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Original Articles

The aliasing‐phenomenon in visual terms

Pages 39-49 | Received 11 Jul 1991, Published online: 26 Aug 2010
 

In a recent paper it was shown that the aliasing phenomenon, which leads to a severe identification problem in the estimation of stochastic differential equations, can be overcome by using a polygonal (or higher) approximation for the time paths of the exogenous variables. This work attempts to visualize the problem and presents several simulated trajectories of a continuous time AR(2)‐process (Ornstein‐Uhlenbeck‐process) together with the observationally equivalent structures. Furthermore it is shown that aliasing can even change the analytical properties of the time paths of the system: whereas the first component of the Ornstein‐Uhlenbeck‐process is differentiable, the trajectories of the aliasing structures are continuous, but not differentiable any more.

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