing dynamic causal relationships in the time–frequency domain and detecting the activation timing of each channel. Results show that in the short run, exchange rate growth strongly causes inflation, consistent with liquidity endogeneity (inflation → liquidity). In the medium run, liquidity growth positively causes inflation, confirming the quantity theory of money with a 2–4-year lag, and a feedback loop among exchange rate, liquidity, and inflation forms. In the long run, fiscal dominance becomes entrenched: inflation stably causes liquidity, and inflation positively causes exchange rate growth, consistent with the monetary theory of exchange rate. Thus, chronic inflation is rooted in institutionalized endogenous money creation under fiscal dominance, not just exchange rate shocks. Sustained disinflation requires short-run exchange rate shock management, medium-run liquidity control, and long-run institutional reforms to break the fiscal dominance loop.