Matrix: Marini/eurqsa

Description: Economic time series reconciliation; Di Fonzo (Univ Padua) & Marini (ISTAT)

Marini/eurqsa graph
(undirected graph drawing)

Marini/eurqsa dmperm of Marini/eurqsa
scc of Marini/eurqsa

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  • download as a MATLAB mat-file, file size: 245 KB. Use UFget(1891) or UFget('Marini/eurqsa') in MATLAB.
  • download in Matrix Market format, file size: 146 KB.
  • download in Rutherford/Boeing format, file size: 137 KB.

    Matrix properties
    number of rows7,245
    number of columns7,245
    structural full rank?yes
    structural rank7,245
    # of blocks from dmperm3
    # strongly connected comp.3
    explicit zero entries0
    nonzero pattern symmetrysymmetric
    numeric value symmetrysymmetric
    Cholesky candidate?no
    positive definite?no

    authorT. Di Fonzo, M. Marini
    editorT. Davis
    kindeconomic problem
    2D/3D problem?no

    Additional fieldssize and type
    bfull 7245-by-1


    Economic statistics are often published in the form of time series, as a   
    collection of observations sampled at equally-spaced time periods (months, 
    quarters). Economic concepts behind such statistics are often linked by a  
    system of linear relationships, deriving from the economic theory. However,
    these restrictions are rarely met by the original time series for various  
    reasons.  Then, data sets of real-world variables generally show           
    discrepancies with respect to prior restrictions on their values.  The     
    adjustment of a set of data in order to satisfy a number of accounting     
    restrictions -and thus to remove any discrepancy -is generally known as    
    the reconciliation problem.                                                
    The matrix comes from a real application composed of 183 quarterly time    
    series observed over 28 quarters, which form the system of European        
    national accounts by institutional sectors (EURQSA). Then, the number of   
    observations to be reconciled is n = 28 x 183 = 5124. The variables are    
    connected by a system of 30 linear relationships. Moreover, each quarterly 
    time series must be in line with the same variables observed yearly (due   
    to different compilation practices quarterly and annual estimates might    
    differ). The total number of constraints of the system is k = 2121. On     
    the whole, matrix A has dimension 7245, with block (1,1) of dimension 5124.

    Ordering statistics:result
    nnz(chol(P*(A+A'+s*I)*P')) with AMD153,155
    Cholesky flop count1.3e+07
    nnz(L+U), no partial pivoting, with AMD299,065
    nnz(V) for QR, upper bound nnz(L) for LU, with COLAMD1,174,854
    nnz(R) for QR, upper bound nnz(U) for LU, with COLAMD2,203,468

    SVD-based statistics:
    null space dimension210
    full numerical rank?no
    singular value gap3.03054e+08

    singular values (MAT file):click here
    SVD method used:s = svd (full (A)) ;

    Marini/eurqsa svd

    For a description of the statistics displayed above, click here.

    Maintained by Tim Davis, last updated 12-Mar-2014.
    Matrix pictures by cspy, a MATLAB function in the CSparse package.
    Matrix graphs by Yifan Hu, AT&T Labs Visualization Group.