2020-03-17 Research Assignment
Question Part (b)
Chen Lianghe
17 March 2020
Overview
You are tasked to develop an electricity demand forecasting model for ABC. The objective of the forecasting model is to better inform ABC and the industry so as to ensure that sufficient infrastructure is to be put in place to cater for increasing electricity demand.
We used the following abbreviations to denote the Different Sectors and Types of Household in Energy Consumption:
- MFG = Manufacturing
- CON = Construction
- UTI = Utilities
- OIR = Other Industrial-related
- WRT = Wholesale and Retail Trade
- AFS = Accommodation and Food Services
- ICM = Information and Communications
- FIA = Financial and Insurance Activities
- REA = Real Estate Activities
- PST = Professional, Scientific & Technical, Administration & Support Activities
- OCS = Other Commerce and Services-related
- TRP = Transport-related
- OTH = Others
- X1R2R = 1-Room / 2-Room HDB
- X3R = 3-Room HDB
- X4R = 4-Room HDB
- X5REX = 5-Room and Executive HDB
- PAC = Private Apartments and Condominiums
- LPP = Landed Properties
Loading Libraries
# Loading Libraries
library(datetime)## Warning: package 'datetime' was built under R version 3.6.3library(Hmisc)## Warning: package 'Hmisc' was built under R version 3.6.3## Loading required package: lattice## Loading required package: survival## Loading required package: Formula## Loading required package: ggplot2##
## Attaching package: 'Hmisc'## The following objects are masked from 'package:base':
##
## format.pval, unitslibrary(corrplot)## corrplot 0.84 loadedlibrary(caret)##
## Attaching package: 'caret'## The following object is masked from 'package:survival':
##
## clusterlibrary(vars)## Warning: package 'vars' was built under R version 3.6.3## Loading required package: MASS## Warning: package 'MASS' was built under R version 3.6.3## Loading required package: strucchange## Warning: package 'strucchange' was built under R version 3.6.3## Loading required package: zoo## Warning: package 'zoo' was built under R version 3.6.3##
## Attaching package: 'zoo'## The following objects are masked from 'package:base':
##
## as.Date, as.Date.numeric## Loading required package: sandwich## Warning: package 'sandwich' was built under R version 3.6.3## Loading required package: urca## Warning: package 'urca' was built under R version 3.6.3## Loading required package: lmtest## Warning: package 'lmtest' was built under R version 3.6.3library(forecast)## Warning: package 'forecast' was built under R version 3.6.3## Registered S3 method overwritten by 'quantmod':
## method from
## as.zoo.data.frame zoolibrary(strucchange)Loading and Cleaning Data on Energy Consumption
# Loading Data on Energy Consumption
ecData <- read.csv('./EC_05_18.csv', header = TRUE)
ecData$Year <- as.year(ecData$Year)
# Cleaning Data on Energy Consumption
ecData <- ecData[, colSums(is.na(ecData)) == 0]
summary(ecData)## Year MFG CON UTI
## Min. :2005 Min. :13836 Min. :234.8 Min. : 411.0
## 1st Qu.:2008 1st Qu.:14966 1st Qu.:302.7 1st Qu.: 674.2
## Median :2012 Median :16932 Median :397.6 Median : 953.7
## Mean :2012 Mean :16712 Mean :395.4 Mean : 958.2
## 3rd Qu.:2015 3rd Qu.:18205 3rd Qu.:489.0 3rd Qu.:1227.4
## Max. :2018 Max. :19582 Max. :551.6 Max. :1518.7
## OIR WRT AFS ICM FIA
## Min. :25.88 Min. :1821 Min. :1031 Min. : 667.2 Min. :1292
## 1st Qu.:29.34 1st Qu.:1913 1st Qu.:1170 1st Qu.: 849.9 1st Qu.:1946
## Median :35.58 Median :1972 Median :1263 Median :1036.5 Median :2110
## Mean :36.26 Mean :1994 Mean :1265 Mean :1190.6 Mean :2114
## 3rd Qu.:41.66 3rd Qu.:2060 3rd Qu.:1346 3rd Qu.:1393.7 3rd Qu.:2355
## Max. :48.26 Max. :2293 Max. :1464 Max. :2230.5 Max. :2718
## REA PST OCS TRP OTH
## Min. :3712 Min. :650.2 Min. :3613 Min. :1200 Min. :237.7
## 1st Qu.:3961 1st Qu.:706.3 1st Qu.:4244 1st Qu.:1452 1st Qu.:277.1
## Median :4455 Median :759.4 Median :4393 Median :2276 Median :325.2
## Mean :4280 Mean :787.9 Mean :4384 Mean :2071 Mean :369.6
## 3rd Qu.:4516 3rd Qu.:874.8 3rd Qu.:4697 3rd Qu.:2444 3rd Qu.:446.7
## Max. :4701 Max. :934.1 Max. :4860 Max. :2944 Max. :612.1
## X1R2R X3R X4R X5REX PAC
## Min. : 70.90 Min. :690.1 Min. :1475 Min. :1486 Min. :1349
## 1st Qu.: 77.05 1st Qu.:708.4 1st Qu.:1511 1st Qu.:1517 1st Qu.:1444
## Median : 87.75 Median :731.5 Median :1597 Median :1564 Median :1605
## Mean : 96.62 Mean :733.2 Mean :1620 Mean :1568 Mean :1647
## 3rd Qu.:117.60 3rd Qu.:747.9 3rd Qu.:1731 3rd Qu.:1592 3rd Qu.:1831
## Max. :135.63 Max. :801.8 Max. :1839 Max. :1708 Max. :2001
## LPP
## Min. : 953.6
## 1st Qu.: 970.2
## Median :1016.9
## Mean :1012.0
## 3rd Qu.:1037.8
## Max. :1098.0Plotting a Correlation Matrix for Data on Energy Consumption
# Plotting a Correlation Matrix for Data on Energy Consumption
ecMatrix <- rcorr(as.matrix(ecData))
flattenCorrMatrix <- function(cormat, pmat){
ut <- upper.tri(cormat)
data.frame(row = rownames(cormat)[row(cormat)[ut]],
column = rownames(cormat)[col(cormat)[ut]],
cor = (cormat)[ut],
p = pmat[ut])}
flattenecMatrix <- flattenCorrMatrix(ecMatrix$r, ecMatrix$P)
summary(flattenecMatrix)## row column cor p
## Year :19 LPP :19 Min. :-0.9540 Min. :0.0000000
## MFG :18 PAC :18 1st Qu.: 0.5072 1st Qu.:0.0000009
## CON :17 X5REX :17 Median : 0.8389 Median :0.0000789
## UTI :16 X4R :16 Mean : 0.5731 Mean :0.0631629
## OIR :15 X3R :15 3rd Qu.: 0.9313 3rd Qu.:0.0016110
## WRT :14 X1R2R :14 Max. : 0.9951 Max. :0.8441051
## (Other):91 (Other):91Plotting a Correlation Plot for Data on Energy Consumption
# Plotting a Correlation Plot for Data on Energy Consumption
corrplot(ecMatrix$r, type = "upper", order = "FPC", method = "color",
p.mat = ecMatrix$P, sig.level = 0.01, insig = "pch",
tl.cex = 0.8, tl.col = "black", tl.srt = 45)
In the Correlation Plot shown above, the variables that are highly correlated are highlighted at the dark blue intersections. We used a level of significance of 0.01 to determine correlations that are statistically significant. Correlations with a p-value > 0.01 are considered statistically insignificant and marked with a cross.
Unlike for Question Part (a) where we used Highly Uncorrelated Variables to build our Forecasting Model, we will use Highly Uncorrelated Variables to build our Forecasting Model in this Question. From the Correlation Plot, there are 3 out of 19 variables that are highly uncorrelated with the rest of the variables in our Data on Energy Consumption. They have correlations that are statistically insignificant at the level of significance of 0.01. These correlations have been marked with a cross in the Correlation Plot. We will use these variables to build our Forecasting Model. Therefore, we will only be using the variables, “WRT”, “PST”, and “OTH” to build our Forecasting Model.
Building our Forecasting Model
For this Research Assignment, we will use a Vector Autoregression (VAR) Model as our Forecasting Model. It is a causal / Econometric Forecasting Method used to identify underlying factors that might influence the variable that is being forecasted.
Converting Data on Energy Consumption to a Time Series Object
# Define Manufacturing (MFG) as a Time Series Object
MFG <- ts(ecData$MFG, start = c(2005), end = c(2018), frequency = 1)
# Define Construction (CON) as a Time Series Object
CON <- ts(ecData$CON, start = c(2005), end = c(2018), frequency = 1)
# Define Utilities (UTI) as a Time Series Object
UTI <- ts(ecData$UTI, start = c(2005), end = c(2018), frequency = 1)
# Define Other Industrial-related (OIR) as a Time Series Object
OIR <- ts(ecData$OIR, start = c(2005), end = c(2018), frequency = 1)
# Define Wholesale and Retail Trade (WRT) as a Time Series Object
WRT <- ts(ecData$WRT, start = c(2005), end = c(2018), frequency = 1)
# Define Accommodation and Food Services (AFS) as a Time Series Object
AFS <- ts(ecData$AFS, start = c(2005), end = c(2018), frequency = 1)
# Define Information and Communications (ICM) as a Time Series Object
ICM <- ts(ecData$ICM, start = c(2005), end = c(2018), frequency = 1)
# Define Financial and Insurance Activities (FIA) as a Time Series Object
FIA <- ts(ecData$FIA, start = c(2005), end = c(2018), frequency = 1)
# Define Real Estate Activities (REA) as a Time Series Object
REA <- ts(ecData$REA, start = c(2005), end = c(2018), frequency = 1)
# Define Professional, Scientific & Technical, Administration
# & Support Activities (PST) as a Time Series Object
PST <- ts(ecData$PST, start = c(2005), end = c(2018), frequency = 1)
# Define Other Commerce and Services-related (OCS) as a Time Series Object
OCS <- ts(ecData$OCS, start = c(2005), end = c(2018), frequency = 1)
# Define Transport-related (TRP) as a Time Series Object
TRP <- ts(ecData$TRP, start = c(2005), end = c(2018), frequency = 1)
# Define Others (OTH) as a Time Series Object
OTH <- ts(ecData$OTH, start = c(2005), end = c(2018), frequency = 1)
# Define 1-Room / 2-Room HDB (X1R2R) as a Time Series Object
X1R2R <- ts(ecData$X1R2R, start = c(2005), end = c(2018), frequency = 1)
# Define 3-Room HDB (X3R) as a Time Series Object
X3R <- ts(ecData$X3R, start = c(2005), end = c(2018), frequency = 1)
# Define 4-Room HDB (X4R) as a Time Series Object
X4R <- ts(ecData$X4R, start = c(2005), end = c(2018), frequency = 1)
# Define 5-Room and Executive HDB (X5REX) as a Time Series Object
X5REX <- ts(ecData$X5REX, start = c(2005), end = c(2018), frequency = 1)
# Define Private Apartments and Condominiums (PAC) as a Time Series Object
PAC <- ts(ecData$PAC, start = c(2005), end = c(2018), frequency = 1)
# Define Landed Properties (LPP) as a Time Series Object
LPP <- ts(ecData$LPP, start = c(2005), end = c(2018), frequency = 1)Plotting Data on Energy Consumption by Different Sectors and Types of Household
# Plotting Data on Energy Consumption by Different Sectors and Types of Household
plot(cbind(MFG, CON, UTI, OIR, WRT, AFS, ICM, FIA, REA, PST),
main = "Energy Consumption by Different Sectors and Households")
plot(cbind(OCS, TRP, OTH, X1R2R, X3R, X4R, X5REX, PAC, LPP),
main = "Energy Consumption by Different Sectors and Households")
Model Selection and Estimation
# Model Selection and Estimation
VAR_Data <- cbind(WRT, PST, OTH)
colnames(VAR_Data) <- c("WRT", "PST", "OTH")
VAR_Data_info <- VARselect(VAR_Data, lag.max = 10, type = "const")
VAR_Data_info## $selection
## AIC(n) HQ(n) SC(n) FPE(n)
## 1 1 1 2
##
## $criteria
## 1 2 3 4 5 6 7 8 9 10
## AIC(n) -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf
## HQ(n) -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf
## SC(n) -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf
## FPE(n) NaN 0 0 0 0 0 0 0 0 0VAR_Est <- VAR(VAR_Data, p = 2, type = "const", season = NULL, exogen = NULL)
summary(VAR_Est)##
## VAR Estimation Results:
## =========================
## Endogenous variables: WRT, PST, OTH
## Deterministic variables: const
## Sample size: 12
## Log Likelihood: -164.588
## Roots of the characteristic polynomial:
## 0.8378 0.8378 0.6709 0.6709 0.4706 0.4706
## Call:
## VAR(y = VAR_Data, p = 2, type = "const", exogen = NULL)
##
##
## Estimation results for equation WRT:
## ====================================
## WRT = WRT.l1 + PST.l1 + OTH.l1 + WRT.l2 + PST.l2 + OTH.l2 + const
##
## Estimate Std. Error t value Pr(>|t|)
## WRT.l1 -0.63428 0.61676 -1.028 0.3509
## PST.l1 -0.33718 0.43745 -0.771 0.4757
## OTH.l1 -3.52879 2.98519 -1.182 0.2903
## WRT.l2 0.09707 0.63132 0.154 0.8838
## PST.l2 -0.91284 0.68010 -1.342 0.2372
## OTH.l2 1.82163 2.43680 0.748 0.4884
## const 4598.69602 2078.27730 2.213 0.0778 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
##
## Residual standard error: 86.01 on 5 degrees of freedom
## Multiple R-Squared: 0.7891, Adjusted R-squared: 0.5359
## F-statistic: 3.117 on 6 and 5 DF, p-value: 0.1164
##
##
## Estimation results for equation PST:
## ====================================
## PST = WRT.l1 + PST.l1 + OTH.l1 + WRT.l2 + PST.l2 + OTH.l2 + const
##
## Estimate Std. Error t value Pr(>|t|)
## WRT.l1 -0.7871 0.6357 -1.238 0.271
## PST.l1 0.2475 0.4509 0.549 0.607
## OTH.l1 -0.1763 3.0769 -0.057 0.957
## WRT.l2 -0.1673 0.6507 -0.257 0.807
## PST.l2 -0.2950 0.7010 -0.421 0.691
## OTH.l2 0.1640 2.5117 0.065 0.950
## const 2711.4388 2142.1264 1.266 0.261
##
##
## Residual standard error: 88.65 on 5 degrees of freedom
## Multiple R-Squared: 0.656, Adjusted R-squared: 0.2431
## F-statistic: 1.589 on 6 and 5 DF, p-value: 0.314
##
##
## Estimation results for equation OTH:
## ====================================
## OTH = WRT.l1 + PST.l1 + OTH.l1 + WRT.l2 + PST.l2 + OTH.l2 + const
##
## Estimate Std. Error t value Pr(>|t|)
## WRT.l1 0.08011 0.05996 1.336 0.23911
## PST.l1 -0.24098 0.04253 -5.666 0.00238 **
## OTH.l1 0.81154 0.29022 2.796 0.03816 *
## WRT.l2 -0.07224 0.06138 -1.177 0.29215
## PST.l2 0.08167 0.06612 1.235 0.27164
## OTH.l2 0.08695 0.23690 0.367 0.72863
## const 124.80651 202.04763 0.618 0.56381
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
##
## Residual standard error: 8.361 on 5 degrees of freedom
## Multiple R-Squared: 0.9957, Adjusted R-squared: 0.9905
## F-statistic: 191.9 on 6 and 5 DF, p-value: 9.623e-06
##
##
##
## Covariance matrix of residuals:
## WRT PST OTH
## WRT 7397.0 -2868.17 408.14
## PST -2868.2 7858.46 -46.31
## OTH 408.1 -46.31 69.91
##
## Correlation matrix of residuals:
## WRT PST OTH
## WRT 1.0000 -0.37619 0.56756
## PST -0.3762 1.00000 -0.06248
## OTH 0.5676 -0.06248 1.00000While a R-Squared value does not provide a formal hypothesis test for goodness-of-fit, it provides an estimate for the strength of the relationship between our variables. We determined the Simple Linear Regression Models for each of our Highly Uncorrelated Variables, “WRT”, “PST”, and “OTH”. They gave Adjusted R-Squared values of 0.54, 0.24, and 0.99, respectively. This suggests that “WRT” and “PST” are highly uncorrelated with the rest of the variables, while “OTH” is highly negatively correlated with the rest of the variables. The models also gave p-values of 0.1164, 0.314, and 9.623e-06, respectively. This suggests that the correlations for “WRT” and “PST” are statistically insignificant, while the correlations for “OTH” are statistically significant.
Diagnostic Tests on Residuals of our Model
To consider the Model Fit, we performed some Diagnostic Tests on Residuals of our Model.
Portmanteau Test
To test for Serial Correlation, we performed a Portmanteau Test. Serial Correlation is the relationship between a given variable and a lagged version of itself over various time intervals. A variable that is serially correlated has a pattern and is not random.
# Portmanteau Test
VAR_Est_serial <- serial.test(VAR_Est, lags.pt = 10, type = "PT.asymptotic")
VAR_Est_serial##
## Portmanteau Test (asymptotic)
##
## data: Residuals of VAR object VAR_Est
## Chi-squared = 51.296, df = 72, p-value = 0.9692# Plotting Serial Correlations of Highly Uncorrelated Variables
plot(VAR_Est_serial, names = "WRT")
plot(VAR_Est_serial, names = "PST")
plot(VAR_Est_serial, names = "OTH")
From the Portmanteau Test shown above, we obtained a p-value of 0.9692 which does not reject the null hypothesis at the level of significance of 0.05. This suggests that there is an absence of Serial Correlation for our Highly Uncorrelated Variables, “WRT”, “PST”, and “OTH”. There is no apparent relationship between these variables and the lagged versions of themselves over various time intervals. The variables are not serially correlated and their predictions are random and do not display a pattern.
Engle’s Autoregressive Conditional Heteroscedasticity (ARCH) Lagrange Multiplier (LM) Test
To test for Heteroscedasticity, we performed an Engle’s Autoregressive Conditional Heteroscedasticity (ARCH) Lagrange Multiplier (LM) Test. An uncorrelated time series can still be serially dependent due to a dynamic conditional variance process. A time series exhibiting Conditional Heteroscedasticity is said to have ARCH effects. Engle’s ARCH LM Test assesses the significance of these effects.
# Engle's ARCH LM Test
VAR_Est_ARCH <- arch.test(VAR_Est, lags.multi = 1, multivariate.only = TRUE)
VAR_Est_ARCH##
## ARCH (multivariate)
##
## data: Residuals of VAR object VAR_Est
## Chi-squared = 38.337, df = 36, p-value = 0.364From the Engle’s ARCH LM Test shown above, we obtained a p-value of 0.364 which does not reject the null hypothesis at the level of significance of 0.05. This suggests that there is an absence of ARCH effects for our Highly Uncorrelated Variables, “WRT”, “PST”, and “OTH”. There is no apparent Heteroscedasticity for these variables.
Normality Test
To consider the distribution of residuals in our model, we performed a Normality Test. It is used to determine if a dataset is well modelled by a normal distribution and to compute how likely it is for a random variable underlying the dataset to be normally distributed.
# Normality Test
VAR_Est_norm <- normality.test(VAR_Est, multivariate.only = TRUE)
VAR_Est_norm## $JB
##
## JB-Test (multivariate)
##
## data: Residuals of VAR object VAR_Est
## Chi-squared = 2.3569, df = 6, p-value = 0.8841
##
##
## $Skewness
##
## Skewness only (multivariate)
##
## data: Residuals of VAR object VAR_Est
## Chi-squared = 1.9951, df = 3, p-value = 0.5734
##
##
## $Kurtosis
##
## Kurtosis only (multivariate)
##
## data: Residuals of VAR object VAR_Est
## Chi-squared = 0.3618, df = 3, p-value = 0.948From the Normality Test shown above, we obtained p-values of 0.8841 for the Jarque-Bera (JB) Test, 0.5734 for Skewness, and 0.948 for Kurtosis. They do not reject the null hypothesis at the level of significance of 0.05. This suggests that the distribution of residuals in our model is a fairly normal distribution.
Cumulative Sum Control Chart (CUSUM) Test
To test for Structural Breaks in the residuals of our model, we performed a Cumulative Sum Control Chart (CUSUM) Test. It is a sequential analysis technique used to monitor change detection for statistical quality control. In econometrics and statistics, a Structural Break is an unexpected change over time in the parameters of regression models, which can lead to huge forecasting errors and reduced reliability of the model. Structural Stability is the time-invariance of regression coefficients and a central issue in all applications of linear regression models. The lack of Structural Stability of coefficients frequently caused forecast failure and should be tested for routinely.
# Cumulative Sum Control Chart (CUSUM) Test
VAR_Est_CUSUM <- stability(VAR_Est, type = "OLS-CUSUM")
plot(VAR_Est_CUSUM)
From the CUSUM Test shown above, there is no apparent Structural Break in the respective Confidence Intervals of our Highly Uncorrelated Variables, “WRT”, “PST”, and “OTH”.
The Chow Test
The Chow Test is used to test whether the true coefficients in two linear regressions on different data sets are equal. In econometrics, it is most commonly used in time series analysis to test for the presence of a structural break at a period which can be assumed to be known a priori. In program evaluation, The Chow Test is often used to determine whether the independent variables have different impacts on different subgroups of the population.
# Finding Structural Breaks in Energy Consumption for Manufacturing (MFG)
MFG_bp <- breakpoints(MFG ~ 1)
summary(MFG_bp)##
## Optimal (m+1)-segment partition:
##
## Call:
## breakpoints.formula(formula = MFG ~ 1)
##
## Breakpoints at observation number:
##
## m = 1 5
## m = 2 5 9
## m = 3 5 9 12
## m = 4 2 5 9 12
## m = 5 2 5 7 9 12
##
## Corresponding to breakdates:
##
## m = 1 2009
## m = 2 2009 2013
## m = 3 2009 2013 2016
## m = 4 2006 2009 2013 2016
## m = 5 2006 2009 2011 2013 2016
##
## Fit:
##
## m 0 1 2 3 4 5
## RSS 4.738e+07 1.101e+07 3.434e+06 1.393e+06 7.675e+05 4.373e+05
## BIC 2.555e+02 2.403e+02 2.293e+02 2.220e+02 2.189e+02 2.163e+02# Plotting Structural Breaks in Energy Consumption for Manufacturing (MFG)
MFG_ci <- confint(MFG_bp)
plot(MFG)
lines(MFG_bp)
lines(MFG_ci)
# Finding Structural Breaks in Energy Consumption for Construction (CON)
CON_bp <- breakpoints(CON ~ 1)
summary(CON_bp)##
## Optimal (m+1)-segment partition:
##
## Call:
## breakpoints.formula(formula = CON ~ 1)
##
## Breakpoints at observation number:
##
## m = 1 7
## m = 2 3 7
## m = 3 3 7 12
## m = 4 3 7 9 12
## m = 5 2 5 7 9 12
##
## Corresponding to breakdates:
##
## m = 1 2011
## m = 2 2007 2011
## m = 3 2007 2011 2016
## m = 4 2007 2011 2013 2016
## m = 5 2006 2009 2011 2013 2016
##
## Fit:
##
## m 0 1 2 3 4 5
## RSS 161986.9 24737.3 15679.9 12040.7 6250.8 3696.8
## BIC 176.0 155.0 153.9 155.4 151.5 149.5# Plotting Structural Breaks in Energy Consumption for Construction (CON)
CON_ci <- confint(CON_bp)
plot(CON)
lines(CON_bp)
lines(CON_ci)## Warning: Overlapping confidence intervals
# Finding Structural Breaks in Energy Consumption for Utilities (UTI)
UTI_bp <- breakpoints(UTI ~ 1)
summary(UTI_bp)##
## Optimal (m+1)-segment partition:
##
## Call:
## breakpoints.formula(formula = UTI ~ 1)
##
## Breakpoints at observation number:
##
## m = 1 8
## m = 2 5 9
## m = 3 5 8 11
## m = 4 2 5 8 11
## m = 5 2 5 7 9 11
##
## Corresponding to breakdates:
##
## m = 1 2012
## m = 2 2009 2013
## m = 3 2009 2012 2015
## m = 4 2006 2009 2012 2015
## m = 5 2006 2009 2011 2013 2015
##
## Fit:
##
## m 0 1 2 3 4 5
## RSS 1789444.8 463239.5 169872.2 95870.1 39499.5 24758.2
## BIC 209.6 196.0 187.2 184.5 177.4 176.1# Plotting Structural Breaks in Energy Consumption for Utilities (UTI)
UTI_ci <- confint(UTI_bp)
plot(UTI)
lines(UTI_bp)
lines(UTI_ci)## Warning: Overlapping confidence intervals
# Finding Structural Breaks in Energy Consumption for Other Industrial-related (OIR)
OIR_bp <- breakpoints(OIR ~ 1)
summary(OIR_bp)##
## Optimal (m+1)-segment partition:
##
## Call:
## breakpoints.formula(formula = OIR ~ 1)
##
## Breakpoints at observation number:
##
## m = 1 7
## m = 2 7 11
## m = 3 4 7 11
## m = 4 3 5 7 11
## m = 5 3 5 7 10 12
##
## Corresponding to breakdates:
##
## m = 1 2011
## m = 2 2011 2015
## m = 3 2008 2011 2015
## m = 4 2007 2009 2011 2015
## m = 5 2007 2009 2011 2014 2016
##
## Fit:
##
## m 0 1 2 3 4 5
## RSS 796.02 166.75 69.98 25.67 17.17 12.57
## BIC 101.58 84.97 78.09 69.33 68.98 69.89# Plotting Structural Breaks in Energy Consumption for Other Industrial-related (OIR)
OIR_ci <- confint(OIR_bp)## Warning in confint.breakpointsfull(OIR_bp): Confidence interval 3 cannot be
## computed: P(argmax V <= 0) = 0.0089plot(OIR)
lines(OIR_bp)
# Finding Structural Breaks in Energy Consumption for Wholesale and Retail Trade (WRT)
WRT_bp <- breakpoints(WRT ~ 1)
summary(WRT_bp)##
## Optimal (m+1)-segment partition:
##
## Call:
## breakpoints.formula(formula = WRT ~ 1)
##
## Breakpoints at observation number:
##
## m = 1 10
## m = 2 2 9
## m = 3 2 8 10
## m = 4 2 8 10 12
## m = 5 2 5 8 10 12
##
## Corresponding to breakdates:
##
## m = 1 2014
## m = 2 2006 2013
## m = 3 2006 2012 2014
## m = 4 2006 2012 2014 2016
## m = 5 2006 2009 2012 2014 2016
##
## Fit:
##
## m 0 1 2 3 4 5
## RSS 189907.5 104723.4 75971.6 65470.9 62629.4 61182.0
## BIC 178.2 175.2 176.0 179.1 183.8 188.8# Plotting Structural Breaks in Energy Consumption for Wholesale and Retail Trade (WRT)
WRT_ci <- confint(WRT_bp)
plot(WRT)
lines(WRT_bp)
lines(WRT_ci)
# Finding Structural Breaks in Energy Consumption
# for Accommodation and Food Services (AFS)
AFS_bp <- breakpoints(AFS ~ 1)
summary(AFS_bp)##
## Optimal (m+1)-segment partition:
##
## Call:
## breakpoints.formula(formula = AFS ~ 1)
##
## Breakpoints at observation number:
##
## m = 1 7
## m = 2 5 11
## m = 3 2 6 11
## m = 4 2 5 8 11
## m = 5 2 4 6 8 11
##
## Corresponding to breakdates:
##
## m = 1 2011
## m = 2 2009 2015
## m = 3 2006 2010 2015
## m = 4 2006 2009 2012 2015
## m = 5 2006 2008 2010 2012 2015
##
## Fit:
##
## m 0 1 2 3 4 5
## RSS 247295.7 67943.9 27709.9 12648.4 4606.7 4401.8
## BIC 181.9 169.1 161.8 156.1 147.3 151.9# Plotting Structural Breaks in Energy Consumption
# for Accommodation and Food Services (AFS)
AFS_ci <- confint(AFS_bp)
plot(AFS)
lines(AFS_bp)
lines(AFS_ci)
# Finding Structural Breaks in Energy Consumption
# for Information and Communications (ICM)
ICM_bp <- breakpoints(ICM ~ 1)
summary(ICM_bp)##
## Optimal (m+1)-segment partition:
##
## Call:
## breakpoints.formula(formula = ICM ~ 1)
##
## Breakpoints at observation number:
##
## m = 1 11
## m = 2 7 11
## m = 3 5 9 11
## m = 4 3 7 9 11
## m = 5 3 5 7 9 11
##
## Corresponding to breakdates:
##
## m = 1 2015
## m = 2 2011 2015
## m = 3 2009 2013 2015
## m = 4 2007 2011 2013 2015
## m = 5 2007 2009 2011 2013 2015
##
## Fit:
##
## m 0 1 2 3 4 5
## RSS 3086051.5 682801.0 243179.3 158961.9 119331.5 108966.2
## BIC 217.3 201.4 192.2 191.6 192.8 196.8# Plotting Structural Breaks in Energy Consumption
# for Information and Communications (ICM)
ICM_ci <- confint(ICM_bp)
plot(ICM)
lines(ICM_bp)
lines(ICM_ci)
# Finding Structural Breaks in Energy Consumption
# for Financial and Insurance Activities (FIA)
FIA_bp <- breakpoints(FIA ~ 1)
summary(FIA_bp)##
## Optimal (m+1)-segment partition:
##
## Call:
## breakpoints.formula(formula = FIA ~ 1)
##
## Breakpoints at observation number:
##
## m = 1 7
## m = 2 2 7
## m = 3 2 9 11
## m = 4 2 7 9 11
## m = 5 2 4 7 9 11
##
## Corresponding to breakdates:
##
## m = 1 2011
## m = 2 2006 2011
## m = 3 2006 2013 2015
## m = 4 2006 2011 2013 2015
## m = 5 2006 2008 2011 2013 2015
##
## Fit:
##
## m 0 1 2 3 4 5
## RSS 1790176.2 623655.0 281779.6 198527.2 97398.5 89160.3
## BIC 209.6 200.1 194.3 194.7 190.0 194.0# Plotting Structural Breaks in Energy Consumption
# for Financial and Insurance Activities (FIA)
FIA_ci <- confint(FIA_bp)## Warning in confint.breakpointsfull(FIA_bp): Confidence interval 4 cannot be
## computed: P(argmax V <= 0) = 0.9869plot(FIA)
lines(FIA_bp)
# Finding Structural Breaks in Energy Consumption for Real Estate Activities (REA)
REA_bp <- breakpoints(REA ~ 1)
summary(REA_bp)##
## Optimal (m+1)-segment partition:
##
## Call:
## breakpoints.formula(formula = REA ~ 1)
##
## Breakpoints at observation number:
##
## m = 1 5
## m = 2 5 12
## m = 3 3 5 12
## m = 4 3 5 7 12
## m = 5 3 5 7 9 12
##
## Corresponding to breakdates:
##
## m = 1 2009
## m = 2 2009 2016
## m = 3 2007 2009 2016
## m = 4 2007 2009 2011 2016
## m = 5 2007 2009 2011 2013 2016
##
## Fit:
##
## m 0 1 2 3 4 5
## RSS 1547808.7 158582.6 97551.1 37704.9 23974.0 21164.6
## BIC 207.6 181.0 179.5 171.4 170.4 173.9# Plotting Structural Breaks in Energy Consumption for Real Estate Activities (REA)
REA_ci <- confint(REA_bp)
plot(REA)
lines(REA_bp)
lines(REA_ci)
# Finding Structural Breaks in Professional, Scientific
# & Technical, Administration & Support Activities (PST)
PST_bp <- breakpoints(PST ~ 1)
summary(PST_bp)##
## Optimal (m+1)-segment partition:
##
## Call:
## breakpoints.formula(formula = PST ~ 1)
##
## Breakpoints at observation number:
##
## m = 1 9
## m = 2 2 9
## m = 3 2 5 9
## m = 4 2 5 7 9
## m = 5 2 5 7 9 12
##
## Corresponding to breakdates:
##
## m = 1 2013
## m = 2 2006 2013
## m = 3 2006 2009 2013
## m = 4 2006 2009 2011 2013
## m = 5 2006 2009 2011 2013 2016
##
## Fit:
##
## m 0 1 2 3 4 5
## RSS 138267.0 78663.7 27410.2 9355.5 8878.5 8439.0
## BIC 173.8 171.2 161.7 151.9 156.5 161.0# Plotting Structural Breaks in Professional, Scientific
# & Technical, Administration & Support Activities (PST)
PST_ci <- confint(PST_bp)
plot(PST)
lines(PST_bp)
lines(PST_ci)
# Finding Structural Breaks in Energy Consumption
# for Other Commerce and Services-related (OCS)
OCS_bp <- breakpoints(OCS ~ 1)
summary(OCS_bp)##
## Optimal (m+1)-segment partition:
##
## Call:
## breakpoints.formula(formula = OCS ~ 1)
##
## Breakpoints at observation number:
##
## m = 1 7
## m = 2 2 8
## m = 3 2 7 9
## m = 4 2 8 10
## m = 5 2 4 7 9 11
##
## Corresponding to breakdates:
##
## m = 1 2011
## m = 2 2006 2012
## m = 3 2006 2011 2013
## m = 4 2006 2012 2014
## m = 5 2006 2008 2011 2013 2015
##
## Fit:
##
## m 0 1 2 3 4 5
## RSS 1773883.7 565284.5 152763.0 92536.4 71005.7 65095.4
## BIC 209.5 198.8 185.7 184.0 185.6 189.6# Plotting Structural Breaks in Energy Consumption
# for Other Commerce and Services-related (OCS)
OCS_ci <- confint(OCS_bp)
plot(OCS)
lines(OCS_bp)
lines(OCS_ci)## Warning: Overlapping confidence intervals
# Finding Structural Breaks in Energy Consumption for Transport-related (TRP)
TRP_bp <- breakpoints(TRP ~ 1)
summary(TRP_bp)##
## Optimal (m+1)-segment partition:
##
## Call:
## breakpoints.formula(formula = TRP ~ 1)
##
## Breakpoints at observation number:
##
## m = 1 5
## m = 2 5 11
## m = 3 3 5 11
## m = 4 3 5 7 11
## m = 5 3 5 7 10 12
##
## Corresponding to breakdates:
##
## m = 1 2009
## m = 2 2009 2015
## m = 3 2007 2009 2015
## m = 4 2007 2009 2011 2015
## m = 5 2007 2009 2011 2014 2016
##
## Fit:
##
## m 0 1 2 3 4 5
## RSS 4702156.2 666651.4 243111.0 164897.3 91601.9 78537.9
## BIC 223.2 201.1 192.2 192.1 189.1 192.3# Plotting Structural Breaks in Energy Consumption for Transport-related (TRP)
TRP_ci <- confint(TRP_bp)
plot(TRP)
lines(TRP_bp)
lines(TRP_ci)
# Finding Structural Breaks in Energy Consumption for Others (OTH)
OTH_bp <- breakpoints(OTH ~ 1)
summary(OTH_bp)##
## Optimal (m+1)-segment partition:
##
## Call:
## breakpoints.formula(formula = OTH ~ 1)
##
## Breakpoints at observation number:
##
## m = 1 5
## m = 2 3 7
## m = 3 2 4 7
## m = 4 2 4 6 8
## m = 5 2 4 6 8 10
##
## Corresponding to breakdates:
##
## m = 1 2009
## m = 2 2007 2011
## m = 3 2006 2008 2011
## m = 4 2006 2008 2010 2012
## m = 5 2006 2008 2010 2012 2014
##
## Fit:
##
## m 0 1 2 3 4 5
## RSS 185510.9 40193.6 15202.7 7827.7 5754.9 4849.6
## BIC 177.9 161.8 153.4 149.4 150.4 153.3# Plotting Structural Breaks in Energy Consumption for Others (OTH)
OTH_ci <- confint(OTH_bp)
plot(OTH)
lines(OTH_bp)
lines(OTH_ci)## Warning: Overlapping confidence intervals
# Finding Structural Breaks in Energy Consumption for 1-Room / 2-Room HDB (X1R2R)
X1R2R_bp <- breakpoints(X1R2R ~ 1)
summary(X1R2R_bp)##
## Optimal (m+1)-segment partition:
##
## Call:
## breakpoints.formula(formula = X1R2R ~ 1)
##
## Breakpoints at observation number:
##
## m = 1 9
## m = 2 7 10
## m = 3 6 9 11
## m = 4 5 7 9 11
## m = 5 2 5 7 9 11
##
## Corresponding to breakdates:
##
## m = 1 2013
## m = 2 2011 2014
## m = 3 2010 2013 2015
## m = 4 2009 2011 2013 2015
## m = 5 2006 2009 2011 2013 2015
##
## Fit:
##
## m 0 1 2 3 4 5
## RSS 7741.4 1184.1 456.7 259.4 166.5 164.9
## BIC 133.4 112.4 104.4 101.7 100.8 105.9# Plotting Structural Breaks in Energy Consumption for 1-Room / 2-Room HDB (X1R2R)
X1R2R_ci <- confint(X1R2R_bp)
plot(X1R2R)
lines(X1R2R_bp)
lines(X1R2R_ci)## Warning: Overlapping confidence intervals
# Finding Structural Breaks in Energy Consumption for 3-Room HDB (X3R)
X3R_bp <- breakpoints(X3R ~ 1)
summary(X3R_bp)##
## Optimal (m+1)-segment partition:
##
## Call:
## breakpoints.formula(formula = X3R ~ 1)
##
## Breakpoints at observation number:
##
## m = 1 5
## m = 2 4 10
## m = 3 4 10 12
## m = 4 4 8 10 12
## m = 5 4 6 8 10 12
##
## Corresponding to breakdates:
##
## m = 1 2009
## m = 2 2008 2014
## m = 3 2008 2014 2016
## m = 4 2008 2012 2014 2016
## m = 5 2008 2010 2012 2014 2016
##
## Fit:
##
## m 0 1 2 3 4 5
## RSS 13617.4 5240.3 2234.0 1245.5 1101.3 1065.3
## BIC 141.3 133.2 126.6 123.7 127.2 132.0# Plotting Structural Breaks in Energy Consumption for 3-Room HDB (X3R)
X3R_ci <- confint(X3R_bp)
plot(X3R)
lines(X3R_bp)
lines(X3R_ci)## Warning: Confidence intervals outside data time interval
## from 2005 to 2018 (14 observations)
# Finding Structural Breaks in Energy Consumption for 4-Room HDB (X4R)
X4R_bp <- breakpoints(X4R ~ 1)
summary(X4R_bp)##
## Optimal (m+1)-segment partition:
##
## Call:
## breakpoints.formula(formula = X4R ~ 1)
##
## Breakpoints at observation number:
##
## m = 1 9
## m = 2 5 10
## m = 3 4 8 10
## m = 4 4 8 10 12
## m = 5 2 4 8 10 12
##
## Corresponding to breakdates:
##
## m = 1 2013
## m = 2 2009 2014
## m = 3 2008 2012 2014
## m = 4 2008 2012 2014 2016
## m = 5 2006 2008 2012 2014 2016
##
## Fit:
##
## m 0 1 2 3 4 5
## RSS 189287.7 40785.4 15637.0 8159.4 7237.7 7146.5
## BIC 178.2 162.0 153.8 150.0 153.6 158.7# Plotting Structural Breaks in Energy Consumption for 4-Room HDB (X4R)
X4R_ci <- confint(X4R_bp)
plot(X4R)
lines(X4R_bp)
lines(X4R_ci)
# Finding Structural Breaks in Energy Consumption for 5-Room and Executive HDB (X5REX)
X5REX_bp <- breakpoints(X5REX ~ 1)
summary(X5REX_bp)##
## Optimal (m+1)-segment partition:
##
## Call:
## breakpoints.formula(formula = X5REX ~ 1)
##
## Breakpoints at observation number:
##
## m = 1 9
## m = 2 4 10
## m = 3 4 10 12
## m = 4 4 8 10 12
## m = 5 4 6 8 10 12
##
## Corresponding to breakdates:
##
## m = 1 2013
## m = 2 2008 2014
## m = 3 2008 2014 2016
## m = 4 2008 2012 2014 2016
## m = 5 2008 2010 2012 2014 2016
##
## Fit:
##
## m 0 1 2 3 4 5
## RSS 50728.6 20559.9 11020.2 5514.5 4625.3 3882.7
## BIC 159.7 152.4 148.9 144.5 147.3 150.2# Plotting Structural Breaks in Energy Consumption for 5-Room and Executive HDB (X5REX)
X5REX_ci <- confint(X5REX_bp)
plot(X5REX)
lines(X5REX_bp)
lines(X5REX_ci)## Warning: Confidence intervals outside data time interval
## from 2005 to 2018 (14 observations)
# Finding Structural Breaks in Energy Consumption
# for Private Apartments and Condominiums (PAC)
PAC_bp <- breakpoints(PAC ~ 1)
summary(PAC_bp)##
## Optimal (m+1)-segment partition:
##
## Call:
## breakpoints.formula(formula = PAC ~ 1)
##
## Breakpoints at observation number:
##
## m = 1 9
## m = 2 5 10
## m = 3 4 7 10
## m = 4 4 7 9 11
## m = 5 2 4 7 9 11
##
## Corresponding to breakdates:
##
## m = 1 2013
## m = 2 2009 2014
## m = 3 2008 2011 2014
## m = 4 2008 2011 2013 2015
## m = 5 2006 2008 2011 2013 2015
##
## Fit:
##
## m 0 1 2 3 4 5
## RSS 677875.4 151956.0 46720.7 23562.3 14560.8 12916.5
## BIC 196.0 180.4 169.1 164.8 163.4 167.0# Plotting Structural Breaks in Energy Consumption
# for Private Apartments and Condominiums (PAC)
PAC_ci <- confint(PAC_bp)
plot(PAC)
lines(PAC_bp)
lines(PAC_ci)## Warning: Overlapping confidence intervals
# Finding Structural Breaks in Energy Consumption for Landed Properties (LPP)
LPP_bp <- breakpoints(LPP ~ 1)
summary(LPP_bp)##
## Optimal (m+1)-segment partition:
##
## Call:
## breakpoints.formula(formula = LPP ~ 1)
##
## Breakpoints at observation number:
##
## m = 1 4
## m = 2 4 9
## m = 3 4 10 12
## m = 4 4 8 10 12
## m = 5 4 6 8 10 12
##
## Corresponding to breakdates:
##
## m = 1 2008
## m = 2 2008 2013
## m = 3 2008 2014 2016
## m = 4 2008 2012 2014 2016
## m = 5 2008 2010 2012 2014 2016
##
## Fit:
##
## m 0 1 2 3 4 5
## RSS 25743.1 7970.4 4603.1 2287.6 1593.0 1468.6
## BIC 150.2 139.1 136.7 132.2 132.4 136.5# Plotting Structural Breaks in Energy Consumption for Landed Properties (LPP)
LPP_ci <- confint(LPP_bp)
plot(LPP)
lines(LPP_bp)
lines(LPP_ci)