SG Household’sElectrical consumption prediction

| MTech EBAC 3 | March 09, 2016Bala Gowtham ChandrasekaranJoshua Johnson Samuel JohnsonPrem Kumar Ram ThilakTan Aik Chong

TIME SERIES

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

“Jan Feb Mar Apr May Jun July Aug Sep Oct Nov Dec

0

100

200

300

400

500

600

700

Household Electricity Consumption GWH- Singapore

2005 2006 2007 2008 2009 20102011 2012 2013 2014 2015

Household electricity consumption has a seasonal component

Seasonality -12 months February - May increase

in consumption

June - January reduction in consumption

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.

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

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

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)

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]

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

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

Year & Month

Actual Forecast Values Mean Absolute Deviation RMSE

SARIMA(1,0,2)(1,2,1)[12]

SARIMA(3,0,2)(2,1,0)[12]

SARIMA(1,0,2)(1,2,1)[12]

SARIMA(3,0,2)

(2,1,0)[12]

SARIMA(1,0,2)

(1,2,1)[12]

SARIMA(3,0,2)

(2,1,0)[12]

2015-01 526.10 539.86 537.57 13.76 11.48 189.46 131.742015-02 494.40 508.71 516.48 14.31 22.09 204.75 487.932015-03 514.80 502.92 519.60 11.88 4.80 141.02 23.0722015-04 594.20 582.66 579.01 11.54 15.18 133.17 230.552015-05 610.70 626.70 611.61 16.00 0.92 255.98 0.832015-06 632.30 656.91 646.49 24.61 14.19 605.68 201.402015-07 647.00 644.48 629.16 2.52 17.83 6.38 318.012015-08 656.70 651.80 633.15 4.90 23.54 23.98 554.14

2015-09 635.70 596.20 590.35 39.50 45.35 1560.10 2056.4515.45 17.26 18.62 21.09

Forecast 2015 Electricity consumption(GWH)

Value PropositionThe Forecasted Values

will enable the Government of Singapore

to assess the electricity requirement for House

Holding requirements in Advance.

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