NONLINEAR TIME SERIES/SYSTEM ANALYSIS (STATE-SPACE, DYNAMICS, INTERVENTION, RESILIENCE, KALMAN)

A discussion of nonlinear dynamics, demonstrated by the familiar automobile, is followed by the development of a systematic method of analysis of a possibly nonlinear time series using difference equations in the general state-space format. This format allows recursive state-dependent parameter estimation after each observation thereby revealing the dynamics inherent in the system in combination with random external perturbations.^ The one-step ahead prediction errors at each time period, transformed to have constant variance, and the estimated parametric sequences provide the information to (1) formally test whether time series observations y(,t) are some linear function of random errors (ELEM)(,s), for some t and s, or whether the series would more appropriately be described by a nonlinear model such as bilinear, exponential, threshold, etc., (2) formally test whether a statistically significant change has occurred in structure/level either historically or as it occurs, (3) forecast nonlinear system with a new and innovative (but very old numerical) technique utilizing rational functions to extrapolate individual parameters as smooth functions of time which are then combined to obtain the forecast of y and (4) suggest a measure of resilience, i.e. how much perturbation a structure/level can tolerate, whether internal or external to the system, and remain statistically unchanged. Although similar to one-step control, this provides a less rigid way to think about changes affecting social systems.^ Applications consisting of the analysis of some familiar and some simulated series demonstrate the procedure. Empirical results suggest that this state-space or modified augmented Kalman filter may provide interesting ways to identify particular kinds of nonlinearities as they occur in structural change via the state trajectory.^ A computational flow-chart detailing computations and software input and output is provided in the body of the text. IBM Advanced BASIC program listings to accomplish most of the analysis are provided in the appendix. ^

Process to develop a State Model Law to reduce prescription drug trafficking while protecting pain management

This paper will discuss the intersection of pill mills and the under-treatment of pain, while addressing the unintended consequence that cracking down on pill mills actually has on medical professionals' treatment of legitimate pain in clinical settings. Moreover, the impact each issue has on the spectrum of related policy, regulatory issues and legislation will be analyzed while addressing the national impact on medical care. Lastly, this paper will outline a process to develop a State Model Law on this subject. This process will include suggestions for the future and how we can move forward to adequately address public safety needs and how we can attempt to mitigate the unintended impact prescription drug trafficking has had on a patient's right to appropriate pain management. This balance is achievable and this paper will address ways we can find this elusive balancing point through the development of a State Model Law. ^