2. SINGAPORE HOUSEHOLD ELECTRICAL CONSUMPTION
◉ The data explains monthly electricity consumption by sector for contestable and non-contestable consumers
(in GWh).
◉ Our objective is to design the predictive model to forecast the household electricity consumption in
Singapore.
Train Data Test
Data
◉ Source: https://data.gov.sg/dataset/monthly-electricity-consumption-by-sector-total
Household
Electricity
Consumption
3. “
0
100
200
300
400
500
600
700
Jan Feb Mar Apr May Jun July Aug Sep Oct Nov Dec
Household Electricity Consumption
GWH- Singapore
2005 2006 2007 2008 2009 2010
2011 2012 2013 2014 2015
Household electricity
consumption has a
seasonal component
Seasonality -12 months
February - May
increase in
consumption
June - January
reduction in
consumption
4. Lesser the ADF values, higher is the tendency to
reject Null-Hypothesis of the ADF test.
For the given sample with trend, critical value
for ADF is -4.04.
Hence, the data is stationary.
No differentiation is needed
Number of
Samples
120
Trend ADF
Values
-4.35
The Decomposition graph decomposes the Trend,
Seasonality and Randomness of the given Time series.
5. ACF & PACF Plots to find (p,d,q) (P,D,Q) • All Ljung-Box Q values are Significant (i.e. p
value are < 0.05)
• Auto correlations drop to zero quickly (At lag 3)
• Identify the numbers of AR and/or MA terms (p
and q values)
JMP R
6. MAPE 2.75 RMSE 18.82
Holt Winter’s Test
Although the Predicted values
seems to supersede the actual
values from the above graph, the
residual ACF and PACF plots
show that the Lag values exceed
the critical values
Hence this determines that the Holt
– Winters model is not suitable to
forecast this time series.Residuals are not White Noise
7. MAPE 1.72 RMSE 13.08
SARIMA(3,0,2)(2,1,0)[12] with drift
This model was suggested by the
auto.arima fn().
The graph plotted through R foor
the above (p,d,q) & (P,D,Q) s
indicates that the residuals lie well
within the critical Line and
the forecasts are in line with the
actual Test values
TRADE OFF – There are two
insignificant variables (drift)
8. Parameters Values Remarks
DF 90 No of values in the final calculation of a statistic that are free to vary
SSE 22426.11 Sum of squared errors of prediction
Variance Estimates 249.18 Degree of the dispersion
SD 15.78 Standard Deviation
AIC Values 847.07 Signifies the information lost in the model
SBC 862.46 Criterion for model selection. Lowest SBC is preferred
R square adjusted 0.828 Indicates how well data fit a statistical model
MAPE 2.56 Bias -component of total calculated forecast error
MAE 13.7 how close forecasts or predictions are to the eventual outcomes
-2Loglikelihood 835.07 Maximizes to determine optimal values of the estimated coefficients (β).
Higher the values-it is better
Model Selection Criteria - SARIMA(1,0,2)(1,2,1)[12]
9. Model Selection Criteria - SARIMA(1,0,2)(1,2,1)[12]
MAPE 2.56 MAE 13.70
The Parameter Estimates for all terms are Highly Significant (p<0.05)
and can be considered for modelling
This Model has Low AIC, low MAE and RMSE values and hence
adheres to good modelling standards
The general Equation for SARIMA is:
Φp B(1-B)d Ψp B4 (1-B4)D Yt= (θqB)(ʘQB4) εt
For the Model - SARIMA (1,0,2) (1,2,1) [12]
The Equation is:
Φ1 B(1-B)0 ψ1 B4 (1-B4)2 Yt= (θ2B)(ʘ1B4) εt
Yt = (Φ1- 1) Yt-1 + Φ1 Yt-2 + (ψ1+2) Yt-4 – (2 Φ1 + ψ1* Φ1 - ψ1) Yt-5 - Φ1*ψ1 Yt-6 – 2 ψ1 Yt-8 - Φ1 Yt-9 + εt - θ2 εt-1 - ʘ1 εt-4 + θ2
10. Forecast & Test Data - SARIMA(1,0,2)(1,2,1)[12]
95% Confidence Interval
Forecast
Forecast & Test data is
within the confidence
interval level
Test Data
JMP – This graph
plots the forecast
Values and CI for the
Respective values
R – This
ARIMApred plot
compares the
forecasted value
with the Test
Values
12. Value Proposition
The Forecasted Values
will enable the
Government of Singapore
to assess the electricity
requirement for House
Holding requirements in
Advance.
