In this dissertation, I study model misspecification in applications of dynamic factor models to finance. In Chapter 1, my co-author Jacob Warren and I examine factors for volatility of equities. Historical literature on the subject decomposes volatility into a factor component and an idiosyncratic remainder. Recent work has suggested that idiosyncratic volatility of US equities data has a factor structure, with the factor highly correlated with, and possibly precisely the market volatility. In this paper we attempt to characterize the underlying factor and find that it can be decomposed into a statistical (PCA) and structural (market volatility) factor. We also show that this feature is not unique to equities, appearing in diverse sets of financial data. Lastly, we find that this dual-factor approach is slightly dominated in forecasting environments by a single statistical factor, suggesting that accurate measurement of the factors provides a direction for future work. In Chapter 2, I explore the use of dynamic factor models in yield curve forecasting and an exploration of the spanning hypothesis – that is, whether all information necessary for forecasting yields is contained in the current yield curve. Only linear tests of the spanning hypothesis are typically conducted in the literature, and the results are subject to substantial disagreement. In this paper, I explore a key modern nonlinearity, namely the zero lower bound (ZLB). I first demonstrate in simulation that only very small nonlinearities in the measurement equation are necessary to break down the assumed linear spanning relationship. Because bond yields are determined by forward-looking behavior of investors, the effect of the ZLB affects spanning results as early as 1995. New nonlinear spanning tests are found to behave appropriately. Using the full set of yields instead of truncating to a small number of principal components is quantitatively important but does not eliminate the omitted nonlinearity effect.