Locally Stationary Functional Time Series

The literature on time series of functional data has focused on processes of which the probabilistic law is either constant over time or constant up to its second-order structure. Especially for long stretches of data it is desirable to be able to weaken this assumption. This paper introduces a framework that will enable meaningful statistical inference of functional data of which the dynamics change over time. We put forward the concept of local stationarity in the functional setting and establish a class of processes that have a functional time-varying spectral representation. Subsequently, we derive conditions that allow for fundamental results from nonstationary multivariate time series to carry over to the function space. In particular, time-varying functional ARMA processes are investigated and shown to be functional locally stationary according to the proposed definition. As a side-result, we establish a Cram\'er representation for an important class of weakly stationary functional processes. Important in our context is the notion of a time-varying spectral density operator of which the properties are studied and uniqueness is derived. Finally, we provide a consistent nonparametric estimator of this operator and show it is asymptotically Gaussian using a weaker tightness criterion than what is usually deemed necessary

Shaking the Tree: An Agency Theoretic Model of Asset Pricing

In this paper, we develop an agency-theoretic extension of the Lucas asset pricing model and examine the resulting asset price dynamics. In the model, an agent of the firm can expand or contract the firm's output and dividend payments in response to exogenous shocks, although expansions become increasingly costly for the agent to maintain. Analysis of numerical simulations shows that the time-series of equilibrium asset prices exhibits both significant time-varying conditional heteroskedasticity, and longer memory persistence.