Forecasting Indonesia GDP in 2023

In the past two years, Indonesia experienced economic slowdown because of the pandemic. Nevertheless, the pandemic is become endemic and about 73% citizen has been vaccinated twice. Indonesia is in economic recovery. Then, how is the prosect of Indonesia economy for the next 5 quarters? To answer that question, we will forecast Indonesia GDP using ARIMA model.

Installing Libraries

Before started, we need to install some libraries.

library(readxl)
library(aTSA)
library(forecast)
library(lmtest)

Importing and Manipulating the Data

Then, we import the data. Data consist of Indonesia GDP quarterly ranging from 2010Q1 to 2022Q3. After that, it has to cast into time series format in order to be able performing the analysis in ARIMA.

gdp <- read_excel("D:/KARIR/R Portofolio/arima/univariate/gdpq.xlsx") 
gdp <- gdp[,c(-1)] 
gdp <-  ts(gdp, start= c(2010, 1), frequency = 4)

Plotting the Data

As we can see, Indonesia economy had plummeted in 2020. Then, began to recover starting in the end of 2021.

Model Selcetion

In the model selection, we need to find the apprpriate order of Autroregressive and Moving Avarage. Through Autocorrelation Function (ACF), and Partial Autocorrelation Function (PACF) plots, we can determine the AR and MA orders.

As we can see, ACF is decreasing gradually but PACF drops sharply. Thus, the appropriate model is AR(1). Nonetheles, there is a function called auto.arima() in forecast package that can perform the best selection model in ARIMA.

auto.arima(gdp, trace = T)

## 
##  ARIMA(2,0,2)(1,1,1)[4] with drift         : Inf
##  ARIMA(0,0,0)(0,1,0)[4] with drift         : 1171.054
##  ARIMA(1,0,0)(1,1,0)[4] with drift         : 1140.655
##  ARIMA(0,0,1)(0,1,1)[4] with drift         : Inf
##  ARIMA(0,0,0)(0,1,0)[4]                    : 1231.949
##  ARIMA(1,0,0)(0,1,0)[4] with drift         : 1146.211
##  ARIMA(1,0,0)(2,1,0)[4] with drift         : 1134.265
##  ARIMA(1,0,0)(2,1,1)[4] with drift         : Inf
##  ARIMA(1,0,0)(1,1,1)[4] with drift         : Inf
##  ARIMA(0,0,0)(2,1,0)[4] with drift         : 1168.568
##  ARIMA(2,0,0)(2,1,0)[4] with drift         : 1136.836
##  ARIMA(1,0,1)(2,1,0)[4] with drift         : 1136.844
##  ARIMA(0,0,1)(2,1,0)[4] with drift         : 1147.267
##  ARIMA(2,0,1)(2,1,0)[4] with drift         : Inf
##  ARIMA(1,0,0)(2,1,0)[4]                    : 1138.73
## 
##  Best model: ARIMA(1,0,0)(2,1,0)[4] with drift

## Series: gdp 
## ARIMA(1,0,0)(2,1,0)[4] with drift 
## 
## Coefficients:
##          ar1     sar1     sar2      drift
##       0.7846  -0.6568  -0.5197  24340.830
## s.e.  0.0967   0.1455   0.1564   2772.202
## 
## sigma^2 = 1.402e+09:  log likelihood = -561.4
## AIC=1132.8   AICc=1134.26   BIC=1142.05

So, the best model is ARIMA(1,0,0) with seasonal (2,1,0) in 4 period and include a drift (constant).

ARIMA Model

After we have the best model, we will run it to get the estimation.

model <- Arima(gdp, order = c(1,0,0), 
               seasonal = list(order=c(2,1,0), period = 3), 
               include.drift = T)
coeftest(model)

## 
## z test of coefficients:
## 
##          Estimate  Std. Error z value  Pr(>|z|)    
## ar1       0.54167     0.13389  4.0458 5.215e-05 ***
## sar1     -0.29326     0.11302 -2.5947  0.009469 ** 
## sar2     -0.65533     0.10336 -6.3404 2.292e-10 ***
## drift 25066.46407  2846.94550  8.8047 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1