Forecasting with Alternative Data

Abstract

We consider the problem of forecasting fine-grained company financials, such as daily revenue, from two input types: noisy proxy signals a la alternative data (e.g. credit card transactions) and sparse ground-truth observations (e.g. quarterly earnings reports). We utilize a classical linear systems model to capture both the evolution of the hidden or latent state (e.g. daily revenue), as well as the proxy signal (e.g. credit cards transactions). The linear system model is particularly well suited here as data is extremely sparse (4 quarterly reports per year). In classical system identification, where the central theme is to learn parameters for such linear systems, unbiased and consistent estimation of parameters is not feasible: the likelihood is non-convex; and worse, the global optimum for maximum likelihood estimation is often non-unique.As the main contribution of this work, we provide a simple, consistent estimator of all parameters for the linear system model of interest; in addition the estimation is unbiased for some of the parameters. In effect, the additional sparse observations of aggregate hidden state (e.g. quarterly reports) enable system identification in our setup that is not feasible in general. For estimating and forecasting hidden state (actual earnings) using the noisy observations (daily credit card transactions), we utilize the learned linear model along with a natural adaptation of classical Kalman filtering (or Belief Propagation). This leads to optimal inference with respect to mean-squared error. Analytically, we argue that even though the underlying linear system may be unstable,'' uncontrollable,'' or undetectable'' in the classical setting, our setup and inference algorithm allow for estimation of hidden state with bounded error. Further, the estimation error of the algorithm monotonically decreases as the frequency of the sparse observations increases. This, seemingly intuitive insight contradicts the word on the Street. Finally, we utilize our framework to estimate quarterly earnings of 34 public companies using credit card transaction data. Our data-driven method convincingly outperforms the Wall Street consensus (analyst) estimates even though our method uses only credit card data as input, while the Wall Street consensus is based on various data sources including experts' input.