acp (version 2.1)

acp: Autoregressive Conditional Poisson (ACP) Regression

Description

Fit an ACP(p,q) regression model.

Usage

acp(x, ...)
"acp"(x, y, p, q ,startval, varopt,...)
"acp"(formula, data=list(), p, q ,startval=NULL, varopt=T, family="acp",...)
"print"(x, ...)
"summary"(object, ...)
"predict"(object, newydata=NULL, newxdata=NULL,...)

Arguments

x

a numeric design matrix for the model.

y

a numeric vector of responses.

p

number of lags for the dependent variable.

q

number of lags for the conditional mean.

startval

a numeric vector of starting values. If not provided the package will obtain starting values for the covariate parameters from a poisson regression and for the autoregressive parameters from an arma(1,1) regression.

family

A description of the specification to be used. If family="acp" or not provided an Autoregressive Poisson regression will be estimated whereas if family="poisson" a plain Poisson regression is provided.

formula

a symbolic description of the model to be fit.

data

an optional data frame containing the variables in the model.

varopt

an optional logical operator T (TRUE) or F (FALSE) determining whether the covariance matrix will be calculated (T) or not (F).

object

an object of class "acp", i.e., a fitted model.

newxdata

a data frame containing the covariates data upon which a static forecast will be performed.

newydata

a data frame containing the dependent variable upon which a static forecast will be performed.

...

not used.

Value

An object of class logreg, basically a list including elements

coefficients

a named vector of coefficients

vcov

covariance matrix of coefficients

fitted.values

fitted values

residuals

residuals

logl

log-likelihood

AIC

AKAIKE information criterion

BIC

Bayesian information criterion

Details

This model has been proposed by Heinen (2003) for cases of count data exhibiting autoregressive behaviour. As pointed by Cameron and Trivedi (1998), when a count data set exhibits time dependence the plain Poisson regression is not adequate. Heinen (2003) proposed the ACP model in close analogy to the Autoregressive Conditional Duration model (ACD) of Engle and Russel (1998) and the GARCH model of Bollerslev (1986). The model can be also found in the international bibliography as Integer GARCH (Fokianos and Fried, 2010).

References

• Bollerslev, T., 1986. Generalized autoregressive conditional heteroskedasticity. Journal of Econometrics 31, 307-327.
• Cameron, A., and Trivedi, P., 1998. Regression Analysis of Count Data. New York: Cambridge University Press.
• Engle, RF., Russell, JR., 1998. Autoregressive conditional duration: a new model for irregularly spaced transaction data. Econometrica 66, 1127-1162.
• Fokianos, K., Fried, R., 2010. Interventions in INGARCH processes. Journal of Time Series Analysis 31/3, 210-225.
• Heinen, A., 2003. Modelling Time Series Count Data: An Autoregressive Conditional Poisson Model. University Library of Munich.MPRA paper, 8113.

Examples

data(polio)

trend=(1:168/168)
cos12=cos((2*pi*(1:168))/12)
sin12=sin((2*pi*(1:168))/12)
cos6=cos((2*pi*(1:168))/6)
sin6=sin((2*pi*(1:168))/6)


#Autoregressive Conditional Poisson Model with explaning covariates
polio_data<-data.frame(polio, trend , cos12, sin12, cos6, sin6)
mod1 <- acp(polio~-1+trend+cos12+sin12+cos6+sin6,data=polio_data, p = 1 ,q = 2)
summary(mod1)

#Static out-of-sample fit example
train<-data.frame(polio_data[c(1: 119),])
mod1t <- acp(polio~-1+trend+cos12+sin12+cos6+sin6,data=train, p = 1  ,q = 2)
xpolio_data<-data.frame(trend , cos12, sin12, cos6, sin6)
test<-xpolio_data[c(120:nrow(xpolio_data)),]
yfor<-polio_data[120:nrow(polio_data),1]
predict(mod1t,yfor,test)

#Autoregressive Conditional Poisson Model without explaning covariates
polio_data<-data.frame(polio)
mod2 <- acp(polio~-1,data=polio_data, p = 3 ,q = 1)
summary(mod2)

#Poisson Model with explaning covariates
polio_data<-data.frame(polio, trend , cos12, sin12, cos6, sin6)
mod3 <- acp(polio~trend+cos12+sin12+cos6+sin6,data=polio_data,family="poisson")
summary(mod3)

#Default method for ACP regression
X<-cbind(trend , cos12, sin12, cos6, sin6)
mod4<-acp(X,polio,3,1,startval=NULL,varopt=TRUE)
print(mod4)
summary(mod4)
residuals(mod4)
mod4$vcov
mod4$AIC
mod4$BIC