In edxu96/tidynamics: Tidy Multivariate (Non)Linear Dynamic Systems

# Clear variables
rm(list=ls())
library(knitr)
source('LinearStocSystem_EDXU.R')
source("Data.R")

Question 3.2

Raw Data

plotTimeSeries(dat.f$heating, num_lag = 100, "Heating")

Question 3.3: ARIMA Model of Heating

mod_3 <- arima(dat.f$heating, order = c(0, 1, 0), include.mean = F)
mod_3
plotTimeSeriesResidual(mod_3, num_lag = 100, "Model 3")

Except for the seasonal effect, the ACF and PACF become 0 after lag 2. So it's hard to decide whether it's a AR2 or MA2 model.

mod_3.1 <- arima(mod_3$residuals, seasonal = list(order = c(0, 0, 1), period = 48), include.mean = F)
mod_3.1
plotTimeSeriesResidual(mod_3.1, num_lag = 100, "Model 3.1")

mod_3.2 <- arima(mod_3$residuals, seasonal = list(order = c(1, 0, 0), period = 48), include.mean = F)
mod_3.2
plotTimeSeriesResidual(mod_3.2, num_lag = 100, "Model 3.2")

mod_3.1.1 <- arima(mod_3.1$residuals, order = c(2, 0, 0), include.mean = F)
mod_3.1.1
plotTimeSeriesResidual(mod_3.1.1, num_lag = 100, "Model 3.1.1")

mod_3.1.2 <- arima(mod_3.1$residuals, order = c(2, 0, 0), fixed = c(0, NA), include.mean = F)
mod_3.1.2
plotTimeSeriesResidual(mod_3.1.2, num_lag = 100, "Model 3.1.2")

mod_3.1.3 <- arima(mod_3.1$residuals, order = c(0, 0, 2), include.mean = F)
mod_3.1.3
plotTimeSeriesResidual(mod_3.1.3, num_lag = 100, "Model 3.1.3")

mod_3.1.4 <- arima(mod_3.1$residuals, order = c(0, 0, 2), fixed = c(0, NA), include.mean = F)
mod_3.1.4
plotTimeSeriesResidual(mod_3.1.4, num_lag = 100, "Model 3.1.4")

mod_3.1.5 <- arima(mod_3.1$residuals, order = c(2, 0, 2), fixed = c(0, NA, 0, NA), include.mean = F)
mod_3.1.5
plotTimeSeriesResidual(mod_3.1.5, num_lag = 100, "Model 3.1.5")

mod_3.2 <- arima(mod_3$residuals, order = c(0, 0, 0), seasonal = list(order = c(1, 0, 0), period = 48), include.mean = F)
mod_3.2
plotTimeSeriesResidual(mod_3.2, num_lag = 100, "Model 3.2")

mod_3.2.1 <- arima(mod_3.2$residuals, order = c(2, 0, 0), include.mean = F)
mod_3.2.1
plotTimeSeriesResidual(mod_3.2.1, num_lag = 100, "Model 3.2.1")

mod_3.2.2 <- arima(mod_3.2$residuals, order = c(2, 0, 0), fixed = c(0, NA), include.mean = F)
mod_3.2.2
plotTimeSeriesResidual(mod_3.2.2, num_lag = 100, "Model 3.2.2")

mod_3.2.3 <- arima(mod_3.2$residuals, order = c(0, 0, 2), include.mean = F)
mod_3.2.3
plotTimeSeriesResidual(mod_3.2.3, num_lag = 100, "Model 3.2.3")

mod_3.2.4 <- arima(mod_3.2$residuals, order = c(0, 0, 2), fixed = c(0, NA), include.mean = F)
mod_3.2.4
plotTimeSeriesResidual(mod_3.2.4, num_lag = 100, "Model 3.2.4")

mod_3.3 <- arima(mod_3$residuals, order = c(0, 0, 0), seasonal = list(order = c(0, 1, 0), period = 48), include.mean = F)
mod_3.3
plotTimeSeriesResidual(mod_3.3, num_lag = 100, "Model 3.3")

mod_3.3.1 <- arima(mod_3$residuals, order = c(2, 0, 0), seasonal = list(order = c(1, 0, 0), period = 48), 
                   include.mean = F)
mod_3.3.1
plotTimeSeriesResidual(mod_3.3.1, num_lag = 100, "Model 3.3.1")

Test

mod_3.1.4 <- arima(dat.f$heating[1: num_obs], order = c(0, 1, 2), seasonal = list(order = c(0, 0, 2), period = 48), 
    fixed = c(0, NA, NA, NA), include.mean = T)
mod_3.1.3 <- arima(dat.f$heating[1: num_obs], order = c(0, 1, 2), seasonal = list(order = c(0, 0, 2), period = 48), 
    include.mean = T)
mod_3.1.1 <- arima(dat.f$heating[1: num_obs], order = c(2, 1, 0), seasonal = list(order = c(0, 0, 2), period = 48), 
    include.mean = T)
mod_3.1.2 <- arima(dat.f$heating[1: num_obs], order = c(2, 1, 0), seasonal = list(order = c(0, 0, 2), period = 48), 
    fixed = c(0, NA, NA, NA), include.mean = T)

table <- testModel(list(mod_3.1.4, mod_3.1.1, mod_3.1.2, mod_3.1.3), 
                   c("mod_3.1.4", "mod_3.1.1", "mod_3.1.2", "mod_3.1.3"))
kable(table, col.names = c('Name', 'Type', 'Coefficients', 'AIC', 'LogLikRatio Test', 'F-Dist Test'), 
      caption = 'Comparison Between Different Model for Heating', align = "l")