# Soft Periodic Convolutional Recurrent Network for Spatiotemporal Climate Forecast
## 2 Related Work
Meanwhile, in time series analysis, the Autoregressive Integrated Moving Average (ARIMA), a statistical prediction model, is applied to a non-stationary time series to eliminate the non-stationary mean function (trend) corresponding to the \"integrated\" part of the model. ARIMA [36] is used in near-term regional temperature and precipitation forecasting. Seasonal ARIMA (SARIMA) [37] is an extension of ARIMA that supports a seasonal component for time series prediction. It adds difference operators to remove the seasonal component to transform the non-stationary time series into a stationary one. SARIMA analysis was found are acceptable for predicting the monthly mean temperature of Nanjing, China [38]. SARIMA was also used in the precipitation and temperature predictions at the Tehri and Uttarkashi stations in the Bhagirathi river basin in the state of Uttarakhand, India [39]. SARIMA was applied to a coastal Tuscany watershed to study hydrological cycle changes at the local scales (area) [40]. Furthermore, SARIMA was applied for the spatiotemporal analysis in the Highlands region, Algeria, to predict the local scale ofprecipitation [41]. However, SARIMA does not work well on multiple seasonalities [42], the daily and yearly patterns in the same time series of a climate variable (e.g., surface temperature). Empirical mode decomposition (EMD) [43] can also modify such a time series, from high to low frequency, into multi-resolution intrinsic mode functions (IMFs) while leaving the monotonous time series as the estimated trend time series. Ensemble EMD (EEMD) [44] is a variant of EMD, and is used to extract the seasonal component from a time series by selecting the IMFs of the decomposed original time series that corresponds to the seasonal averaged model. In summary, ConvLSTM and spatiotemporal climate forecasting models [24; 25; 26] consider only sequential input, which is the short sequence that does not cover the periodicity patterns. SSAE [33] focuses on the long sequence that covers the entire season, but the model does not regard changes in multiple periodic cycles. SARIMA [37], EMD [43], and EEMD [44] do not address the spatial dependencies, and the decomposed time series by EMD and EEMD may not refer to the seasonality of the observations. Meanwhile, Periodic-CRN [27] has been proposed as a spatiotemporal forecasting model in a taxi transportation domain, where it will use daily and weekly periodicity components along with the load and save mechanism in the PRD. Although Periodic-CRN improves prediction accuracy by using periodicity, it assumes stationary periodicity as PRD refers to exactly the same index of the previous cycle, which means \"hard\" periodicity. In this paper, we proposed SP-CRN by adapting the PRD to be a decent mechanism in the non-stationary climate domain. Our PRD approaches are novel ideas that consider phase shift and the non-stationarity of periodicity. This paper focuses on \"soft\" yearly periodicity, which includes nearby months and a multiple-year cycle, and use of three proposals from the PRD, satisfies climate data behavior.