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Besides, the Brownian motions are assumed to be correlated by a constant correlation (rhoin[-1,1]) which is a measure of co-movements between (S_{t}) and (R_{t}).
One might notice a constant correlation between the date of the first frost and fluctuations in the price of wheat.
Instead of assuming a constant correlation, correlation has to be modelled as a stochastic process.
However, for the long maturities ((T>3)), the generated correlations will tend to the mean reversion value (mu=0.003) which are less than the value of the constant correlation, the prices with the constant correlation are thus higher.
In Figure 8b we present the relative difference between the price with constant correlation and stochastic correlation.
The numerical results showed that the correlation risk caused by using a wrong (constant) correlation model cannot be neglected.
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We also estimate 2-, 3- and 4-variable multivariate GARCH models, without imposing the assumption of constant correlations, to investigate volatility interaction amongst the currencies.
More recently, Schäfer and Strimmer [ 27] considered shrinkage towards a number of target matrices with diagonal structure or constant correlations.
We also used multivariate models with various alternative correlation structures between data streams, but use of these more complex models did not appear to improve performance (Table), possibly because correlation between streams vary year to year; the multivariate model is based on constant correlations (Technical Appendix).
The experimental values of qe, computed values of qe, rate constants and correlation constants (R 2 ) for both pseudo-first-order and pseudo-second-order equations are tabulated in Table 3.
In summary, the effect of soil strength on crop yield was not expressed in a constant negative correlation across all spatial scales and locations: the negative correlation occurred mainly at fine spatial scales, and the correlation changed according to the position in the landscape and the prevailing local soil conditions.
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