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Application of time series models for heating degree day forecasting

Merve Kuru
Merve Kuru
 e 
Gulben Calis
Gulben Calis
   | 27 apr 2020
Organization, Technology and Management in Construction: an International Journal's Cover Image
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Article Category: Research Paper
Pubblicato online: 27 apr 2020
Pagine: 2137 - 2146
Ricevuto: 27 dic 2019
Accettato: 10 feb 2020
DOI: https://doi.org/10.2478/otmcj-2020-0009
Parole chiave
© 2020 Merve Kuru et al., published by Sciendo
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Fig. 1

Time series graph of the HHD series.
Time series graph of the HHD series.

Fig. 2

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

Fig. 3

The plot of actual and seasonal adjusted HDD data sets.
The plot of actual and seasonal adjusted HDD data sets.

Fig. 4

The plot of seasonally adjusted data and trend line.
The plot of seasonally adjusted data and trend line.

Fig. 5

The graph of trend corrected data.
The graph of trend corrected data.

Fig. 6

Distribution of cyclic indices.
Distribution of cyclic indices.

Fig. 7

Actual and forecasted values obtained by the decomposition method.
Actual and forecasted values obtained by the decomposition method.

Fig. 8

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

Fig. 9

ACF plot of residuals.
ACF plot of residuals.

Fig. 10

PACF plot of residuals.
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.
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.

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

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

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

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

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

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
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