ConfZIC (version 1.0.1)

tsZIC.test: Test whether two ZIC values differ significantly based on minimum ZIC for time series data

Description

Test whether two ZIC values differ significantly based on minimum ZIC for time series data.

Usage

tsZIC.test(x,model1,model2,model_ZIC="AIC",alpha=0.05)

Value

p-value with significance status.

Arguments

x

time series data (maximum of 1000 data points).

model1

AR and MA coefficients of Model 1.

model2

AR and MA coefficients of Model 2.

model_ZIC

type of the information criterion, it can be "AIC", "BIC", or "AICc" (Default is the "AIC").

alpha

significance level \(\alpha\) for the hypothesis testing (Default is 0.05).

Details

Consider the hypothesis: Under the null hypothesis that the two expected discrepancies are equal.

$$H_0: ZIC_i=ZIC_j , H_1: ZIC_i\neq ZIC_j$$

$$Z_0=\frac{(\hat{ZIC_i}-\hat{ZIC_j})-0}{\sqrt{SD(ZIC_i,ZIC_j)}} \sim N(0,1)$$ is calculated empirically.

References

Linhart, H. (1988). A test whether two AIC's differ significantly. South African Statistical Journal, 22(2), 153-161.

Examples

library(ConfZIC)
data(Sunspots)
x=Sunspots
model1=try(arima(x,order=c(1,0,1),method="ML",include.mean=FALSE),silent = TRUE)
model2=try(arima(x,order=c(1,0,0),method="ML",include.mean=FALSE),silent = TRUE)
tsZIC.test(x,model1,model2,model_ZIC="AIC",alpha=0.05)