tmpyr {arfima} | R Documentation |

Central England mean yearly temperatures from 1659 to 1976

A ts tmpyr

Hosking notes that while the ARFIMA(1, d, 1) has a lower AIC, it is not much lower than the AIC of the ARFIMA(1, d, 0).

Bhansali and Kobozka find: muHat = 9.14, d = 0.28, phi = -0.77, and theta =
-0.66 for the ARFIMA(1, d, 1), which is close to our result, although our
result reveals trimodality if `numeach`

is large enough. The third
mode is close to Hosking's fit of an ARMA(1, 1) to these data, while the
second is very antipersistent.

Our package gives a very close result to Hosking for the ARFIMA(1, d, 0)
case, although there is also a second mode. Given how close it is to the
boundary, it may or may not be spurious. A check with `dmean = FALSE`

shows that it is not the optimized mean giving a spurious mode.

If, however, we use `whichopt = 1`

, we only have one mode. Note that
Nelder-Mead sometimes does take out non-spurious modes, or add spurious
modes to the surface.

http://www.metoffice.gov.uk/hadobs/hadcet/

Parker, D.E., Legg, T.P., and Folland, C.K. (1992). A new daily Central England Temperature Series, 1772-1991. Int. J. Clim., Vol 12, pp 317-342

Manley,G. (1974). Central England Temperatures: monthly means 1659 to 1973. Q.J.R. Meteorol. Soc., Vol 100, pp 389-405.

Hosking, J. R. M. (1984). Modeling persistence in hydrological time series using fractional differencing, Water Resour. Res., 20(12)

Bhansali, R. J. and Koboszka, P. S. (2003) Prediction of Long-Memory Time Series In Doukhan, P., Oppenheim, G. and Taqqu, M. S. (Eds) Theory and Applications of Long-Range Dependence (pp355-368) Birkhauser Boston Inc.

Veenstra, J.Q. Persistence and Antipersistence: Theory and Software (PhD Thesis)

data(tmpyr) fit <- arfima(tmpyr, order = c(1, 0, 1), numeach = c(3, 3), dmean = TRUE, back=TRUE) fit ##suspect that fourth mode may be spurious, even though not close to a boundary ##may be an induced mode from the optimization of the mean fit <- arfima(tmpyr, order = c(1, 0, 1), numeach = c(3, 3), dmean = FALSE, back=TRUE) fit ##perhaps so plot(tacvf(fit), maxlag = 30, tacf = TRUE) fit1 <- arfima(tmpyr, order = c(1, 0, 0), dmean = TRUE, back=TRUE) fit1 fit2 <- arfima(tmpyr, order = c(1, 0, 0), dmean = FALSE, back=TRUE) fit2 ##still bimodal. Second mode may or may not be spurious. fit3 <- arfima(tmpyr, order = c(1, 0, 0), dmean = FALSE, whichopt = 1, numeach = c(3, 3)) fit3 ##Unimodal. So the second mode was likely spurious. plot(tacvf(fit2), maxlag = 30, tacf = TRUE) ##maybe not spurious. Hard to tell without visualizing the surface. ##compare to plotted tacf of fit1: looks alike plot(tacvf(fit1), maxlag = 30, tacf = TRUE) tacfplot(list(fit1, fit2))

[Package *arfima* version 1.7-0 Index]