Deterministic and Stochastic Models

Charlie Nelson
March 2010




Deterministic models describe behaviour on the basis of some physical law.  For example, the planets move around the sun according to Newton's laws and their position can be predicted with great accuracy well into the future.  In practice, a totally deterministic relationship is unlikely due to unpredictable factors - for example, a comet moving through the solar system could collide with a planet or a moon and perturb its orbit.  What's more, Newton's laws can only predict the positions of two bodies, such as the sun and the earth exactly.  If there is a third body, such as the moon, there is no longer a simple mathematical that can describe and predict the paths of all three with unlimited accuracy for all time.  When applied to the whole solar system, even supercomputers can't use Newton's laws to predict the resulting chaos.

Where the influence of several unknown factors is sizable, exact prediction is not possible, but it may be possible to predict to within a known confidence interval - or to predict the probability that a particular value will be observed at a particular time.  This is called a stochastic (or probabilistic) process.

A time series, such as gross domestic product, is a sample outcome from a stochastic process.  Many "agents" act independently to influence the economy.  While we know there is a relationship between interest rates, say, and economic growth the relationship is not deterministic and there is also "noise" caused by the random actions of the many agents.


Interested in forecasting?  See my book Forecasting: the essential skills