For example, if people want to create an expectation of the inflation rate in the future, they can refer to past inflation rates to infer some consistencies and could derive a more accurate expectation the more years they consider.
The importance of considering the error prevents over and under expecting values of in the above example inflation rates.
When an agent makes a forecasting error (as in incorrectly recording a value or mistyping), the stochastic shock will cause the agent to incorrectly forecast the price expectation level again even if the price level experiences no further shocks, since the previous expectations only ever incorporates part of their errors.
However, it must be stressed that confronting adaptive expectations and rational expectations aren't necessarily justified by either use, in other words, there are situations in which following the adaptive scheme is a rational response.
[3] Adaptive expectations were instrumental in the consumption function (1957) and Phillips curve outlined by Milton Friedman.
Friedman suggests that workers form adaptive expectations of the inflation rate, the government can easily surprise them through unexpected monetary policy changes.
As agents are trapped by the money illusion, they are unable to correctly perceive price and wage dynamics, so based on Friedman's theory, unemployment can always be reduced through monetary expansions.
If the government chooses to fix a low unemployment rate the result is an increasing level of inflation for an extended period of time.
Agents are arbitrarily supposed to ignore sources of information which, otherwise, would affect their expectations.
This is the reason why the theory of adaptive expectations is often regarded as a deviation from the rational tradition of economics.