Introduction to Time-Series Analysis and Dependence

Introduction to Time-Series Analysis and Dependence........................................285 Time-Series Analysis — Why? .............................................................................285 Time-Series Analysis — How? .............................................................................286 Time-Series Analysis — Results...........................................................................287 Some Things to Consider ......................................................................................288 Dependence — What Is It? ...................................................................................290 Independent and Dependent Variables ..................................................................291 Degree of Dependence ..........................................................................................291 Multiple Dependencies and Circular Dependence................................................294 Effect of Dependence on Monte Carlo Output.....................................................295 Dependence — It’s Ubiquitous .............................................................................295

Time-series analysis and dependence are functions that help risk models better emulate actual situations. Time-series analysis allows us to break free of the singleperiod assessment and to project the analysis through time. This is a facility that is critical in most business applications, for example, in which cash flows over time are combined to generate project-representative values such as net present value (NPV). Dependence is a technique that allows a risk model to respect the relationships between variables. Without application of dependence technology, any hope of emulating real-world processes is folly. Both time-series analysis and dependence are treated in the following sections.