Behavior of the NORTA method for correlated random vector generation as the dimension increases
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Fitting Time-Series Input Processes for Simulation
Operations Research
Generating random correlation matrices based on partial correlations
Journal of Multivariate Analysis
Modeling covariance matrices via partial autocorrelations
Journal of Multivariate Analysis
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Methods are proposed for generating random (p+1)x(p+1) Toeplitz correlation matrices that are consistent with a causal AR(p) Gaussian time series model. The main idea is to first specify distributions for the partial autocorrelations that are algebraically independent and take values in (-1,1), and then map to the Toeplitz matrix. Similarly, starting with pseudo-partial autocorrelations, methods are proposed for generating (q+1)x(q+1) Toeplitz correlation matrices that are consistent with an invertible MA(q) Gaussian time series model. The density can be uniform or non-uniform over the space of autocorrelations up to lag p or q, or over the space of autoregressive or moving average coefficients, by making appropriate choices for the densities of the (pseudo)-partial autocorrelations. Important intermediate steps are the derivations of the Jacobians of the mappings between the (pseudo)-partial autocorrelations, autocorrelations and autoregressive/moving average coefficients. The random generating methods are useful for models with a structured Toeplitz matrix as a parameter.