Development of the GSTARIMA(1,1,1) model order for climate data forecasting

The space-time model combines spatial and temporal elements. One example is the Generalized Space-Time Autoregressive (GSTAR) Model, which improves the Space-Time Autoregressive (STAR) model. The GSTAR model assumes that each location has heterogeneity characteristics, and that the data is stationary. In this research, the moving average component is calculated by involving the relationship between variable values at a certain time and residual values at a previous time, and it is assumed that the data is not stationary, so the model used is the Generalized Space-Time Autoregressive Integrated Moving Average (GSTARIMA) Model. The model order for GSTARIMA is determined through the Space-Time Autocorrelation Function (STACF) and Space-Time Partial Autocorrelation Function (STPACF) to ensure accurate forecasting. Previous research only discussed the GSTARIMA(1,1,1) model, so in this research, the GSTARIMA(3,1,1) model will be addressed as a form of development of the GSTARIMA(1,1,1) model and applied to climate data. The climate data used in this research is sourced from NASA POWER and consists of rainfall variables with large data sizes, requiring the use of the data analytics lifecycle method to analyse Big Data. The lifecycle includes six phases: discovery, data preparation, model planning, model building, communicating results, and operationalization. Based on the data processing results with Python software, the GSTARIMA(3,1,1) model has a MAPE value of 9% for out-sample data and 11% for in-sample data. In contrast, the GSTARIMA(1,1,1) model has a MAPE value of 11% for out-sample data and 12% for in-sample data. So the GSTARIMA(3,1,1) model provides more accurate forecasting results. Therefore, selecting the correct model order is crucial for accurate forecasting

PRICE OF SUGAR MODELING AND FORECASTING BASED ON STIMA MODEL AND GSTIMA MODEL

STIMA (space-time integrated moving average) model is a special form of Vector IMA model that combines the interdependence of time and location that is known by space-time model. STIMA model requires the same parameter values for all locations, so Generalized-STIMA (GSTIMA) model is developed to overcome this problem. This paper compares the implementation of two models in forecasting the price of sugar in capital provinces in Sumatra Island, Indonesia. The first step is model building for each model. This step is similar to Box-Jenkins’s procedure. It is begun with the determination of temporal order by using AICC, while spatial order is restricted on order 1, the parameter estimation uses nonlinear least square method that are minimized by a Gauss-Newton algorithm, and then diagnostic checking of white noise errors. The normalization of cross-correlation between the locations at the appropriate time lag is used as space weight. The last, the implementation of forecast is evaluated by using the Root Mean Square Error (RMSE) where the error is defined as the differences between the actual value and the forecast value. The implementation of STIMA model is better compared with GSTIMA model in forecasting the price of sugar, although STIMA model produces the same parameters for each location. Key words: Space-time, STIMA, GSTIMA, Modeling, Forecasting

Dynamic spatial weight matrix and localised STARIMA for network modelling

Various statistical model specifications for describing spatiotemporal processes have been proposed over the years, including the space–time autoregressive integrated moving average (STARIMA) and its various extensions. These model specifications assume that the correlation in data can be adequately described by parameters that are globally fixed spatially and/or temporally. They are inadequate for cases in which the correlations among data are dynamic and heterogeneous, such as network data. The aim of this article is to describe autocorrelation in network data with a dynamic spatial weight matrix and a localized STARIMA model that captures the autocorrelation locally (heterogeneity) and dynamically (nonstationarity). The specification is tested with traffic data collected for central London. The result shows that the performance of estimation and prediction is improved compared with standard STARIMA models that are widely used for space–time modeling. En los últimos años, se han propuesto diversas especificaciones de modelado estadístico para describir procesos espacio-temporales. Esto incluye el modelo espacio-temporal autorregresivo integrado de media móvil (STARIMA) y sus varios derivados. Estas especificaciones de modelo asumen que la correlación de los datos puede ser adecuadamente descrita por parámetros que se fijan a nivel global en el espacio y/o tiempo. Dichos parámetros son inadecuados para los casos en los que las correlaciones entre los datos son dinámicas y heterogéneas, como en el contexto de los datos de la red. El objetivo de este artículo es describir la autocorrelación en los datos de red con una matriz de ponderación espacial dinámica y un modelo STARIMA localizado (LSTARIMA) que captura la autocorrelación local (heterogeneidad) de forma dinámica (no estacionariedad). La especificación del modelo es evaluada con datos de tráfico recolectados en el centro de Londres. Los resultados demuestran que los rendimientos de estimación y predicción mejoran con el método propuesto en comparación con los modelos STARIMA estándar que son ampliamente utilizados para el modelado de espacio-temporal

Pengembangan Model Gstarimax dengan Pendekatan SUR untuk Peramalan Data Indeks Harga Konsumen Kelompok Bahan Makanan di Pulau Jawa

Indeks Harga Konsumen (IHK) adalah indeks yang digunakan untuk mengukur perubahan harga pada sekelompok barang dan jasa yang dikonsumsi oleh rumah tangga pada periode tertentu. IHK bahan makanan termasuk komponen yang mudah bergejolak, artinya dominan dipengaruhi oleh shocks seperti gangguan alam dan pengembangan harga komoditas. Pemodelan untuk peramalan data IHK yang melibatkan aspek waktu dan lokasi (spatio temporal) dapat menggunakan Generalized Space Time Autoregressive Moving Average (GSTARIMA). Untuk menambah akurasi dalam peramalan, model GSTARIMA dikembangkan menjadi model GSTARIMAX dengan melibatkan variabel eksogen. Variabel eksogen yang digunakan dalam pemodelan GSTARIMAX untuk peramalan IHK ini adalah kejadian Idul Fitri, kejadian Idul Adha, hari libur Natal dan Tahun Baru yang merupakan efek variasi kalender, dan kenaikan harga BBM. Studi kasus dalam pemodelan GSTARIMAX ini diterapkan untuk peramalan IHK enam kota di Jawa, yaitu Jakarta, Yogyakarta, Bandung, Semarang, Surabaya, dan Serang. Tujuan penelitian ini adalah untuk mendapatkan model GSTARIMAX yang sesuai untuk peramalan IHK kelompok bahan makanan enam kota di Jawa, dan melkukan pengembangan peramalan interval, sehingga hasil ramalan bisa dijadikan informasi awal bagi pemerintah dalam menentukan kebijakan. Analisis data time series menunjukan model GSTARIMA dengan penambahan variabel eksogen (variasi kalender dan intervensi kenaikan BBM) memeperoleh nilai RMSE sebesar 1,001% ysng berarti, pemodelan semakin baik dibandingkan model tanpa variabel eksogen. Model terbaik pada GSTARIMAX yaitu dengan bobot iners jarak tidak semua lokasi menunjukan adanya keterkaitan dengan wilayah lain. Hal tersebut berarti, pada fenomena harga bahan makanan di pulau Jawa tidak terbukti bahwa setiap lokasi memiliki keterkaitan, keterkaitan IHK kelompok bahan makanan hanya berlaku di Jakarta, Bandung, Yogyakarta, dan Serang

Traffic Prediction using Artificial Intelligence: Review of Recent Advances and Emerging Opportunities

Traffic prediction plays a crucial role in alleviating traffic congestion which represents a critical problem globally, resulting in negative consequences such as lost hours of additional travel time and increased fuel consumption. Integrating emerging technologies into transportation systems provides opportunities for improving traffic prediction significantly and brings about new research problems. In order to lay the foundation for understanding the open research challenges in traffic prediction, this survey aims to provide a comprehensive overview of traffic prediction methodologies. Specifically, we focus on the recent advances and emerging research opportunities in Artificial Intelligence (AI)-based traffic prediction methods, due to their recent success and potential in traffic prediction, with an emphasis on multivariate traffic time series modeling. We first provide a list and explanation of the various data types and resources used in the literature. Next, the essential data preprocessing methods within the traffic prediction context are categorized, and the prediction methods and applications are subsequently summarized. Lastly, we present primary research challenges in traffic prediction and discuss some directions for future research.Comment: Published in Transportation Research Part C: Emerging Technologies (TR_C), Volume 145, 202

Spatio-temporal forecasting of network data

In the digital age, data are collected in unprecedented volumes on a plethora of networks. These data provide opportunities to develop our understanding of network processes by allowing data to drive method, revealing new and often unexpected insights. To date, there has been extensive research into the structure and function of complex networks, but there is scope for improvement in modelling the spatio-temporal evolution of network processes in order to forecast future conditions. This thesis focusses on forecasting using data collected on road networks. Road traffic congestion is a serious and persistent problem in most major cities around the world, and it is the task of researchers and traffic engineers to make use of voluminous traffic data to help alleviate congestion. Recently, spatio-temporal models have been applied to traffic data, showing improvements over time series methods. Although progress has been made, challenges remain. Firstly, most existing methods perform well under typical conditions, but less well under atypical conditions. Secondly, existing spatio-temporal models have been applied to traffic data with high spatial resolution, and there has been little research into how to incorporate spatial information on spatially sparse sensor networks, where the dependency relationships between locations are uncertain. Thirdly, traffic data is characterised by high missing rates, and existing methods are generally poorly equipped to deal with this in a real time setting. In this thesis, a local online kernel ridge regression model is developed that addresses these three issues, with application to forecasting of travel times collected by automatic number plate recognition on London’s road network. The model parameters can vary spatially and temporally, allowing it to better model the time varying characteristics of traffic data, and to deal with abnormal traffic situations. Methods are defined for linking the spatially sparse sensor network to the physical road network, providing an improved representation of the spatial relationship between sensor locations. The incorporation of the spatio-temporal neighbourhood enables the model to forecast effectively under missing data. The proposed model outperforms a range of benchmark models at forecasting under normal conditions, and under various missing data scenarios

Understanding and Modeling Taxi Demand Using Time Series Models

The spatio-temporal variations in demand for transportation, particularly taxis, are impacted by various factors such as commuting, weather, road work and closures, disruption in transit services, etc. Identifying the factors that influence taxi demand and understanding its dynamic provide planners with the information necessary to improve the transportation systems and also help drivers to reduce their vacant time. This dissertation focuses on important factors affecting the demand. In the beginning, the impact of price changes on the demand is studied. Chapter One discusses how the seasonal effects and trends are removed from the demand, and then price elasticity for demand is calculated as a measure to quantify the impact of each factor. Furthermore, the first chapter provides elasticity values for the New York City and each of the five boroughs, and studies the relationship between these values and some socio-economic characteristics. The second part of this dissertation studies the demand of taxi and how it is affected by other public transportation modes and weather. This demand modeling technique utilizes a combination of time series and linear regression models. The proposed method is then applied to yellow cab data in New York City. The pick-up points of yellow cab data in April, May, and June of 2014 are considered and aggregated every hour. The results show a significant correlation between taxi demand and demand for other transportation modes, as well as weather conditions. It is shown that combining time series models with linear regression will improve the performance of the model. This study then follows by working on the time series models and considering the spatial variation of the demand. To understand the user demand for taxis through space and time, a generalized spatio-temporal autoregressive (STAR) model is proposed. In order to deal with the high dimensionality of the model, LASSO-type penalized methods are proposed to tackle the parameter estimation. The forecasting performance of the proposed models is measured using the out-of-sample mean squared prediction error (MSPE), and it is found that the proposed models outperform other alternative models such as vector autoregressive (VAR) models. The proposed modeling framework has an easily interpretable parameter structure and can feasibly be applied by taxi operators. The efficiency of the proposed model shows advantages for model estimation in real-time applications. Furthermore, this dissertation studies the demand for e-hailing services which are growing rapidly especially in large cities. Similar to taxi demand, Uber demand is not distributed uniformly, either spatially or temporally, and this study proposes using spatio-temporal models to predict Uber demand as well. Moreover, the prediction performances of several statistical models are compared with each other: a) one temporal model (vector autoregressive (VAR)), b) two proposed spatio-temporal models (spatial-temporal autoregressive (STAR), c) least absolute shrinkage and selection operator applied on STAR (LASSO-STAR)). They are compared in different scenarios (based on the number of time and space lags), and for both peak and off-peak periods (rush hours and non-rush hours). This section additionally proposes different weighting matrices to improve the performance of the model. The results show the need to consider spatial models for e-hailing services and demonstrate significant improvement in the prediction of demand using the two proposed models