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Issues Concerning the Approximation Underlying the Spectral Representation Theorem


  • Marco Lippi


In many important textbooks the formal statement of the Spectral RepresentationTheorem is followed by a process version, usually informal, stating thatany stationary stochastic process g is the limit in quadratic mean of asequence of processes, each consisting of a finite sum of harmonicoscillations with stochastic weights. The natural issues, whether the approximationerror is stationary, or whether at least it converges to zero uniformly int , have not been explicitly addressed in the literature. The paper shows that in allrelevant cases, for T unbounded the process convergence is not uniform in t. Equivalently, when T is unbounded the numberof harmonic oscillations necessary to approximate a stationary stochastic process with a preassigned accuracydepends on t . The conclusion is that the process version of the Spectral RepresentationTheorem should explicitely mention that in general the approximation of a stationary stochastic processby a finite sum of harmonic oscillations, given the accuracy, is valid for t belongingto a bounded subset of the real axis (of the set of integers in the discrete-parametercase).

Suggested Citation

  • Marco Lippi, 2003. "Issues Concerning the Approximation Underlying the Spectral Representation Theorem," LEM Papers Series 2003/14, Laboratory of Economics and Management (LEM), Sant'Anna School of Advanced Studies, Pisa, Italy.
  • Handle: RePEc:ssa:lemwps:2003/14

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    1. Langlois, Richard N., 2002. "Modularity in technology and organization," Journal of Economic Behavior & Organization, Elsevier, vol. 49(1), pages 19-37, September.
    2. Jan W. Rivkin & Nicolaj Siggelkow, 2003. "Balancing Search and Stability: Interdependencies Among Elements of Organizational Design," Management Science, INFORMS, vol. 49(3), pages 290-311, March.
    3. Marengo, Luigi, et al, 2000. "The Structure of Problem-Solving Knowledge and the Structure of Organizations," Industrial and Corporate Change, Oxford University Press, vol. 9(4), pages 757-788, December.
    4. Christoph H. Loch & Christian Terwiesch & Stefan Thomke, 2001. "Parallel and Sequential Testing of Design Alternatives," Management Science, INFORMS, vol. 47(5), pages 663-678, May.
    5. Herbert A. Simon, 1996. "The Sciences of the Artificial, 3rd Edition," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262691914, July.
    6. Fleming, Lee & Sorenson, Olav, 2001. "Technology as a complex adaptive system: evidence from patent data," Research Policy, Elsevier, vol. 30(7), pages 1019-1039, August.
    7. Schaefer, Scott, 1999. "Product design partitions with complementary components," Journal of Economic Behavior & Organization, Elsevier, vol. 38(3), pages 311-330, March.
    8. Radner, Roy, 1993. "The Organization of Decentralized Information Processing," Econometrica, Econometric Society, vol. 61(5), pages 1109-1146, September.
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    Stochastic processes. Stationarity. Spectral analysis.;

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