Fuzzy rule–based weighted space–time autoregressive moving average models for temperature forecasting

Abstract

In an agriculturally dependent country like India, efficient and reliable forecasting techniques for various climatic parameters are essential. Temperature is one of the most significant climatic factors on agriculture and allied industry output. Because of the existence of a spatiotemporal pattern, temperature forecasting is one of the most difficult tasks in this context. For modeling and forecasting spatiotemporal time series data, STARMA (space–time autoregressive moving average) models are widely used. Using a spatial weight matrix, the STARMA model incorporates the spatial effects of neighboring sites into the model. The uniform weightage scheme is the most commonly used weight assigning method in the development of spatial weight matrices. One of the major disadvantages of uniform spatial weight matrices is that they do not account for spatial dynamics and heterogeneity. Hence, there is a need to develop a new weight matrix that is statistically sound and can address the shortcomings of the uniform matrix. In this study, an improved STARMA model based on the weight matrix of a fuzzy inference system (FIS) has been proposed to address the issue. The FIS weights are calculated using the crow distance between the central points of the sites and the time series correlation. Using spatial–temporal temperature series data from seven districts in West Bengal, India, from January 1998 to December 2013, the proposed approach was empirically illustrated. To validate the proposed model, it was used to look at similar space–time temperature data from nine districts in the Indian state of Karnataka from January 2000 to December 2016. For both datasets, the proposed fuzzy rule–based weighted STARMA model was found to be superior to the STARMA as well as the autoregressive integrated moving average (ARIMA) models. The average mean absolute percentage error (MAPE) of the proposed model for all locations considered was 1.78, whereas the average MAPE of the conventional STARMA model and the ARIMA model were 2.09 and 4.39, respectively.