# Mitigating the effects of measurement noise on Granger causality

## Abstract

Computing Granger causal relations among bivariate experimentally observed time series has received increasing attention over the past few years. Such causal relations, if correctly estimated, can yield significant insights into the dynamical organization of the system being investigated. Since experimental measurements are inevitably contaminated by noise, it is thus important to understand the effects of such noise on Granger causality estimation. The first goal of this paper is to provide an analytical and numerical analysis of this problem. Specifically, we show that, due to noise contamination (1) spurious causality between two measured variables can arise and (2) true causality can be suppressed. The second goal of the paper is to provide a denoising strategy to mitigate this problem. Specifically, we propose a denoising algorithm based on the combined use of the Kalman filter theory and the expectation-maximization algorithm. Numerical examples are used to demonstrate the effectiveness of the denoising approach.

- Authors:

- J. Crayton Pruitt Family Department of Biomedical Engineering, University of Florida, Gainesville, Florida 32611 (United States)
- (India)

- Publication Date:

- OSTI Identifier:
- 21072394

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics; Journal Volume: 75; Journal Issue: 3; Other Information: DOI: 10.1103/PhysRevE.75.031123; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND TECHNOLOGY; ALGORITHMS; CALCULATION METHODS; CAUSALITY; NOISE; NUMERICAL ANALYSIS; OPTIMIZATION; QUANTUM MECHANICS; SIGNALS

### Citation Formats

```
Nalatore, Hariharan, Ding Mingzhou, Rangarajan, Govindan, and Department of Mathematics, Indian Institute of Science, Bangalore 560 012.
```*Mitigating the effects of measurement noise on Granger causality*. United States: N. p., 2007.
Web. doi:10.1103/PHYSREVE.75.031123.

```
Nalatore, Hariharan, Ding Mingzhou, Rangarajan, Govindan, & Department of Mathematics, Indian Institute of Science, Bangalore 560 012.
```*Mitigating the effects of measurement noise on Granger causality*. United States. doi:10.1103/PHYSREVE.75.031123.

```
Nalatore, Hariharan, Ding Mingzhou, Rangarajan, Govindan, and Department of Mathematics, Indian Institute of Science, Bangalore 560 012. Thu .
"Mitigating the effects of measurement noise on Granger causality". United States.
doi:10.1103/PHYSREVE.75.031123.
```

```
@article{osti_21072394,
```

title = {Mitigating the effects of measurement noise on Granger causality},

author = {Nalatore, Hariharan and Ding Mingzhou and Rangarajan, Govindan and Department of Mathematics, Indian Institute of Science, Bangalore 560 012},

abstractNote = {Computing Granger causal relations among bivariate experimentally observed time series has received increasing attention over the past few years. Such causal relations, if correctly estimated, can yield significant insights into the dynamical organization of the system being investigated. Since experimental measurements are inevitably contaminated by noise, it is thus important to understand the effects of such noise on Granger causality estimation. The first goal of this paper is to provide an analytical and numerical analysis of this problem. Specifically, we show that, due to noise contamination (1) spurious causality between two measured variables can arise and (2) true causality can be suppressed. The second goal of the paper is to provide a denoising strategy to mitigate this problem. Specifically, we propose a denoising algorithm based on the combined use of the Kalman filter theory and the expectation-maximization algorithm. Numerical examples are used to demonstrate the effectiveness of the denoising approach.},

doi = {10.1103/PHYSREVE.75.031123},

journal = {Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics},

number = 3,

volume = 75,

place = {United States},

year = {Thu Mar 15 00:00:00 EDT 2007},

month = {Thu Mar 15 00:00:00 EDT 2007}

}