s2dverification (version 2.5.0)

FitAcfCoef: Fits an AR1 AutoCorrelation Function Using the Cardano Formula

Description

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. Thanks to the Cardano formula, provided a and b in [0 1], the problem is well posed, delta > 0 and there is only one solution to the 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 estimated autocorrelation function estacf, using only the first two lags.

Usage

FitAcfCoef(a, b)

Arguments

a

Coefficient a : first estimate of the autocorrelation at lag 1

b

Coefficient b : first estimate of the autocorrelation at lag 2

Value

Examples

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)