Search research articles

ABOUT JoVE

Overview Leadership Blog JoVE Help Center

AUTHORS

Publishing Process Editorial Board Scope & Policies Peer Review FAQ Submit

LIBRARIANS

Testimonials Subscriptions Access Resources Library Advisory Board FAQ

RESEARCH

JoVE Journal Methods Collections JoVE Encyclopedia of Experiments Archive

EDUCATION

JoVE Core JoVE Business JoVE Science Education JoVE Lab Manual Faculty Resource Center Faculty Site

Terms & Conditions of Use

Related Concept Videos

Prediction Intervals

Prediction Intervals

The interval estimate of any variable is known as the prediction interval. It helps decide if a point estimate is dependable.
However, the point estimate is most likely not the exact value of the population parameter, but close to it. After calculating point estimates, we construct interval estimates, called confidence intervals or prediction intervals. This prediction interval comprises a range of values unlike the point estimate and is a better predictor of the observed sample value, y.
The...

Parametric Survival Analysis: Weibull and Exponential Methods

Parametric Survival Analysis: Weibull and Exponential Methods

Parametric survival analysis models survival data by assuming a specific probability distribution for the time until an event occurs. The Weibull and exponential distributions are two of the most commonly used methods in this context, due to their versatility and relatively straightforward application.
Weibull Distribution
The Weibull distribution is a flexible model used in parametric survival analysis. It can handle both increasing and decreasing hazard rates, depending on its shape parameter...

Linear time-invariant Systems

Linear time-invariant Systems

A system is linear if it displays the characteristics of homogeneity and additivity, together termed the superposition property. This principle is fundamental in all linear systems. Linear time-invariant (LTI) systems include systems with linear elements and constant parameters.
The input-output behavior of an LTI system can be fully defined by its response to an impulsive excitation at its input. Once this impulse response is known, the system's reaction to any other input can be calculated...

Linear Approximation in Time Domain

Linear Approximation in Time Domain

Nonlinear systems often require sophisticated approaches for accurate modeling and analysis, with state-space representation being particularly effective. This method is especially useful for systems where variables and parameters vary with time or operating conditions, such as in a simple pendulum or a translational mechanical system with nonlinear springs.
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length, the...

Determination of Expected Frequency

Determination of Expected Frequency

Suppose one wants to test independence between the two variables of a contingency table. The values in the table constitute the observed frequencies of the dataset. But how does one determine the expected frequency of the dataset? One of the important assumptions is that the two variables are independent, which means the variables do not influence each other. For independent variables, the statistical probability of any event involving both variables is calculated by multiplying the individual...

Quadratic Models

Quadratic Models

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...

You might also read

Related Articles

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

Sort by

Same author

Triptolide protects rat heart against pressure overload-induced cardiac fibrosis.

International journal of cardiology·2013

Same author

Multiresidue pesticide analysis of botanical dietary supplements using salt-out acetonitrile extraction, solid-phase extraction cleanup column, and gas chromatography-triple quadrupole mass spectrometry.

Analytical chemistry·2013

Same author

Interaction domains of p62: a bridge between p62 and selective autophagy.

DNA and cell biology·2013

Same author

Predictors of seizure freedom after surgical management of tuberous sclerosis complex: a systematic review and meta-analysis.

Epilepsy research·2013

Same author

Temporary ileostomy versus colostomy for colorectal anastomosis: evidence from 12 studies.

Scandinavian journal of gastroenterology·2013

Same author

Localized leptin release may be an important mechanism of curcumin action after acute ischemic injuries.

The journal of trauma and acute care surgery·2013

Same journal

Modeling Nonstationary Time Series Using Locally Stationary Basis Processes.

Journal of time series analysis·2026

Same journal

Spatiotemporal Heterogeneity Learning: Generalized SpatioTemporal Semi-Varying Coefficient Models With Structure Identification.

Journal of time series analysis·2025

Same journal

Extracting Conditionally Heteroskedastic Components using Independent Component Analysis.

Journal of time series analysis·2020

Same journal

Discriminant Analysis of Time Series in the Presence of Within-Group Spectral Variability.

Journal of time series analysis·2016

Same journal

NON-PARAMETRIC ESTIMATION UNDER STRONG DEPENDENCE.

Journal of time series analysis·2014

Same journal

Enveloping Spectral Surfaces: Covariate Dependent Spectral Analysis of Categorical Time Series.

Journal of time series analysis·2014

See all related articles

Search research articles

Related Experiment Video

Updated: May 8, 2026

A Method of Trigonometric Modelling of Seasonal Variation Demonstrated with Multiple Sclerosis Relapse Data

A Method of Trigonometric Modelling of Seasonal Variation Demonstrated with Multiple Sclerosis Relapse Data

Published on: December 9, 2015

FORECASTING WITH PREDICTION INTERVALS FOR PERIODIC ARMA MODELS.

Paul L Anderson¹, Mark M Meerschaert, Kai Zhang

¹Department of Mathematics and Computer Science, Albion College, Albion MI 49224. Panderson@albion.edu.

Journal of Time Series Analysis

|August 20, 2013

Summary

This summary is machine-generated.

This study introduces forecasting methods for Periodic Autoregressive Moving Average (PARMA) models, suitable for seasonal time series data. The research provides a way to calculate prediction intervals for more accurate river flow forecasts.

Related Experiment Videos

Last Updated: May 8, 2026

A Method of Trigonometric Modelling of Seasonal Variation Demonstrated with Multiple Sclerosis Relapse Data

A Method of Trigonometric Modelling of Seasonal Variation Demonstrated with Multiple Sclerosis Relapse Data

Published on: December 9, 2015

Area of Science:

Statistics
Time Series Analysis

Background:

Time series data exhibiting seasonal patterns in mean, variance, and covariance require specialized modeling.
Traditional time series models may not adequately capture these periodic fluctuations.

Purpose of the Study:

To develop and implement effective forecasting procedures for Periodic Autoregressive Moving Average (PARMA) models.
To provide a method for calculating prediction intervals for PARMA model forecasts.

Main Methods:

Utilized the innovations algorithm for forecast generation.
Incorporated Ansley's approach for developing forecasting procedures.
Derived a formula for asymptotic error variance to enable Gaussian prediction interval computation.

Main Results:

Successfully developed and implemented forecasting procedures for PARMA models.
Provided a formula for asymptotic error variance, facilitating the computation of prediction intervals.
Demonstrated the practical application of the developed methods through monthly river flow forecasting.

Conclusions:

The developed forecasting procedures are effective for PARMA models.
The method allows for the computation of Gaussian prediction intervals, enhancing forecast reliability.
The application to river flow forecasting illustrates the practical utility of PARMA models in seasonal time series analysis.