## Abstract

We compute spectral densities of large sample auto-covariance matrices of stationary stochastic processes at fixed ratio alpha = N/M of matrix dimension N and sample size M. We find a remarkable scaling relation which expresses the spectral density rho(alpha)(lambda) of sample auto-covariance matrices for processes with correlations as a continuous superposition of copies of the spectral density rho((0))(alpha)(lambda) for a sequence of uncorrelated random variables at the same value of alpha, rescaled in terms of the Fourier transform (C) over cap (q) of the true auto-covariance function. We also obtain a closed-form approximation for the scaling function rho((0))(alpha)(lambda). Our results are in excellent agreement with numerical simulations using auto-regressive processes, and processes exhibiting a power-law decay of correlations. Copyright (C) EPLA, 2012

Original language | English |
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Article number | 20008 |

Pages (from-to) | - |

Number of pages | 6 |

Journal | EUROPHYSICS LETTERS |

Volume | 99 |

Issue number | 2 |

DOIs | |

Publication status | Published - Jul 2012 |