RankTS {ConfZIC}

Rank the time series (ARMA) models based on the confidence envelope for minimum ZIC

Description

Narrow down the number of models to look at in model selection using the confidence envelope based on the minimum ZIC values for time series data. Here, we compute the ZIC values ("AIC", "BIC", or "AICc") for time-series data, confidence envelope for the minimum ZIC values for the given confidence limit, and rank the top models which lie in the confidence envelope.

Usage

RankTS(x,max.p,max.q,alphaval=0.95,model_ZIC="AIC")

Arguments

x

a vector of time series data (should be included with the maximum of 1000 data points).

max.p

maximum value for AR coefficient.

max.q

maximum value for MA coefficient.

alphaval

confidence limit (1-\alpha) (Default is 0.95).

model_ZIC

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

Details

This program involves the computation of multivariate normal-probabilities with covariance matrices based on minimum ZIC inverting the CDF of the minimum ZIC. It involves both the computation of singular and non-singular probabilities. The methodology is described in Genz (1992).

Let X_j be the ZIC value for the j^{th} fitted model. Compute the cdf values of the minimum ZIC, F_{X_{(1)}}(\cdot) numerically and then obtain the 100\cdot (1-\alpha)\% confidence envelope:

CE(\alpha)=F^{-1}_{X_{(1)}}(1-\alpha)

See details:

Jayaweera I.M.L.N, Trindade A.A., “How Certain are You in Your Minimum AIC and BIC Values?", Sankhya A (2023+)

Value

a list of ranked models which lies in the confidence envelope, CE(\alpha).

Ranked_Models

A set of top ranked time series models which lie in the confidence envelope CE(\alpha) (with AR and MA coefficients, ZIC values ("AIC", "BIC", or "AICc")).

Confidence_Envelope

gives the confidence envelope CE(\alpha) for the minimum ZIC.

Confidence_Limit

the confidence limit, 1-\alpha.

Total_Models

number of total fitted models.

References

Genz, A. (1992). Numerical computation of multivariate normal probabilities. Journal of computational and graphical statistics, 1(2), 141-149.

Examples

library("ConfZIC")
data(Sunspots)
x=Sunspots
RankTS(x,max.p=13,max.q=13,0.95,"AICc")