influence {sym.arma}

Assessment of local influence in SYMARMA models

Description

This function discusses local influence analysis in SYMARMA models with Student-t and Gaussian distributions through Billor and Loyne's slope, Cook's curvature and Lesaffre and Verbeke's curvature using the methodology of benchmarks proposed by Zhang and King. Although this function is concerned primarily with local influence, some discussion of assessing global influence is presented.

Usage

influence(model, diag="slope", scheme="additive",iter=2000,
 alpha=0.95, theta=0.05, plot="TRUE")

Arguments

model

a result of a call to elliptical.ts.

diag

a description of the diagnostic method: “slope” for Billor and Loyne's, “cook” for Cook's and “lv” for Lesaffre and Verbeke's. The default is to slope.

scheme

a description of the perturbation scheme: “additive” for data additive perturbation and “dispersion” for dispersion parameter perturbation. The default is to additive.

iter

integer giving the number of iterations for construction of benckmarks. Default is 2,000 iterations.

alpha

percentile for benchmarks in assessing global influence (BS_0 and BC_0) and first assessing local influence (BS_1 and BC_1), e.g., 0.95.

theta

percentile for benchmarks in assessing global influence second assessing local influence (BS_2 and BC_2), e.g., 0.05.

plot

a logical indicating if plot should be produced.

Value

Indiv1

individual benchmark type I.

Indiv2

individual benchmark type II.

VectorInd

slope or curvature vector.

Author(s)

Vinicius Quintas Souto Maior and Francisco Jose A. Cysneiros

Maintainer: Vinicius Quintas Souto Maior <[e-mail]>

References

Cook, R.D. (1986). Assessment of local influence (with discussion). Journal of the Royal Statistical Society, B 48, 133-169.

Billor, N. and Loynes, R.M. (1993). Local influence: A new approach. Communications in Statistics Theory and Methods, 22, 1595-1611. doi: 10.1080/03610929308831105.

Lesaffre, F. and Verbeke, G. (1998). Local influence in linear mixed models. Biometrics, 38, 963-974. doi: 10.2307/3109764.

Zhang, X. and King, M.L. (2005). Influence diagnostics in generalized autoregressive conditional heteroscedasticity processes. J. Business Econ. Statist., 23, 118-129. doi: 10.1198/073500104000 000217.

Examples

data(assets)
attach(assets)

# Return in the prices on Microsoft and SP500 index

N = length(msf)
.sp500 = ((sp500[2:N]-sp500[1:(N-1)])/sp500[1:(N-1)])*100
.msf = ((msf[2:N]-msf[1:(N-1)])/msf[1:(N-1)])*100

# The T-bill rates were divided by 253 to convert to a daily rate

.tbill = tbill/253

# Excess return in the d prices on Microsoft and SP500 index

Y = .msf - .tbill[1:(N-1)]
X = .sp500 - .tbill[1:(N-1)]

# Period from April 4, 2002 to October 4, 2002

serie = Y[2122:2240]
aux = cbind(X[2122:2240])

# Fit SYMARMA models

fit.1 = elliptical.ts(serie,order=c(0,0,1),xreg=aux,include.mean=FALSE,
 family="Normal")
fit.2 = elliptical.ts(serie,order=c(0,0,1),xreg=aux,include.mean=FALSE,
 family="Student", index1=4)

# Assessment of local influence

influence(fit.1,diag="slope",scheme="additive",iter=20,plot="FALSE") 
influence(fit.2,diag="lv",scheme="additive",iter=20,plot="FALSE")