Kişi Başına Elektrik Tüketiminin Dalgacık Dönüşümüne Dayalı Tahmini

Zaman serisi analizi, finans, ekonomi, istatistik, mühendislik gibi birçok alanda gelecekle ilgili karar verme olanağı sunduğu için oldukça önemlidir. Zaman serisi analizinde otoregresif model, hareketli ortalama modeli ve otoregresif hareketli ortalama modelini kapsayan Box-Jenkins modelleri yaygın olarak kullanılmaktadır. Ancak bu modellerden elde edilen tahmin sonuçlarının güvenilir olabilmesi için, serinin durağan olması, gürültülü veri içermemesi ve trend ya da mevsimsel hareket bileşenlerinden arındırılmış olması gerekir ki özellikle finansal zaman serilerinde bu oldukça güçtür. Bu problemin üstesinden gelmek amacıyla, son zamanlarda veri önişleme adımında dalgacık dönüşümü (DD) kullanılmaktadır. DD, zaman serisinin uzun dönemli trend ve varyasyon şeklinde iki bileşene ayrılmasına dayanır. Böylece zaman serisinin her bir bileşeni için ayrı bir tahmin modeli elde edilmesi ve davranışının daha doğru bir şekilde tahmin edilmesini sağlar. Bu çalışmada Kişi Başına Elektrik Tüketiminin (KBET) DD ile tahmin edilmesi ve tahmin sonuçlarının geleneksel modeller ile karşılaştırılması amaçlanmıştır. Bu amaca yönelik olarak 26 farklı ülkenin 1960-2014 yıllarını kapsayan KBET verileri kullanılmıştır. Performans karşılaştırmaları için R2, Hata Kareler Ortalamasının Karekökü (HKOK) ve Ortalama Mutlak Yüzde Hata (OMYH) kriterleri kullanılmıştır. Bu karşılaştırma kriterlerine göre dalgacık dönüşümüne dayalı tahmin performansının daha iyi olduğu gözlenmiştir.

Anahtar Kelimeler:

İstatistik, Zaman Serileri, Box Jenkins Model, Dalgacık Dönüşüm

Forecasting of Per Capita Consumption of Electricity Based on Wavelet Decomposition

Time series analysis is essential and takes a critical role in the areas such as finance, economics, statistic and engineering since it provides the opportunity of making decisions about the future. In time series analysis, Autoregressive (AR) models, Moving Average (MA) models, and Box-Jenkins, which includes Autoregressive Moving Average (ARMA) models, are widely used. However, in order: for the predicted results to be reliable from these models, the series must be stationary, has no noisy data and must be detrended or has no seasosanility, which is particularly problematic in financial time series. Wavelet transform (WT), which is based on the separation of time series into two components which are long-term trend and variation, has been recently used in the data preprocessing step in order to overcome that kind of problem. Thus, it provides a separate estimation model for each component of the time series and provides a more accurate estimation of its behavior. In this study, it is aimed to estimate Electricity Consumption per Capita (kWh per capita) by WT and compare the results with the traditional models. For this purpose, kWh per capita data covering the period of 1960 and 2014 of 26 different countries are used. R2, Root Mean Square Error (RMSE) and Mean Absolute Percentage Error (MAPE) criteria are used for performance comparison. According to these comparison criteria, it is observed that the performance of the prediction based on wavelet transform is better.

Keywords:

Statistic, Time Series, Box-Jenkins Models, Wavelet Decomposition,

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[1] Rocha T., Paredes S., Carvalho P., Henriques J., Harris M. 2010. Wavelet based time series forecast with application to acute hypotensive episodes prediction, 32nd Annual International, Conference of IEEE EMBS, August 31-September, Buenos Alres, Argentina, 2403-2406.
[2] Hiden, H., Willis, M., Tham, M., Montague, G. 1999. Non-linear principal components analysis using genetic programming, Computers and Chemical Engineering, 23, 413-425.
[3] Schoukens, J., Pintelon, R. 1991. Identification of Linear Systems: a Practical Guideline to Accurate Modeling, Pergamon Press, London, 332s.
[4] Yao, S., Song, Y., Zhang, L., Cheng, X. 2000. Wavelet transform and neural networks for short-term electrical load, Energy Conversion and Management, 41, 1975-1988.
[5] Chong T. 2009. Financial Time Series Forecasting Using Improved Wavelet Neural Network, Master's Thesis, 113s.
[6] Ng, K. Y., Awang, N. 2018. Multiple linear regression and regression with time series error models in forecasting PM10 concentrations in Peninsular Malaysia. Environmental monitoring and assessment, 190(2), 63.
[7] Bhardwaj, S., Chandrasekhar, E., Padiyar, P., Gadre, V.M. 2020. A comparative study of wavelet-based ANN and classical techniques for geophysical time-series forecasting. Computers & Geosciences, 138, 104461.
[8] Khan, M.M.H., Muhammad, N.S., El-Shafe, A. 2020. Wavelet based hybrid ANN-ARIMA models for meteorological drought forecasting. Journal of Hydrology, 590, 125380.
[9] Karthikeyan L., Kumar D.N. 2013. Predictability of nonstationary time series using wavelet and EMD based ARMA models, Journal of Hydrology, 502, 103-119.
[10] Doucoure B., Agbossou K., Cardenas A. 2016. Time series prediction using artificial wavelet neural network and multi-resolution analysis: Application to wind speed data, Renewable Energy, 92, 202-211.
[11] Box G.E.P., Jenkins G.M. 1970. Time Series Analysis Forecasting and Control Holden-Day, San Francisco, USA, 553s.
[12] Mallat S. 1999. A wavelet tour of signal processing, Academic Press, London, UK, 832s.
[13] Aggarwal S. K., Saini L.M., Kumar A., 2008. Electricity price forecasting in Ontario electricity market using wavelet transform in artificial neural network-based model, International Journal of Control, Automation, and Systems, 6(5), 639-650.
[14] Aggarwal S. K., Saini L. M., Kumar A. 2008. Price forecasting using wavelet transform and LSE based mixed model in Australian electricity market, International Journal of Energy Sector Management, 2(4), 521-546.
[15] An X., Jiang D., Liu C., Zhao M. 2011. Wind farm power prediction based on wavelet decomposition and chaotic time series, Expert Systems with Applications, 38(9), 11280-11285.