Forecast Bi-Annual Electricity Price in Malta

library(tidyverse)
library(readxl)
library(ggplot2)
library(lubridate)
library(forecast)
library(writexl)
library(tseries)
library(magrittr)

1, Data

Here is the bi-snnual electricity price in Malta (Euro / Kilowatt-hour) with all taxes and levies included, which is downloaded from https://ec.europa.eu/eurostat/data/database and https://www.statista.com/statistics/418104/electricity-prices-for-households-in-malta/. The data in 2008 and 2009 is missing.

head(ti)

ti %>%
  ggplot() +
    geom_line(mapping = aes(x = bi_annual, y = price)) +
    labs(
      title = "Bi-Annual Electricity Price in Malta",
      subtitle = "with All taxes and levies included from 2003f to 2009s",
      y = "Price (Euro / Kilowatt-hour)",
      x = "Index (Bi-Annual)"
      )

2, Linear Regression

acf(ti$price, na.action = na.pass)

pacf(ti$price, na.action = na.pass)

There is no obvious seasonal variation or fluctuation. So linear regression is used to model the trend. Then, arima model is used to remove the correlation in residuals.

lm <- lm(price ~ bi_annual, ti)

acf(lm$residuals)

pacf(lm$residuals)

3, ARIMA Model of Residuals from Linear Regression

mod_resi_lm <- auto.arima(lm$residuals)
mod_resi_lm

Series: lm$residuals 
ARIMA(1,0,0) with zero mean 

Coefficients:
         ar1
      0.8613
s.e.  0.0854

sigma^2 estimated as 0.0001835:  log likelihood=83.43
AIC=-162.87   AICc=-162.4   BIC=-160.13

acf(mod_resi_lm$residuals)

pacf(mod_resi_lm$residuals)

3, Forecast

Forecast is the combination of those from linear regression model and arima model.

pred_resi_lm <- predict(mod_resi_lm, n.ahead = 21 * 2)
pred_lm <- predict(
  lm, newdata = data.frame(bi_annual = seq(2019.5, 2019.5 + 20.5, by = 0.5))
  )
ti_fore <- ti %>%
  bind_rows(
    tibble(
      bi_annual = seq(2019.5, 2019.5 + 20.5, by = 0.5),
      price = as.numeric(pred_resi_lm$pred) + pred_lm,
      observation = rep(FALSE, length(pred_lm))
      )
    )

ti_fore %>%
  ggplot() +
    geom_line(mapping = aes(x = bi_annual, y = price, color = observation)) +
    labs(
      title = "Forecast of Bi-Annual Electricity Price in Malta",
      subtitle = "with all included from 19F to 40F using data from 03f to 09s",
      y = "Price (Euro / Kilo-Watt-Hour)",
      x = "Bi-Annual"
      )

4, Annual Averaged Price Forecast

ti_annual <-
  tibble(
    year = round(seq(2019 - 0.01, 2019 - 0.01 + 20.5, by = 0.5)), 
    price = c(0.1305, (pred_resi_lm$pred + pred_lm)[1:41]), bi = rep(1:2, 21)
    ) %>%
  spread(key = "bi", value = "price") %>%
  mutate(price_ave = (.$`1` + .$`2`) / 2) %>%
  select(year, price_ave)

ti_annual