Forecasting temperature data with complex seasonality using time series methods

Predicting air temperature is crucial in climate change and global warming studies. Due to the significance of seasonal behaviour in weather, selecting a model capable of handling the temperature's seasonal patterns is crucial. Seasonal fluctuations in high-frequency time-series data, such as daily data, are more complex and persist for extended periods, making them challenging for traditional seasonal forecasting models, which work best with monthly or quarterly data. The current study presents and evaluates state-of-the-art univariate time-series forecasting algorithms for high-frequency data with complex seasonal patterns. Four prediction methods were presented, and their effectiveness in predicting high-frequency temperatures was investigated. The models are dynamic harmonic regression, TBATS, Facebook Prophet, and MSTL-ETS. The study provides an empirical application based on daily time series data in Ada, USA, from 2017 to 2020. In addition, a simulation design of 1000 time series using the statistical properties of the real data was created in this study. The validation of the simulated data demonstrates that it has the same statistical properties as the real time series, especially for the annual seasonal pattern and the serial correlations in the long and short terms. The prediction accuracy of the models for both actual and simulated data was determined using the root mean squared error (RMSE) and multiple pairwise comparisons of the Diebold-Mariano test. The four approaches' computational efficiency was evaluated using real and simulated data. The models' residuals were checked to evaluate the capability of the presented approaches to use the largest amount of information available in the time series. The utility of incorporating the ARIMA process into some forecasting techniques to handle the stochastic process of innovations was proven. Also, the evaluation of time-varying estimation-based forecasting approaches was discussed.