A functional autoregressive approach for modeling and forecasting short-term air temperature

Abstract

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A precise forecast of atmospheric temperatures is essential for various applications such as agriculture, energy, public health, and transportation. Modern advancements in technology have led to the development of sensors and other tools to collect high-frequency air temperature data. However, accurate forecasts are challenging due to their specific features including high dimensionality, non-linearity, seasonal dependency, etc. To address these forecasting challenges, this study proposes a functional modeling framework based on the components estimation technique by partitioning the air temperature time series into deterministic and stochastic components. The deterministic component that comprises daily and yearly seasonalities is modeled and forecasted using generalized additive modeling techniques. Similarly, the stochastic component that accounts for the short-term dynamics of the process is modeled and forecasted by a functional autoregressive model, autoregressive integrated moving average, and vector autoregressive models. To evaluate the performance of models, hourly air temperature data are collected from Islamabad, Pakistan, and one-day-ahead out-of-sample forecasts are obtained for a complete year. The forecasting results from all models are compared using the root mean squared error, mean absolute error, and mean absolute percentage error. The results suggest that the proposed FAR model performs relatively well compared to ARIMA and VAR models, resulting in lower out-of-sample forecasting errors. The findings of this research can facilitate informed decision-making across sectors, optimize resource allocation, enhance public safety, and promote socio-economic resilience.

Keywords

• air temperature
• forecasting
• functional autoregressive
• functional data analysis
• ARIMA