A FAMILY OF MODELS EXPLAINING THE LEVEL-SLOPE-CURVATURE EFFECT

2003 ◽  
Vol 06 (03) ◽  
pp. 239-255 ◽  
Author(s):  
LILIANA FORZANI ◽  
CARLOS TOLMASKY
Keyword(s):  
Principal Components Analysis ◽  
Principal Components ◽  
Correlation Matrix ◽  
Yield Curve ◽  
Correlation Structure ◽  
Spectral Structure ◽  
Curvature Effect ◽  
Correlation Matrices ◽  
The Us ◽  
Components Analysis

One of the most widely used methods to build yield curve models is to use principal components analysis on the correlation matrix of the innovations. R. Litterman and J. Scheinkman found that three factors are enough to explain most of the moves in the case of the US treasury curve. These factors are level, steepness and curvature. Working in the context of commodity futures, G. Cortazar and E. Schwartz found that the spectral structure of the correlation matrices is strikingly similar to those found by R. Litterman and J. Scheinkman. We observe that in both cases the correlation between two different contracts maturing at times t and s is roughly of the form ρ|t-s|, for a certain (fixed) 0 ≤ ρ ≤ 1. Assuming this correlation structure we prove that the observed factors are perturbations of cosine waves and we extend the analysis to multiple curves.

ON THE SPECTRAL DECOMPOSITION OF EMPIRICAL CORRELATION MATRICES

2001 ◽  
Vol 10 (08) ◽  
pp. 1201-1213 ◽  
Author(s):  
LILIANA FORZANI ◽  
CARLOS F. TOLMASKY
Keyword(s):  
Principal Components Analysis ◽  
Principal Components ◽  
Spectral Decomposition ◽  
Correlation Matrix ◽  
Yield Curve ◽  
Empirical Correlation ◽  
Spectral Structure ◽  
Correlation Matrices ◽  
The Us ◽  
Components Analysis

One of the most widely used methods to build yield curve models is to use principal components analysis on the correlation matrix of the innovations. R. Litterman and J. Scheinkman found that three factors are enough to explain most of the moves in the case of the US treasury curve. These factors are level, steepness and curvature. Working in the context of commodity futures, G. Cortazar and E. Schwartz found that the spectral structure of the correlation matrices is strikingly similar to those found by R. Litterman and J. Scheinkman. We observe that in both cases the correlation between two different contracts maturing at times t and s is roughly of the form ρ|t-s|, for a certain (fixed) 0≤ρ≤1. Assuming this correlation structure we prove that the observed factors are perturbations of cosine waves.

scholarly journals Measuring the Systematic Risk of Sectors within the US Market Via Principal Components Analysis: Before and during the COVID-19 Pandemic

2022 ◽  
Author(s):  
Jaime González Maiz Jiménez ◽  
Adán Reyes Santiago
Keyword(s):  
Principal Component Analysis ◽  
Stock Market ◽  
Principal Components Analysis ◽  
Principal Components ◽  
Systematic Risk ◽  
Principal Component ◽  
Component Analysis ◽  
Market Capitalization ◽  
The Us ◽  
Components Analysis

This research measures the systematic risk of 10 sectors in the American Stock Market, discerning the COVID-19 pandemic period. The novelty of this study is the use of the Principal Component Analysis (PCA) technique to measure the systematic risk of each sector, selecting five stocks per sector with the greatest market capitalization. The results show that the sectors that have the greatest increase in exposure to systematic risk during the pandemic are restaurants, clothing, and insurance, whereas the sectors that show the greatest decrease in terms of exposure to systematic risk are automakers and tobacco. Due to the results of this study, it seems advisable for practitioners to select stocks that belong to either the automakers or tobacco sector to get protection from health crises, such as COVID-19.

Factor Structure of the College Adjustment Scales

2000 ◽  
Vol 86 (1) ◽  
pp. 79-84 ◽  
Author(s):  
Michael H. Campbell ◽  
Shawn T. Prichard
Keyword(s):  
Principal Components Analysis ◽  
Principal Components ◽  
College Adjustment ◽  
Correlation Matrix ◽  
College Counseling ◽  
Demographic Characteristics ◽  
Underlying Structure ◽  
Counseling Centers ◽  
Components Analysis ◽  
College Counseling Centers

The present study examined the underlying structure of the College Adjustment Scales via principal components analysis. A correlation matrix of the nine subscales showed significant multicolinearity. A subsequent principal components analysis demonstrated that one factor accounted for 57% of the total variance and that the majority of subscales were moderately correlated with this single factor. The results suggest that the College Adjustment Scales may measure the same underlying construct and that the clinical distinctions implied by subscale scores should be regarded with caution. Conclusions are constrained by sample size and demographic characteristics, but the results suggest the need for further empirical validation of the College Adjustment Scales, which may be useful in college counseling centers.

scholarly journals Principal Components Analysis of Urine Caffeine and Caffeine Metabolites in the US Population

2015 ◽  
Vol 29 (S1) ◽  
Author(s):  
Ching‐I Pao ◽  
Michael Rybak ◽  
Maya Sternberg ◽  
Namanjeet Ahluwalia ◽  
Christine Pfeiffer
Keyword(s):  
Principal Components Analysis ◽  
Principal Components ◽  
The Us ◽  
Components Analysis ◽  
Analysis Of Urine

Anhedonia and Alexithymia: Distinct or Overlapping Constructs

1997 ◽  
Vol 84 (2) ◽  
pp. 415-425 ◽  
Author(s):  
Gwenolé Loas ◽  
Didier Fremaux ◽  
Patrice Boyer
Keyword(s):  
Principal Components Analysis ◽  
Principal Components ◽  
Correlation Matrix ◽  
Healthy Subjects ◽  
Factor Solution ◽  
Toronto Alexithymia Scale ◽  
Factor Loadings ◽  
Components Analysis ◽  
Physical Anhedonia ◽  
The Relationship

The aim was to examine the relationship between alexithymia, anhedonia, and capacity for displeasure in a group of 133 healthy subjects using principal components analysis. A correlation matrix comprised of items from both the Communication and Identification scale of the 20-item Toronto Alexithymia Scale and the Physical Pleasure-Displeasure Scale yielded a four-factor solution (one Communication-Identification, two Pleasure, and one Displeasure factor) with no overlap of the significant factor loadings for the items from each scale. Moreover, there were no positive significant correlations between the Communication and Identification Scales and the Physical Anhedonia Scale. Our findings support the view that physical anhedonia is a construct distinct and separate from alexithymia.

Reanalysis of Halstead's Biological Intelligence Factor Matrix

1973 ◽  
Vol 37 (3) ◽  
pp. 699-705 ◽  
Author(s):  
Elbert W. Russell
Keyword(s):  
Factor Analysis ◽  
Principal Components Analysis ◽  
Principal Components ◽  
Correlation Matrix ◽  
Factor Matrix ◽  
Perceptual Factor ◽  
Visual Threshold ◽  
Components Analysis

A recent study by Russell did not duplicate Halstead's factors of biological intelligence. As an approach to understanding this finding, Hal-stead's original correlation matrix was subjected to the same orthogonal principal components analysis used in Russell's study as well as an orthogonal and an oblique factor analysis using communalities. All of Halstead's factors appeared in these analyses. The failure to duplicate Halstead's work was evidently not due to use of different factoring methods. In a second analysis which reduced the number of Halstead's variables to the number used by Russell, one of Halstead's factors (P) did not appear. This factor represented tests measuring the visual threshold, and so it appears to be primarily a perceptual factor.

Non-Graphical Solutions for Cattell’s Scree Test

Methodology ◽  
2013 ◽  
Vol 9 (1) ◽  
pp. 23-29 ◽  
Author(s):  
Gilles Raîche ◽  
Theodore A. Walls ◽  
David Magis ◽  
Martin Riopel ◽  
Jean-Guy Blais
Keyword(s):  
Factor Analysis ◽  
Principal Components Analysis ◽  
Simulation Study ◽  
Principal Components ◽  
Correlation Matrix ◽  
Numerical Solutions ◽  
Number Of Components ◽  
Components Analysis ◽  
Low Dimensional ◽  
Scree Test

Most of the strategies that have been proposed to determine the number of components that account for the most variation in a principal components analysis of a correlation matrix rely on the analysis of the eigenvalues and on numerical solutions. The Cattell’s scree test is a graphical strategy with a nonnumerical solution to determine the number of components to retain. Like Kaiser’s rule, this test is one of the most frequently used strategies for determining the number of components to retain. However, the graphical nature of the scree test does not definitively establish the number of components to retain. To circumvent this issue, some numerical solutions are proposed, one in the spirit of Cattell’s work and dealing with the scree part of the eigenvalues plot, and one focusing on the elbow part of this plot. A simulation study compares the efficiency of these solutions to those of other previously proposed methods. Extensions to factor analysis are possible and may be particularly useful with many low-dimensional components.

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