SB32 {artfima}

Turbulent flow data from Station SB32

Description

Turbulent flow water time series, Lake Huron, during 2009-2010. Sampled every second.

Usage

data("SB32")

Format

The format is: num [1:5374] -2.2 1.4 -0.6 -0.4 -1.5 -2.6 -0.9 0.5 -0.9 1.5 ...

Details

See paper by Meerschaert, Sabzikar, Phanikumar and Zeleke (2014).

References

M.M. Meerschaert, Farzad Sabzikar, M.S. Phanikumar, and A. Zeleke, Tempered fractional time series model for turbulence in geophysical flows, Journal of Statistical Mechanics: Theory and Experiment, Vol. 2014 p. P09023 (13 pp.) doi:10.1088/1742-5468/2014/09/P09023.

Examples

data(SB32)
str(SB32)

#Figure from our paper
## Not run: 
ans0 <- artfima(SB32, fixd=5/6)
ans1 <- artfima(SB32, arimaOrder=c(1,0,2)) #best
p <- ans1$arimaOrder[1]
q <- ans1$arimaOrder[3]
sigmaSq1 <- ans1$sigmaSq
sigmaSq0 <- ans0$sigmaSq
w <- SB32
n <- length(w)
Ip <- Periodogram(w)
fr <- (1/n)*(1:length(Ip))
plot(log(fr), log(Ip), xlab="log frequency", ylab="log power", 
     type="p", col=rgb(0,0,1,0.4), pch=16)
y <- sigmaSq1*artfimaSDF(n=length(SB32), obj=ans1, plot="none")
lines(log(fr), log(y), type="l", lwd=2.5, col="red")
y0 <- sigmaSq0*artfimaSDF(n=length(SB32), obj=ans0, plot="none")
lines(log(fr), log(y0), type="l", lwd=3.5, col="green", lty=2)
TFD_label <- expression(paste("TFD, ", delta == 5/6, ", ", 
                              hat(lambda) == 0.045))
legend(x=-8, y=-5, xjust=0, yjust=0, legend=c("ARTFIMA(1,0,2)", TFD_label), 
       lty=c(1,2), lwd=c(2.5,3.5), col=c("red", "green"), bty="n")

## End(Not run)