<p>This study considers a finite-time consumption-investment problem for investors with homothetic robust utility under a quadratic security market (QSM) model with stochastic volatilities and inflation rates. This leads to a nonlinear partial differential equation for indirect utility. We propose a time-dependent linear approximation method and derive the approximate optimal robust portfolio decomposed into myopic, intertemporal hedging, and inflation-deflation hedging demands. Furthermore, we introduce a method for estimating our QSM model that stabilizes the optimal portfolio estimates. We then apply our estimation method to a two-factor QSM model. Our numerical analysis shows that i) the linear approximate optimal portfolio is highly accurate and ii) the market timing effects in the optimal robust allocation are significant and nonlinear, and are mainly due to inflation-deflation hedging demand in addition to myopic demand.</p>