Market liberalization and the expansion of variable renewable energy sources in power systems have made the dynamics of electricity prices more uncertain, leading them to show high volatility with sudden, unexpected price spikes. Thus, developing more accurate price modeling and forecasting techniques is a challenge for all market participants and regulatory authorities. This paper proposes a forecasting approach based on using auction data to fit supply and demand electricity curves. More specifically, we fit linear (LinX-Model) and logistic (LogX-Model) curves to historical sale and purchase bidding data from the Iberian electricity market to estimate structural parameters from 2015 to 2019. Then we use time series models on structural parameters to predict day-ahead prices. Our results provide a solid framework for forecasting electricity prices by capturing the structural characteristics of markets.