Fits an AR1 AutoCorrelation Function Using the Cardano Formula
This function finds the minimum point of the fourth order polynom
(a - x)2 + 0.25(b - x2)2 written to fit the two autoregression coefficients
a and b.
A consequence of the Cardano formula is that, provided a and b are in [0 1],
the problem is well posed, delta > 0 and there is only one minimum.
This function is called in Alpha() to minimize the mean square differences
between the theoretical autocorrelation function of an AR1 and the first
guess of the estimated autocorrelation function estacf, using only the
first two lags.
FitAcfCoef(a, b)
a |
Coefficient a : first estimate of the autocorrelation at lag 1. |
b |
Coefficient b : first estimate of the autocorrelation at lag 2. |
Best estimate of the autocorrelation at lag 1.
History:
0.1 - 2012-06 (L. Auger, ludovic.auger@meteo.fr) - Original code
1.0 - 2013-09 (N. Manubens, nicolau.manubens@ic3.cat) - Formatting to CRAN
series <- GenSeries(1000, 0.35, 2, 1) estacf <- acf(series[951:1000], plot = FALSE)$acf alpha <- FitAcfCoef(max(estacf[2], 0), max(estacf[3], 0)) print(alpha)
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