Package 'gstar'

Fit Generalized Space-Time Autoregressive Model

Description

gstar function return the paramter estimatation of Generalized Space-Time Autoregressive Model.

Usage

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

Arguments

x	a dataframe, matrix or xts/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 similiar with 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.

See Also

summary for summarises 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)

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Coordinate of several region In Indonesia

Description

A dataset containing the coordinate several region In Indonesia i.e Semarang, Surakarta, Tegal and Purwokerto.

Usage

data(Loc)

Format

A data frame with 4 rows and 3 variables:

City

Name of region/city

lattitude

The lattitude coordinate of each location

longitude

The longitude coordinate of each location

---

Consumer Price Index (CPI) in several region In Indonesia

Description

A dataset containing the Consumer Price Index (CPI) in several region In Indonesia i.e Semarang, Surakarta, Tegal and Purwokerto, it is time series data with monthly periodicity from Jan 2006 to Sep 2014

Usage

data(LocationCPI)

Format

A time series data frame with 105 rows and 5 variables:

Date

date of CPI, monthly

Purwokerto

The CPI of Purwokerto region

Surakarta

The CPI of Purwokerto region

Semarang

The CPI of Purwokerto region

Tegal

The CPI of Purwokerto region

Source

https://www.bps.go.id/

---

Calculate performance of prediction or forecasting

Description

Calculate performance of prediction or forecasting

Usage

performance(object, testing = NULL, ...)

Arguments

object	an object of class "gstar".
testing	a dataframe or matrix or xts object that contain testing data (outsample data). Please be noted, if you use differencing in the model estimation, you do not need difference your data because we already cover that in this function
...	Other arguments

Value

• MSE fol all data - Mean Square Error for all the data combined

• MSE fol each location - Mean Square Error for each spatial location

• MAPE fol all data - Mean Absolute Percentage Error for all the data combined

• MAPE fol each location - Mean Absolute Percentage Error for each spatial location

---

Plotting the gstar object

Description

plotting the gstar object

Usage

## S3 method for class 'gstar'
plot(x, testing = NULL, n_predict = NULL, ...)

Arguments

x	an object of class "gstar".
testing	The outsample or testing data to be plotted.
n_predict	The number of steps ahead for which prediction is required.
...	Other arguments

---

Predicting the gstar object

Description

Predicted values based on gstar object object

Usage

## S3 method for class 'gstar'
predict(object, n = NULL, ...)

Arguments

object	an object of class "gstar".
n	The number of steps ahead for which prediction is required.
...	further arguments passed to or from other methods.

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Summarizing Generalized Space-Time Autoregressive Fits

Description

This function are simmilar to summary of "lm" or "glm" object.

Usage

## S3 method for class 'gstar'
summary(object, ...)

Arguments

object	an object of class "gstar".
...	further arguments passed to or from other methods. coefficients - a named vector of coefficients. AIC - A version of Akaike's An Information Criterion.

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