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ARMA Representation of Two-Factor Models

Many financial time series models are specified through a structural representation. Nonetheless, knowing their reduced ARMA form may be useful for impulse response analysis, filtering, forecasting, and for purposes of statistical inference. This ARMA representation is the analytical steady-state of the unobservable variable and is therefore an alternative approach to Kalman filter-based methods. In this paper, we analytically derive the moving-average roots of a two-factor model. We then provide a financial application. More precisely, we characterize the weak GARCH(2,2) representation of continuous time stochastic volatility models when the variance process is a linear combination of two autoregressive processes, as in affine, GARCH diffusion, CEV, positive Ornstein-Uhlenbeck, eigenfunction, and SR-SARV processes.
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