A Paradox in the Theory of Prediction-Reference-Cited by-同舟云学术

A Paradox in the Theory of Prediction

Published:2023-06-15 Issue:05 Volume:22 Page:
ISSN:0219-4775
Container-title:Fluctuation and Noise Letters
language:en
Short-container-title:Fluct. Noise Lett.

Author:

Mohammadi Mohammad¹,Lindquist W. Brent²

Affiliation:

1. Department of Statistics, Faculty of Science, Behbahan Khatam Alanbia University of Technology, Behbahan, Iran

2. Department of Mathematics and Statistics, Texas Tech University, Lubbock, TX, USA

Abstract

Given the set of past values, [Formula: see text], [Formula: see text], it is known that the conditional mean [Formula: see text] is the best predictor of [Formula: see text], [Formula: see text], where ‘best’ is defined in terms of minimization of mean square error. In this paper, we show that a prediction using the Riemann sum approximation to the spectral (Fourier) representation of a stationary time series produces a smaller mean square error. We attribute the resolution of this apparent paradox to the fact that the Riemann sum approach preserves more information of the spectral (frequency) content of the past time series than does the conditional mean — which effectively represents only the zeroth (constant value) frequency.

Publisher

World Scientific Pub Co Pte Ltd

Subject

General Physics and Astronomy,General Mathematics

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0219477523500384

Reference8 articles.

1. A new hybrid model for wind speed forecasting combining long short-term memory neural network, decomposition methods and grey wolf optimizer

2. Time Series: Theory and Methods

3. A Review of Deep Learning Models for Time Series Prediction

4. Crude oil time series prediction model based on LSTM network with chaotic Henry gas solubility optimization

5. A new method for prediction of stationary time series using the Riemann sum approximation