Data-driven models for atmospheric air temperature forecasting at a continental climate region

2.5 Autoregressive model The autoregressive integrated moving average (ARIMA) is a historical data-based model and is considered the most common time series modeling approach first introduced by Box and Jenkin in 1976 [53]. ARIMA model is considered a hybrid model in which the Autoregressive (AR) and moving average (MA) models generalized forms are combined for modeling non- stationary univariate time series data by approximating the time series using a mathematical model based on past and current values. The utilization of ARIMA model is done by setting the order of three terms: autoregressive, sequence difference, and moving average. The general successive difference equation for dth order can be mathematically expressed as follows. DdTt ¼ 1 B ð ÞdTt ð15Þ Where d is the order of sequence difference and B is the backshift operator. The general ARIMA equation can be briefly presented as follows [54]. ;p B ð Þwt ¼ yq B ð Þet ð16Þ Where ;p(B) is the autoregressive operator of order p, θq(B) is the moving average term of order q and wt = ΔTt. 2.6 Random forest Random forest is a supervised machine learning technique which is made up of large number of small decision trees, known as estimators, which generate their own predictions. ’Forest’ generated by the random forest algorithm is trained through bagging or bootstrap aggregating [55]. Bagging is an ensemble meta-algorithm that fine-tunes the prediction accuracy of machine learning algorithms. The (random forest) algorithm produces the output based on

the predictions of the decision trees. It predicts by taking the average or mean of the output from various trees. Increasing the number of trees increases the precision of the outcome. The various advantages of this technique over other machine learning approaches such as need of less computation time, ease of working with high-dimensional data, strong fault tolerance and parallel processing make it suitable even for very high-dimensional problems like air tempera- ture forecasting. 2.7 Model development In this work, four regression models i.e., SVR, GBR, QRT, and RT have been used to predict the daily and weekly air temperatures over the continental climatic region of North America. The time-series data was collected from the Crary meteorological station from 2000 to 2021. For selecting the best input lags, the autocorrelation function (ACF) and partial autocorrela- tion function (PACF) have been used to analyze the data. According to Fig 2, the ACF provides more information on the time series properties like stationary, trend pattern, seasonality, and randomness. The daily and weekly temperature patterns were examined to determine the most appropriate predictors utilizing correlation statistics such as ACF and PACF, respec- tively. The statistical techniques used the time-lagged data from temperature time series to esti- mate the daily and weekly intervals between the present T value and prior T value for any given observation (i.e., a time lag) [55]. Thus, selecting which lags have a significant correlation

and significant information may benefit. Besides, the lags confined between upper and lower bounds are neglected because they have lower correlations and represent the white noise in the time series, which cannot be predicted. Both ACF and PACF are provided in the following PLOS ONE Air temperature forecasting: Mutli-time scale PLOS ONE | https://doi.org/10.1371/journal.pone.0277079 November 3, 2022 8 / 31