Linear Stochastic Models in Discrete and Continuous Time

D. Stephen G. Pollock
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D. Stephen G. Pollock: Department of Economics, University of Leciceter, Leciceter LE1 7RH, UK

Econometrics, 2020, vol. 8, issue 3, 1-22

Abstract: The econometric data to which autoregressive moving-average models are commonly applied are liable to contain elements from a limited range of frequencies. If the data do not cover the full Nyquist frequency range of [ 0 , π ] radians, then severe biases can occur in estimating their parameters. The recourse should be to reconstitute the underlying continuous data trajectory and to resample it at an appropriate lesser rate. The trajectory can be derived by associating sinc fuction kernels to the data points. This suggests a model for the underlying processes. The paper describes frequency-limited linear stochastic differential equations that conform to such a model, and it compares them with equations of a model that is assumed to be driven by a white-noise process of unbounded frequencies. The means of estimating models of both varieties are described.

Keywords: linear sochastic differential equations; autoregersive moving-average models; frequency-limited processes; Nyquist–Shannon sampling therorem (search for similar items in EconPapers)
JEL-codes: B23 C C00 C01 C1 C2 C3 C4 C5 C8 (search for similar items in EconPapers)
Date: 2020
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