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Related Concept Videos

Prediction Intervals01:03

Prediction Intervals

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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. 
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Accuracy, limits, and approximation01:28

Accuracy, limits, and approximation

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Accuracy, limits, and approximations are common in many fields, especially in engineering calculations. These concepts are imperative for ensuring that a given value is as close as possible to its true value.
Accuracy is defined as the closeness of the measured value to the true or actual value. In engineering mechanics, repeated measurements are taken during theoretical or experimental analyses to ensure that the result is precise and accurate.
The accuracy of any solution is based on the...
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Accuracy and Precision01:52

Accuracy and Precision

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Scientists typically make repeated measurements of a quantity to ensure the quality of their findings and to evaluate both the precision and the accuracy of their results. Measurements are said to be precise if they yield very similar results when repeated in the same manner. A measurement is considered accurate if it yields a result that is very close to the true or the accepted value. Precise values agree with each other; accurate values agree with a true value.  Highly accurate...
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Accuracy and Errors in Hypothesis Testing01:13

Accuracy and Errors in Hypothesis Testing

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Hypothesis testing is a fundamental statistical tool that begins with the assumption that the null hypothesis H0 is true. During this process, two types of errors can occur: Type I and Type II. A Type I error refers to the incorrect rejection of a true null hypothesis, while a Type II error involves the failure to reject a false null hypothesis.
In hypothesis testing, the probability of making a Type I error, denoted as α, is commonly set at 0.05. This significance level indicates a 5%...
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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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Estimating Population Mean with Unknown Standard Deviation01:22

Estimating Population Mean with Unknown Standard Deviation

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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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Related Experiment Video

Updated: Oct 24, 2025

A Simple Stimulatory Device for Evoking Point-like Tactile Stimuli: A Searchlight for LFP to Spike Transitions
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A Simple Stimulatory Device for Evoking Point-like Tactile Stimuli: A Searchlight for LFP to Spike Transitions

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Optimal forecasting accuracy using Lp-norm combination.

Massimiliano Giacalone1

  • 1Department of Economics and Statistics, University of Naples "Federico II", Naples, Italy.

Metron
|August 16, 2021
PubMed
Summary
This summary is machine-generated.

Combining forecasts using Lp-norm estimators improves accuracy, especially with non-Gaussian data and multicollinearity. This method outperforms standard regression techniques in simulations and real-world financial data analysis.

Keywords:
Financial time seriesForecast combinationGARCH modelsGeneralized error distributionLp-norm estimators

Related Experiment Videos

Last Updated: Oct 24, 2025

A Simple Stimulatory Device for Evoking Point-like Tactile Stimuli: A Searchlight for LFP to Spike Transitions
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A Simple Stimulatory Device for Evoking Point-like Tactile Stimuli: A Searchlight for LFP to Spike Transitions

Published on: March 25, 2014

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Area of Science:

  • Statistics
  • Econometrics
  • Computational Finance

Background:

  • Forecast combination methods aim to reduce Mean Square Error (MSE) compared to individual forecasts.
  • Standard regression techniques can fail with multicollinearity or non-Gaussian data distributions.
  • Existing methods include simple average, median, Trimmed Average, and optimization techniques.

Purpose of the Study:

  • To introduce and evaluate a novel forecast combination method using Lp-norm estimators.
  • To address limitations of standard regression-based methods in handling multicollinearity and non-Gaussianity.
  • To demonstrate the effectiveness of Lp-norm estimators in improving forecasting accuracy.

Main Methods:

  • Proposed a forecast combination method based on Lp-norm estimators, utilizing the Generalized Error Distribution.
  • Conducted simulation studies with varying autoregressive parameters, heteroskedasticity, and homoskedasticity.
  • Performed an empirical study using daily Bitcoin price data (Bitfinex, 2014-2020) and 25 Dow Jones historical series.
  • Combined forecasts from GARCH and ARIMA models under both Gaussian and non-Gaussian assumptions.

Main Results:

  • Lp-norm estimators effectively handle multicollinearity and non-Gaussian data, outperforming standard regression approaches.
  • Simulation results indicated improved forecasting accuracy with the proposed Lp-norm method.
  • Empirical analysis on Bitcoin and Dow Jones data confirmed the superior performance of Lp-norm based forecast combinations.

Conclusions:

  • The Lp-norm based forecast combination method offers a robust alternative to standard regression techniques.
  • This approach enhances forecasting accuracy, particularly in complex financial datasets with non-ideal statistical properties.
  • The study validates the utility of Lp-norm estimators for improving forecast reliability in statistical and financial modeling.