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Linear Stochastic Models in Discrete and Continuous Time

Department of Economics, University of Leciceter, Leciceter LE1 7RH, UK
Received: 1 June 2020 / Revised: 27 August 2020 / Accepted: 28 August 2020 / Published: 4 September 2020
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. View Full-Text
Keywords: linear sochastic differential equations; autoregersive moving-average models; frequency-limited processes; Nyquist–Shannon sampling therorem linear sochastic differential equations; autoregersive moving-average models; frequency-limited processes; Nyquist–Shannon sampling therorem
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MDPI and ACS Style

Pollock, D.S.G. Linear Stochastic Models in Discrete and Continuous Time. Econometrics 2020, 8, 35. https://0-doi-org.brum.beds.ac.uk/10.3390/econometrics8030035

AMA Style

Pollock DSG. Linear Stochastic Models in Discrete and Continuous Time. Econometrics. 2020; 8(3):35. https://0-doi-org.brum.beds.ac.uk/10.3390/econometrics8030035

Chicago/Turabian Style

Pollock, D. S.G. 2020. "Linear Stochastic Models in Discrete and Continuous Time" Econometrics 8, no. 3: 35. https://0-doi-org.brum.beds.ac.uk/10.3390/econometrics8030035

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