The development of temperature forecasting models for the state of Kerala using Seasonal Autoregressive Integrated Moving Average (SARIMA) method is presented in this article. Mean maximum and mean minimum monthly temperature data, for a period of 47 years, from seven stations, are studied and applied to develop the model. It is expected that the time-series datasets of temperature to display seasonality (and hence non-stationary), and a possible trend (due to the fact that the data spans 5 decades). Hence, the key step in the development of the models is the determination of the non-stationarity of the temperature time-series, and the transformation of the non-stationary time-series into a stationary time-series. This is carried out using the Seasonal and Trend decomposition using Loess technique and Kwiatkowski–Phillips–Schmidt–Shin test. Before carrying out this process, several preliminary tests are conducted for (1) finding and filling the missing values, (2) studying the characteristics of the data, and (3) investigating the presence of the trend and seasonality. The non-stationary temperature time-series are transformed to stationary temperature time-series, by one seasonal differencing and one first-order differencing. This information, along with the original time-series, is further utilized to develop the models using the SARIMA method. The parsimonious and best-fit SARIMA models are developed for each of the fourteen variables. The study revealed that \(\text{SARIMA}(2,1,1)(1,1,1)_{12}\) as the ideal forecasting model for eight out of the fourteen time-series datasets.

中文翻译：

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印度喀拉拉邦的平均最高和最低平均月平均气温的趋势分析和SARIMA预测

本文介绍了使用季节自回归综合移动平均线（SARIMA）方法开发的喀拉拉邦温度预测模型。研究了来自七个站点的47年期间的平均最高和最低平均月温度数据，并将其用于开发模型。预计温度的时间序列数据集将显示季节性（因此是非平稳的）和可能的趋势（由于数据跨越5年的事实）。因此，模型开发的关键步骤是确定温度时间序列的非平稳性，并将非平稳时间序列转换为平稳时间序列。这是通过使用黄土技术的季节性和趋势分解以及Kwiatkowski-Phillips-Schmidt-Shin检验进行的。在执行此过程之前，需要进行一些初步测试，以（1）查找并填充缺失值，（2）研究数据的特征，（3）调查趋势和季节性的存在。通过一个季节差分和一个一阶差分，将非平稳温度时间序列转换为平稳温度时间序列。该信息与原始时间序列一起被进一步利用SARIMA方法开发模型。为十四个变量中的每个变量开发了简约且最合适的SARIMA模型。研究表明 通过一个季节差分和一个一阶差分，将非平稳温度时间序列转换为平稳温度时间序列。该信息与原始时间序列一起被进一步利用SARIMA方法开发模型。为十四个变量中的每个变量开发了简约且最合适的SARIMA模型。研究表明 通过一个季节差分和一个一阶差分，将非平稳温度时间序列转换为平稳温度时间序列。该信息与原始时间序列一起，进一步利用SARIMA方法开发了模型。为十四个变量中的每个变量开发了简约且最合适的SARIMA模型。研究表明\（\ text {SARIMA}（2,1,1）（1,1,1）_ {12} \）是十四个时间序列数据集中八个的理想预测模型。