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Related Concept Videos

Residuals and Least-Squares Property01:11

Residuals and Least-Squares Property

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The vertical distance between the actual value of y and the estimated value of y. In other words, it measures the vertical distance between the actual data point and the predicted point on the line
If the observed data point lies above the line, the residual is positive, and the line underestimates the actual data value for y. If the observed data point lies below the line, the residual is negative, and the line overestimates the actual data value for y.
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Random Error01:04

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Random or indeterminate errors originate from various uncontrollable variables, such as variations in environmental conditions, instrument imperfections, or the inherent variability of the phenomena being measured. Usually, these errors cannot be predicted, estimated, or characterized because their direction and magnitude often vary in magnitude and direction even during consecutive measurements. As a result, they are difficult to eliminate. However, the aggregate effect of these errors can be...
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Estimating Population Standard Deviation01:26

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When the population standard deviation is unknown and the sample size is large, the sample standard deviation s is commonly used as a point estimate of σ. However, it can sometimes under or overestimate the population standard deviation. To overcome this drawback, confidence intervals are determined to estimate population parameters and eliminate any calculation bias accurately. However, this only applies to random samples from normally distributed populations. Knowing the sample mean and...
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Variance01:15

Variance

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The deviations show how spread out the data are about the mean. A positive deviation occurs when the data value exceeds the mean, whereas a negative deviation occurs when the data value is less than the mean. If the deviations are added, the sum is always zero. So one cannot simply add the deviations to get the data spread. By squaring the deviations, the numbers are made positive; thus, their sum will also be positive.
The standard deviation measures the spread in the same units as the data....
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Estimating Population Mean with Unknown Standard Deviation01:22

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In practice, we rarely know the population standard deviation. In the past, when the sample size was large, this did not present a problem to statisticians. They used the sample standard deviation s as an estimate for σ and proceeded as before to calculate a confidence interval with close enough results. However, statisticians ran into problems when the sample size was small. A small sample size caused inaccuracies in the confidence interval.
William S. Gosset (1876–1937) of the...
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Standard Deviation01:10

Standard Deviation

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The most commonly used measure of variation is the standard deviation. It is a numerical value measuring how far data values are from their mean. The standard deviation value is small when the data are concentrated close to the mean, exhibiting slight variation or spread. The standard deviation value is never negative, it is either positive or zero. The standard deviation is larger when the data values are more spread out from the mean, which means the data values are exhibiting more variation.
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Updated: Nov 4, 2025

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Volatility estimation for COVID-19 daily rates using Kalman filtering technique.

Md Al Masum Bhuiyan1, Suhail Mahmud2, Md Romyull Islam3

  • 1Austin Peay State University, USA.

Results in Physics
|May 24, 2021
PubMed
Summary

This study introduces a Kalman filtering technique with time-varying parameters to predict the stochastic volatility of Corona Virus-Infected Disease 2019 (COVID-19) cases, offering a reliable forecasting model.

Keywords:
COVID-19 time seriesKalman filteringMaximum likelihood estimationVolatility modelWhittle likelihood

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Area of Science:

  • Epidemiology
  • Computational Statistics

Background:

  • Corona Virus-Infected Disease 2019 (COVID-19) is a highly infectious and dangerous global pandemic.
  • Early detection and prognosis of COVID-19 are crucial for timely patient treatment and public health interventions.
  • Stochastic modeling offers potential for predicting disease dynamics.

Purpose of the Study:

  • To develop and evaluate a stochastic modeling approach for predicting COVID-19 case volatility.
  • To implement a filtering technique with time-varying parameters for enhanced COVID-19 prognosis.

Main Methods:

  • Utilized a stochastic volatility (SV) model to analyze COVID-19 case data.
  • Employed Kalman filtering with time-varying parameters to estimate volatility.
  • Applied Maximum Likelihood Estimation for one-step-ahead volatility forecasting.

Main Results:

  • The Kalman filtering technique effectively removes insignificant data noise.
  • Achieved accurate one-step-ahead volatility predictions with minimal standard errors.
  • Demonstrated the model's ability to forecast stochastic volatility in COVID-19 cases.

Conclusions:

  • Kalman filtering combined with the SV model provides a reliable predictive framework for COVID-19.
  • This approach is less constrained by historical autoregressive data, offering a more adaptable prognosis.
  • The method supports improved early detection and management strategies for the pandemic.