Time Series Modelling

Time series are incredibly useful tools for modeling systems. Time series are basically representations of variables that change over time. They can be used to model ocean currents, stocks, population, and pretty much everything that changes over time.

Construction of time series is done by analyzing past data for a number of trends. These things can be as simple as is the data cyclic as in does it repeat a pattern over some time interval. Or it can be more complex such as having various frequency dependencies that cause various smaller cycles to occur within a larger cycle.

Some time series are chaotic in nature meaning that starting out with similar but not equal initial conditions can yield large differences in their progressions over time. Many natural systems are chaotic such as water flow during a storm, double pendulum machines, or turbulence in a vortex.

Time series can also be used to model systems that change with respect to other variables over time. This way it can model things like the stock market which changes due to many variables such as inflation or earnings. Developing an accurate time series model then allows extrapolation to future events and allows for predictions to be made. This also shows some of the limitations of the theoretical uses because clearly we do not have accurate predictors of the stock market.

This occurs because there are so many variables that affect our system that we cannot perfectly model the system. Generally we settle for approximations of systems which gives us a general idea but does not give perfect results. We construct these models to allow general predictions to be made and we strive to improve our models as this gives us results that are closer and closer to reality.