17 lines
662 B
Matlab
17 lines
662 B
Matlab
function m = mean_preserving_spread(autoregressive_parameter,sigma)
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% Computes the mean preserving spread for first order autoregressive process.
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%
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% The mean preserving spread m is a constant such that the mean of the process
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%
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% X_t = X^{\star} * e^{x_t - m}
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% x_t = \rho x_{t-1} + \varepsilon_t
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% \varepsilon_t \sim N(0,\sigma^2)
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%
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% is X^{\star}. This constant is such that the unconditional expectation of X_t is equal
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% to the deterministic steady state of X_t
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%
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% AUTHOR(S)
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% stephane DOT adjemian AT univ DASH lemans DOT fr
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% frederic DOT karame AT univ DASH evry DOT fr
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m = .5*sigma*sigma/(1-autoregressive_parameter*autoregressive_parameter); |