Time Series from Intertemporal Optimization

Economic time series are generated as economic agents engage in intertemporal optimization. Although time is an extra complicating factor, dynamic optimization, i.e., optimization over time arises for the same reason that static optimization (i.e., linear and nonlinear programming) problems arise in economics: Trade-offs must be made in allocating scarce resources; the only difference being that the trade-offs over time also must be made because dynamics constrains choice sets effectively over time. Economic time series are usually nonstationary because circumstances facing optimizing economic agents change with time and do not remain the same. Time series are also nonlinear because the dynamic structure generating data are mostly nonlinear. We are thus faced with nonstationary and nonlinear stochastic processes.