IC {yuima} | R Documentation |
Calculate the information criteria BIC, Quasi-BIC (QBIC) and CIC for the stochastic differential equation.
IC(yuima, data = NULL, start, lower, upper, joint = FALSE, rcpp = FALSE, ...)
yuima |
a yuima object. |
data |
the data to be used. |
start |
a named list of the initial values of the parameters for optimization. |
lower |
a named list for specifying lower bounds of the parameters. |
upper |
a named list for specifying upper bounds of the parameters. |
joint |
perform joint parameter estimation or two stage parameter estimation? (default |
rcpp |
use C++ code? (default |
... |
Please see specifications in https://sites.google.com/site/shoichieguchi90en/specification
par |
the estimators of the parameters. |
BIC |
a value of BIC. |
QBIC |
a value of QBIC. |
CIC |
a value of CIC. |
The function IC
uses the function qmle
with method="L-BFGS-B"
internally.
The YUIMA Project Team
Contacts: Shoichi Eguchi eguchi@sigmath.es.osaka-u.ac.jp
## AIC, BIC
Akaike, H. (1973). Information theory and an extension of the maximum likelihood principle. In Second International Symposium on Information Theory (Tsahkadsor, 1971), 267-281. http://link.springer.com/chapter/10.1007/978-1-4612-1694-0_15
Schwarz, G. (1978). Estimating the dimension of a model. The Annals of Statistics, 6(2), 461-464. http://projecteuclid.org/euclid.aos/1176344136
## BIC, Quasi-BIC
Eguchi, S. and Masuda, H. (2016). Schwarz type model comparison for LAQ models. arXiv:1606.01627v2.
## CIC
Uchida, M. (2010). Contrast-based information criterion for ergodic diffusion processes from discrete observations. Annals of the Institute of Statistical Mathematics, 62(1), 161-187. http://link.springer.com/article/10.1007/s10463-009-0245-1
### Ex.1 set.seed(123) N <- 1000 # number of data h <- N^(-2/3) # sampling stepsize Ter <- N*h # terminal sampling time ## Data generate (dXt = -Xt*dt + exp((-2*cos(Xt) + 1)/2)*dWt) mod <- setModel(drift="theta21*x", diffusion="exp((theta11*cos(x)+theta12)/2)") samp <- setSampling(Terminal=Ter, n = N) yuima <- setYuima(model=mod, sampling=setSampling(Terminal=Ter, n=50*N)) simu.yuima <- simulate(yuima, xinit=1, true.parameter=list(theta11=-2, theta12=1, theta21=-1), subsampling=samp) Xt <- NULL for(i in 1:(N+1)){ Xt <- c(Xt, simu.yuima@data@original.data[50*(i-1)+1]) } ## Parameter settings para.init <- list(theta11=runif(1,max=-1.5,min=-2.5), theta12=runif(1,max=1.5,min=0.5), theta21=runif(1,max=-0.5,min=-1.5)) para.low <- list(theta11=-7, theta12=-4, theta21=-6) para.upp <- list(theta11=3, theta12=6, theta21=4) ## Ex.1.1 (dXt = (theta21*x)*dt + exp((theta11*cos(x)+theta12)/2)*dWt) mod1 <- setModel(drift="theta21*x", diffusion="exp((theta11*cos(x)+theta12)/2)") samp1 <- setSampling(Terminal=Ter, n = N) yuima1 <- setYuima(model=mod1, sampling=samp1) ic1 <- IC(yuima1, data=Xt, start=para.init, upper=para.upp, lower=para.low, rcpp=TRUE) ic1 ## Ex.1.2 (dXt = (theta21*x)*dt + exp(theta11*cos(x)/2)*dWt) mod2 <- setModel(drift="theta21*x", diffusion="exp(theta11*cos(x)/2)") samp2 <- setSampling(Terminal=Ter, n = N) yuima2 <- setYuima(model=mod2, sampling=samp2) ic2 <- IC(yuima2, data=Xt, start=para.init, upper=para.upp, lower=para.low, rcpp=TRUE) ic2 ## Not run: ### Ex.2 (multidimansion case) set.seed(123) N <- 3000 # number of data h <- N^(-2/3) # sampling stepsize Ter <- N*h # terminal sampling time ## Data generate diff.coef.matrix <- matrix(c("beta1+1", "beta3*x1", "-beta2*x1", "beta4+1"), 2, 2) drif.coef.vec <- c("alpha1*x1", "alpha2*x2") mod <- setModel(drift = drif.coef.vec, diffusion = diff.coef.matrix, state.variable = c("x1", "x2"), solve.variable = c("x1", "x2")) samp <- setSampling(Terminal = Ter, n = N) yuima <- setYuima(model = mod, sampling = setSampling(Terminal = Ter, n = 50*N)) simu.yuima <- simulate(yuima, xinit = c(1,1), true.parameter = list(alpha1=-2, alpha2=-1, beta1=1, beta2=1, beta3=1, beta4=2), subsampling = samp) Xt <- matrix(0,(N+1),2) for(i in 1:(N+1)){ Xt[i,] <- simu.yuima@data@original.data[50*(i-1)+1,] } ## Parameter settings para.init <- list(alpha1 = runif(1,min=-3,max=-1), alpha2 = runif(1,min=-2,max=0), alpha3 = runif(1,min=-1,max=1), beta1 = runif(1,min=0,max=2), beta2 = runif(1,min=0,max=2), beta3 = runif(1,min=0,max=2), beta4 = runif(1,min=1,max=3)) para.low <- list(alpha1 = -5, alpha2 = -5, alpha3 = -5, beta1 = 0, beta2 = 0, beta3 = 0, beta4 = 0) para.upp <- list(alpha1 = 5, alpha2 = 5, alpha3 = 5, beta1 = 5, beta2 = 5, beta3 = 5, beta4 = 5) ## Ex.2.1 diff.coef.matrix1 <- matrix(c("beta1+1", "beta3*x1", "-beta2*x1", "beta4+1"), 2, 2) drif.coef.vec1 <- c("alpha1*x1", "alpha2*x2+alpha3") mod1 <- setModel(drift = drif.coef.vec1, diffusion = diff.coef.matrix1, state.variable = c("x1", "x2"), solve.variable = c("x1", "x2")) samp1 <- setSampling(Terminal=Ter, n = N) yuima1 <- setYuima(model=mod1, sampling=samp1) ic1 <- IC(yuima1, data=Xt, start=para.init, upper=para.upp, lower=para.low, rcpp=TRUE) ic1 ## Ex.2.2 diff.coef.matrix2 <- matrix(c("beta1+1", "beta3*x1", "-beta2*x1", "beta4+1"), 2, 2) drif.coef.vec2 <- c("alpha1*x1", "alpha2*x2") mod2 <- setModel(drift = drif.coef.vec2, diffusion = diff.coef.matrix2, state.variable = c("x1", "x2"), solve.variable = c("x1", "x2")) samp2 <- setSampling(Terminal=Ter, n = N) yuima2 <- setYuima(model=mod2, sampling=samp2) ic2 <- IC(yuima2, data=Xt, start=para.init, upper=para.upp, lower=para.low, rcpp=TRUE) ic2 ## End(Not run)