Periodicity in precipitation and temperature for monthly data of Turkey
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ORIGINAL PAPER
Periodicity in precipitation and temperature for monthly data of Turkey Yılmaz Akdi 1 & Kamil Demirberk Ünlü 2 Received: 23 April 2020 / Accepted: 5 November 2020 # Springer-Verlag GmbH Austria, part of Springer Nature 2020
Abstract In this study, we model and forecast monthly average temperature and monthly average precipitation of Turkey by employing periodogram-based time series methodology. We compare autoregressive integrated moving average methodology and harmonic regression. We show that harmonic regression performs better than the classical methodology in both time series. Also, we find that the monthly average temperature and monthly average precipitation have two different periodic structures of 6 months and 12 months which coincide with the seasonal pattern of the time series.
1 Introduction Modeling weather condition is important because it affects economic activities (Pei et al. 2016), natural resource control (Stroombergen et al. 2006), agriculture planning (Adams et al. 1990), and human health (Hales et al. 2002). For that reason, in this study, we aim to model and forecast monthly average temperature and monthly average precipitation of Turkey by using periodogram-based time series methodology. To the best of our knowledge, this is the first study which investigates the hidden periodic structure of temperature and precipitation by employing periodograms. Periodograms are used to find seasonal periodicities in the stationary time series. Some recent works which investigate periodicity in time series literature are Akdi et al. (2020a, 2020b) and Okkaoğlu et al. (2020). Weather temperature forecasting is challenging because of its seasonal structure. In order to forecast weather temperature, there are different techniques. We group them as classical time series methods, fuzzy time series methods, and machine learning algorithms. Weather-related time series show seasonal behavior. It has variations which occur in consecutive and ordered * Kamil Demirberk Ünlü [email protected] Yılmaz Akdi [email protected] 1
Faculty of Science, Department of Statistics, Ankara University, Tandoğan, 06100 Ankara, Turkey
2
Department of Mathematics, Atilim University, Incek, 06830 Ankara, Turkey
time periods. The seasonal behavior of the time series leads researchers to employ seasonal autoregressive integrated moving average (SARIMA) models. For example, Tektaş (2010) utilized autoregressive integrated moving average (ARIMA) model to forecast temperature of Izmir, Turkey. The data set used in the study was the daily average temperature between the periods 2000 and 2008. The results showed that forecasts were highly accurate. Ünlü (2012) modeled Turkish weather temperature by using autoregression. The author divided the temperature into increasing and decreasing cycles and modeled these cycles by autoregression methodology. Khajavi et al. (2012) utilized ARIMA to model air temperature of the Caspian southern coasts. Yixian et al. (2018) employed vector autoregression (VAR) to model temper
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