Band-Limited Stochastic Processes in Discrete and Continuous Time
-
D.S.G. Pollock
A theory of band-limited linear stochastic processes is described and it is related to the familiar theory of ARMA models in discrete time. By ignoring the limitation on the frequencies of the forcing function, in the process of fitting a conventional ARMA model, one is liable to derive estimates that are severely biased. If the maximum frequency in the sampled data is less than the Nyquist value, then the underlying continuous function can be reconstituted by sinc function or Fourier interpolation. The estimation biases can be avoided by re-sampling the continuous process at a rate corresponding to the maximum frequency of the forcing function. Then, there is a direct correspondence between the parameters of the band-limited ARMA model and those of an equivalent continuous-time process.
©2012 Walter de Gruyter GmbH & Co. KG, Berlin/Boston
Articles in the same Issue
- Article
- Band-Limited Stochastic Processes in Discrete and Continuous Time
- Forecasting U.S. Output Growth with Non-Linear Models in the Presence of Data Uncertainty
- Asymmetric Unemployment Rate Dynamics in Australia
- Simultaneity and Asymmetry of Returns and Volatilities: The Emerging Baltic States' Stock Exchanges
- Flexible Modelling of Duration of Unemployment Using Functional Hazard Models and Penalized Splines: A Case Study Comparing Germany and the UK
- The Pricing of Time-Varying Exchange Rate Risk in the Stock Market: A Nonparametric Approach
Articles in the same Issue
- Article
- Band-Limited Stochastic Processes in Discrete and Continuous Time
- Forecasting U.S. Output Growth with Non-Linear Models in the Presence of Data Uncertainty
- Asymmetric Unemployment Rate Dynamics in Australia
- Simultaneity and Asymmetry of Returns and Volatilities: The Emerging Baltic States' Stock Exchanges
- Flexible Modelling of Duration of Unemployment Using Functional Hazard Models and Penalized Splines: A Case Study Comparing Germany and the UK
- The Pricing of Time-Varying Exchange Rate Risk in the Stock Market: A Nonparametric Approach
