Matrix: Marini/eurqsa

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

 (undirected graph drawing)

• Matrix group: Marini
• download as a MATLAB mat-file, file size: 245 KB. Use UFget(1891) or UFget('Marini/eurqsa') in MATLAB.

 Matrix properties number of rows 7,245 number of columns 7,245 nonzeros 46,142 structural full rank? yes structural rank 7,245 # of blocks from dmperm 3 # strongly connected comp. 3 explicit zero entries 0 nonzero pattern symmetry symmetric numeric value symmetry symmetric type real structure symmetric Cholesky candidate? no positive definite? no

 author T. Di Fonzo, M. Marini editor T. Davis date 2008 kind economic problem 2D/3D problem? no

 Additional fields size and type b full 7245-by-1

Notes:

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 AMD 153,155 Cholesky flop count 1.3e+07 nnz(L+U), no partial pivoting, with AMD 299,065 nnz(V) for QR, upper bound nnz(L) for LU, with COLAMD 1,174,854 nnz(R) for QR, upper bound nnz(U) for LU, with COLAMD 2,203,468

 SVD-based statistics: norm(A) 3.47577e+06 min(svd(A)) 1.23888e-14 cond(A) 2.80557e+20 rank(A) 7,035 sprank(A)-rank(A) 210 null space dimension 210 full numerical rank? no singular value gap 3.03054e+08

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