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Application of time series models for heating degree day forecasting Cover

Application of time series models for heating degree day forecasting

Organization, Technology and Management in Construction: an International Journal
Volume 12 (2020): Issue 1 (January 2020)
By:  and    
Open Access
|Apr 2020
Figures & tables

Figures & Tables

Tab. 1

A part of the HDD data from 1974 to 2017.

JanFebMarAprMayJunJulAugSepOctNovDec
1974434.2385.8327.9248.8128.524.714.6582.94030.13150.3297.2398.4
1975368.1345.4386.7270.5186.677.7317.1011.2140.27215.6331.3469.7
.
.
.
2015414.6402.0320.5200.5117.431.289.4288.29577.75184.5222.4279.9
2016363.3341.3347.9254.1135.341.4012.628.04821.08180.9289.1390.3
2017486.8321.9256.0236.1109.424.206.90210.0171.63113.2300.3400.1
Fig. 1

Time series graph of the HHD series.

Fig. 2

The correlogram of the HDD series for k=36 month delays.

Tab. 2

Monthly rate averages and seasonal indices.

JanFebMarAprMayJunJulAugSepOctNovDecTotal
Arithmetic mean of ratios2.091.781.541.130.590.210.060.060.270.791.501.9711.99
Seasonal index2.091.781.541.130,590.210.060.060.270.791.501.9712.00
Seasonal index(%)20917815411359216627791501971200
Fig. 3

The plot of actual and seasonal adjusted HDD data sets.

Fig. 4

The plot of seasonally adjusted data and trend line.

Fig. 5

The graph of trend corrected data.

Fig. 6

Distribution of cyclic indices.

Fig. 7

Actual and forecasted values obtained by the decomposition method.

Tab. 3

Tentative models generated in this study.

Models
*SARIMA (1,0,1)(1,0,1)12SARIMA (1,0,0)(1,1,1)12SARIMA (1,1,1)(1,1,0)12*SARIMA (1,0,2)(0,1,1)12
SARIMA (0,0,1)(1,0,1)12*SARIMA (1,0,1)(0,1,1)12SARIMA (0,1,0)(1,1,1)12SARIMA (1,0,1)(0,1,2)12
SARIMA (1,0,0)(1,0,1)12SARIMA (1,0,1)(1,1,0)12SARIMA (1,1,0)(1,1,0)12*SARIMA (0,0,2)(0,1,1)12
SARIMA (1,0,1)(0,0,1)12SARIMA (1,0,0)(1,1,0)12SARIMA (0,1,1)(1,1,0)12SARIMA (0,0,1)(0,1,2)12
SARIMA (1,0,1)(1,0,0)12SARIMA (0,0,1)(1,1,0)12*SARIMA (0,1,1)(0,1,1)12SARIMA (2,0,0)(0,1,1)12
SARIMA (1,0,0)(1,0,0)12*SARIMA (0,0,1)(0,1,1)12SARIMA (1,1,0)(0,1,1)12SARIMA (1,0,0)(0,1,2)12
SARIMA (0,0,1)(1,0,0)12*SARIMA (1,0,0)(0,1,1)12*SARIMA (2,0,1)(1,0,1)12SARIMA (2,1,1)(0,1,1)12
SARIMA (1,0,0)(0,0,1)12SARIMA (1,1,1)(1,1,1)12SARIMA (1,0,2)(1,0,1)12SARIMA (1,1,2)(0,1,1)12
SARIMA (0,0,1)(0,0,1)12SARIMA (0,1,1)(1,1,1)12SARIMA (1,0,1)(2,0,1)12SARIMA (1,1,1)(0,1,2)12
SARIMA (1,0,1)(1,1,1)12SARIMA (1,1,0)(1,1,1)12SARIMA (1,0,1)(1,0,2)12SARIMA (0,1,2)(0,1,1)12
SARIMA (0,0,1)(1,1,1)12*SARIMA (1,1,1)(0,1,1)12SARIMA (2,0,1)(0,1,1)12SARIMA (0,1,1)(0,1,2)12
Tab. 4

The selected models in the first step and second step selection criteria.

ModelAdjusted R2Residual sum of squaresAICSIC
1SARIMA (1,0,1)(1,0,1)120.936654828032.910.3371610.37759
2SARIMA (1,0,1)(0,1,1)120.475825812361.410.2652910.29820
3SARIMA (0,0,1)(0,1,1)120.464422831655.010.2755710.30026
4SARIMA (1,0,0)(0,1,1)120.6150531090103.010.5743710.59910
5SARIMA (1,1,1)(0,1,1)120.721348787551.510.2708510.30382
6SARIMA (0,1,1)(0,1,1)120.715896804533.510.2809610.30569
7SARIMA (2,0,1)(1,0,1)120.936911816848.710.3256110.37412
8SARIMA (1,0,2)(0,1,1)120.487184793205.510.2601710.30132
9SARIMA (0,0,2)(0,1,1)120.467373825461.210.2732510.30617
Tab. 5

The actual and forecasted HDD values for 2017.

MonthsActual (kWh)Forecasted (°C*day)Forecasted (°C*day)
2017M01497.52490.2417.986
2017M02303.62315.16361.840
2017M03248.77251.1308.607
2017M04233.89228.96217.635
2017M0595.3697.75111.711
2017M0614.7316.7132.316
2017M074.984.954.335
2017M0810.369.845.148
2017M0978.487548.420
2017M010117.86127.85151.317
2017M011321.16313.33294.122
2017M012411.22411.29395.733
Fig. 8

Plots of the HDD series’ residuals according to the selected model.

Fig. 9

ACF plot of residuals.

Fig. 10

PACF plot of residuals.

Fig. 11

The actual values, the forecasted values, and the confidence intervals of the HDD data according to model SARIMA (2,0,1) (1,0,1) 12.

Tab. 6

MAPE, MAD, and MSD values of two methods.

Multiplicative modelSARIMA (2,0,1)(1,0,1)12 model
MAPE3.77118.7363
MAD4.367519.9735
MSD33.3013969.8330
DOI: https://doi.org/10.2478/otmcj-2020-0009 | Journal eISSN: 1847-6228 | Journal ISSN: 1847-5450
Journal RSS Feed
Language: English
Page range: 2137 - 2146
Submitted on: Dec 27, 2019
Accepted on: Feb 10, 2020
Published on: Apr 27, 2020
Published by: University of Zagreb
In partnership with: Paradigm Publishing Services
Publication frequency: 1 issue per year
Keywords:
heating degree days,
short-term forecasting,
time series,
Box–Jenkins method,
SARIMA models
Related subjects:
Engineering,
Introductions and overviews,
Engineering, other

© 2020 Merve Kuru, Gulben Calis, published by University of Zagreb
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Volume 12 (2020): Issue 1 (January 2020)
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