gstar {gstar}

Fit Generalized Space-Time Autoregressive Model

Description

gstar function return the parameter estimation of Generalized Space-Time Autoregressive Model.

Usage

gstar(x, weight, p = 1, d = 0, est = "OLS")

Arguments

x

a dataframe, matrix or xts or ts object that contain time series data.

weight

a spatial weight ncol(x) * ncol(x) with diagonal = 0.

p

an autoregressive order, value must be greater than 0.

d

a lag differencing order, value must be greater than 0.

est

estimation method, currently only OLS available, another estimation will be added later.

Value

gstar returns output similar to lm, the detail are shown in the following list :

• coefficients - a named vector of coefficients.

• AIC - A version of Akaike's An Information Criterion (the calculation is similar to aic in lm method )

References

Budi Nurani Ruchjana, Svetlana A. Borovkova and H. P. Lopuhaa (2012), Least Squares Estimation of Generalized Space Time Autoregressive (GSTAR) Model and Its Properties, The 5th International Conference on Research and Education in Mathematics AIP Conf. Proc. 1450, 61-64 <doi : 10.1063/1.4724118>.

See Also

summary for summarize the model that has been built. Also use predict to predict model to testing or new data.

Examples

library(gstar)
library(xts)
data("LocationCPI")

#-----Use data with xts object----#
x = xts(LocationCPI[, -1], order.by = as.Date(LocationCPI[, 1]))

s <- round(nrow(x) * 0.8) ## split into training and testing (80:20)
x_train <- x[1:s, ]
x_test <- x[-c(1:s), ]


weight = matrix(c(0, 1, 1, 1,                    # create the uniform weight.
                1, 0, 1, 1,
                1, 1, 0, 1,
                1, 1, 1, 0), ncol = 4, nrow = 4)


weight = weight/(ncol(x) - 1) #the sum of weight is equal to 1 every row.


fit <-  gstar(x_train, weight = weight,
    p = 1, d = 0, est = "OLS")
summary(fit)

performance(fit)
performance(fit, x_test) ## to check the performance with testing data

predict(fit, n = 10) #forecast 10 data ahead

plot(fit)
plot(fit, n_predict = 10) #plot with 10 forecasting data
plot(fit, testing = x_test)

#---- Use dataframe or matrix---#
x2 <- LocationCPI
x2$Date <- NULL # remove the date column

data(Loc)
dst <- as.matrix(dist(Loc[, -1], diag = TRUE, upper = TRUE))
dst1 <- matrix(0, nrow = nrow(dst), ncol = ncol(dst))


for(i in 1:nrow(dst)) {
   for(j in 1:ncol(dst)){
     if(j == i) next
     dst1[i, j] <- sum(dst[i, -j])/sum(dst[i,])
 }
}

weight_inverse_distance <- matrix(0, nrow =
       nrow(dst), ncol = ncol(dst))

for(i in 1:nrow(dst)) {
   for(j in 1:ncol(dst)){
     if(j == i) next
     weight_inverse_distance[i, j] <- sum(dst1[i, j])/sum(dst1[i,])

 }
}

fit_inverse_distance <-  gstar(x2, weight =
     weight_inverse_distance, p = 2, d = 1, est = "OLS")

summary(fit_inverse_distance)
performance(fit_inverse_distance)
predict(fit_inverse_distance)
plot(fit_inverse_distance)