TY - GEN
T1 - Generic Variance Bounds on Estimation and Prediction Errors in Time Series Analysis
T2 - 2019 IEEE Information Theory Workshop, ITW 2019
AU - Fang, Song
AU - Skoglund, Mikael
AU - Johansson, Karl Henrik
AU - Ishii, Hideaki
AU - Zhu, Quanyan
N1 - Funding Information:
The work is partially supported by the Knut and Alice Wallenberg Foundation, the Swedish Strategic Research Foundation, the Swedish Research Council, the JSPS under Grant-in-Aid for Scientific Research Grant No. 18H01460, the NSF under grants CNS-1544782 and ECCS-1847056, and the ARO under grant W911NF1910041.
Publisher Copyright:
© 2019 IEEE.
PY - 2019/8
Y1 - 2019/8
N2 - In this paper, we obtain generic bounds on the variances of estimation and prediction errors in time series analysis via an information-theoretic approach. It is seen in general that the error bounds are determined by the conditional entropy of the data point to be estimated or predicted given the side information or past observations. Additionally, we discover that in order to achieve the prediction error bounds asymptotically, the necessary and sufficient condition is that the 'innovation' is asymptotically white Gaussian. When restricted to Gaussian processes and 1-step prediction, our bounds are shown to reduce to the Kolmogorov-Szegö formula and Wiener-Masani formula known from linear prediction theory.
AB - In this paper, we obtain generic bounds on the variances of estimation and prediction errors in time series analysis via an information-theoretic approach. It is seen in general that the error bounds are determined by the conditional entropy of the data point to be estimated or predicted given the side information or past observations. Additionally, we discover that in order to achieve the prediction error bounds asymptotically, the necessary and sufficient condition is that the 'innovation' is asymptotically white Gaussian. When restricted to Gaussian processes and 1-step prediction, our bounds are shown to reduce to the Kolmogorov-Szegö formula and Wiener-Masani formula known from linear prediction theory.
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U2 - 10.1109/ITW44776.2019.8989240
DO - 10.1109/ITW44776.2019.8989240
M3 - Conference contribution
AN - SCOPUS:85081100218
T3 - 2019 IEEE Information Theory Workshop, ITW 2019
BT - 2019 IEEE Information Theory Workshop, ITW 2019
PB - Institute of Electrical and Electronics Engineers Inc.
Y2 - 25 August 2019 through 28 August 2019
ER -