This book addresses inflation persistence, monetary credibility and stability through modelling US macroeconomic and financial data in the post-war period. First, an ARFIMA-EGARCH model is used to generate estimations capturing the stylized facts of inflation dynamics and examine the links between the inflation rate, volatility and inflation persistence. Then a modified and reduced form of accelerationist Phillips curve is employed to analyse the inflation-unemployment trade-off and thus assess monetary policy credibility. Finally, a conditional constant correlation bivariate EGARCH-in-mean model is used to investigate interactions among inflation rates, stock returns and their respective volatilities. Results provide new evidence that inflation and its volatility are involved in more active interactions in a high inflation environment, whereas less or little related when the inflation rate is lower. The core findings also suggest that the degree of inflation persistence is a reliable measure of monetary credibility. Moreover, promoting monetary stability contributes to more mutual interactions between inflation rates, stock returns and their respective volatilities. In particular, common stock is a more effective hedge against inflation, and the level of the inflation rate is central to explaining the relation between the two volatilities.