Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

Correlation and Regression00:53

Correlation and Regression

2.9K
In statistics, correlation describes the degree of association between two variables. In the subfield of linear regression, correlation is mathematically expressed by the correlation coefficient, which describes the strength and direction of the relationship between two variables. The coefficient is symbolically represented by 'r' and ranges from -1 to +1. A positive value indicates a positive correlation where the two variables move in the same direction. A negative value suggests a...
2.9K
Coefficient of Correlation01:12

Coefficient of Correlation

8.1K
The correlation coefficient, r, developed by Karl Pearson in the early 1900s, is numerical and provides a measure of strength and direction of the linear association between the independent variable x and the dependent variable y.
If you suspect a linear relationship between x and y, then r can measure how strong the linear relationship is.
What the VALUE of r tells us:
The value of r is always between –1 and +1: –1 ≤ r ≤ 1.
The size of the correlation r indicates the...
8.1K
Correlation of Experimental Data01:23

Correlation of Experimental Data

450
Dimensional analysis simplifies complex physical problems and guides experimental investigations, but it does not provide complete solutions. It identifies the dimensionless groups that influence a phenomenon, but experimental data is needed to establish the specific relationships and validate theoretical predictions.
For example, a spherical particle moving through a viscous fluid experiences drag. Dimensional analysis shows that the drag force depends on the particle's diameter, velocity,...
450
Friedman Two-way Analysis of Variance by Ranks01:21

Friedman Two-way Analysis of Variance by Ranks

459
Friedman's Two-Way Analysis of Variance by Ranks is a nonparametric test designed to identify differences across multiple test attempts when traditional assumptions of normality and equal variances do not apply. Unlike conventional ANOVA, which requires normally distributed data with equal variances, Friedman's test is ideal for ordinal or non-normally distributed data, making it particularly useful for analyzing dependent samples, such as matched subjects over time or repeated measures...
459
Quadratic Models01:23

Quadratic Models

141
Quadratic models are mathematical representations used to describe relationships in which the rate of change changes at a constant rate. These models appear in a wide variety of natural and engineered systems, especially those involving motion, forces, and optimization. One common application is analyzing the vertical motion of objects influenced by gravity, such as a ball thrown into the air.In such scenarios, the object's height changes over time in a curved pattern, rising to a maximum point...
141
Calculating and Interpreting the Linear Correlation Coefficient01:11

Calculating and Interpreting the Linear Correlation Coefficient

7.6K
The correlation coefficient, r, developed by Karl Pearson in the early 1900s, is numerical and provides a measure of strength and direction of the linear association between the independent variable, x, and the dependent variable, y. Hence, it is also known as the Pearson product-moment correlation coefficient. It can be calculated using the following equation:
7.6K

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

Design Principles for Perfect Adaptation in Biological Networks with Nonlinear Dynamics.

Bulletin of mathematical biology·2024
Same author

Design Principles for Biological Adaptation: A Systems and Control-Theoretic Treatment.

Methods in molecular biology (Clifton, N.J.)·2024
Same author

Sloppiness: Fundamental study, new formalism and its application in model assessment.

PloS one·2023
Same author

On biological networks capable of robust adaptation in the presence of uncertainties: A linear systems-theoretic approach.

Mathematical biosciences·2023
Same author

Discovering design principles for biological functionalities:Perspectives from systems biology.

Journal of biosciences·2022
Same author

Joint clustering and prediction approach for travel time prediction.

PloS one·2022

Related Experiment Video

Updated: Jan 1, 2026

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach
04:35

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach

Published on: July 3, 2020

3.6K

Scalar correlation functions for model structure selection in high-dimensional time-series modelling.

Sudhakar Kathari1, Arun K Tangirala1

  • 1Process Systems Engineering and Data Sciences, Department of Chemical Engineering, Indian Institute of Technology Madras, Chennai 600 036, India.

ISA Transactions
|December 16, 2019
PubMed
Summary

This study introduces novel scalar autocorrelation functions (SACF) and scalar inverse autocorrelation functions (SIACF) for pre-estimation model selection in high-dimensional time-series. These functions efficiently identify vector autoregressive (VAR), vector moving average (VMA), and VARMA model classes and orders.

Keywords:
High-dimensionalModel selectionOrder determinationScalar correlation functionsTime-series modellingVARMA models

More Related Videos

Author Spotlight: Alignment of Synchronized Time-Series Data Using the Characterizing Loss of Cell Cycle Synchrony Model for Cross-Experiment Comparisons
07:59

Author Spotlight: Alignment of Synchronized Time-Series Data Using the Characterizing Loss of Cell Cycle Synchrony Model for Cross-Experiment Comparisons

Published on: June 9, 2023

1.8K
A Psychophysics Paradigm for the Collection and Analysis of Similarity Judgments
08:12

A Psychophysics Paradigm for the Collection and Analysis of Similarity Judgments

Published on: March 1, 2022

2.9K

Related Experiment Videos

Last Updated: Jan 1, 2026

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach
04:35

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach

Published on: July 3, 2020

3.6K
Author Spotlight: Alignment of Synchronized Time-Series Data Using the Characterizing Loss of Cell Cycle Synchrony Model for Cross-Experiment Comparisons
07:59

Author Spotlight: Alignment of Synchronized Time-Series Data Using the Characterizing Loss of Cell Cycle Synchrony Model for Cross-Experiment Comparisons

Published on: June 9, 2023

1.8K
A Psychophysics Paradigm for the Collection and Analysis of Similarity Judgments
08:12

A Psychophysics Paradigm for the Collection and Analysis of Similarity Judgments

Published on: March 1, 2022

2.9K

Area of Science:

  • Statistics
  • Econometrics
  • Time Series Analysis

Background:

  • Model structure selection is critical in high-dimensional time-series analysis.
  • Traditional methods like AIC and BIC are applied post-estimation.
  • Existing penalized regression methods require pre-defined model classes.

Purpose of the Study:

  • To propose a novel pre-estimation approach for identifying time-series model structures.
  • To introduce scalar autocorrelation function (SACF) and scalar inverse autocorrelation function (SIACF) for model class identification.
  • To determine the exact order of VAR and VMA processes efficiently.

Main Methods:

  • Development of two novel correlation functions: SACF and SIACF.
  • Utilizing linear constructs of multivariate processes with a lagged-correlation equivalence constraint.
  • Comparing the proposed method with standard M^2 correlation and inverse correlation plots.

Main Results:

  • SACF and SIACF effectively identify VAR, VMA, and VARMA model classes.
  • Theoretical determination of the exact order for VAR and VMA processes.
  • Computational efficiency, especially for high-dimensional and small-sample time-series data.

Conclusions:

  • The proposed SACF and SIACF offer a computationally light and efficient pre-estimation method for model selection.
  • This approach simplifies structure identification compared to traditional methods.
  • The utility is particularly pronounced in small sample conditions for achieving parsimonious and efficient model estimates.