# Load necessary libraries
library(forecast)
library(dplyr) #create lagged data
library(ggplot2)
library(TSPred) #test the prediction

dataset <- read.csv("C:/Work/DMU Teaching/ECON 5001/Block teaching/Block 4/UK_quarterly_inflation.csv", sep = ",", header = TRUE)
#View(dataset)

# Generate CPI and its lagged
CPI <- dataset$CPI.INDEX.00..ALL.ITEMS.2015.100
CPI_L1 <- dplyr::lag(CPI, n=1)

#Check the new lagged CPI
x <- data.frame(CPI, CPI_L1)

#Compute Inflation 
inflation_data <- ((CPI-CPI_L1)/CPI_L1)*100


# Convert the data into a time series object
ts_inflation <- ts(inflation_data, start = c(2000,1), frequency = 4) #the frequency indicates quarterly data. 1 is monthly and 12 is annually

#Split the data into a learning sample and a test sample
first.q <- 2000.25
last.q <-2018.75
inflation_learning <- window(ts_inflation, end=last.q)
inflation_test <- window(ts_inflation, start=last.q+0.25)

#View inflation
autoplot(ts_inflation) + ggtitle("Quarterly Inflation from 2000 to 2020") +   ylab("Inflation") + xlab("Quarter")


# Build and Fit an ARIMA(Auto-Regressive Integrated Moving Average) model to the data
arima_model <- auto.arima(inflation_learning, seasonal = TRUE)


#Check the model: if the model is correct, the residuals should be white noise (i.e. no pattern), ACF should not exceed the dashed line
checkresiduals(arima_model)


# #Now the model is ready, we can start forecasting future inflation
future_inflation <- forecast(arima_model, h = 12) # This forecasts the next 12 periods

future_inflation <- forecast(arima_model, length(inflation_test))

# Plot the forecast in blue against actual inflation rate in red
autoplot
plot(future_inflation,type="o", pch=16, xlim=c(2000,2023), ylim = c(-1,5), main="MA(0,1) Mod
el Multistep Forecasts")
lines(future_inflation$mean, type="p", pch=16, lty="dashed", col="blue")
lines(inflation_test, type="o", pch=16, lty="dotted", col = "red")


# Print the forecasted values
print(future_inflation)