Autoregressive Integrative Moving Average Research Articles

Time series analysis and development of simulation model for monthly rainfall using ARIMA model

Rainfall holds critical significance for water resource applications, particularly in rainfed agricultural systems. This study employs the Autoregre ssive Integrated Moving Average (ARIMA) technique, a data mining approach commonly used for time series analysis and future forecasting. Given the increasing importance of climate change forecasting in averting unexpected natural hazards such as floods, frost, forest fires, and droughts, accurate weather data forecasting becomes imperative. The objective of this study was to develop a Seasonal Auto-Regressive Integrative Moving Average (SARIMA) model for forecasting monthly rainfall in Junagadh Station, Gujarat. Utilizing 50 years of historical data (1968 to 2016), the SARIMA model predicts weekly rainfall for the subsequent five years (2018 to 2022). Through comprehensive evaluation using ACF and PACF plots, AIC, SBC, MAPE, and MAE values, the study identifies SARIMA (1,0,0)(3,1,1)12 as the optimal model, offering the most accurate prediction. The robust results affirm that the SARIMA model provides reliable and satisfactory weekly rainfall predictions. This research contributes valuable insights into the precision and efficacy of SARIMA models for rainfall forecasting, aiding in strategic water resource management in the Junagadh region.

Stochastic Time Series Analysis, Modeling, and Forecasting of Weekly Rainfall Using Sarima Model

Rainfall holds critical significance for water resource applications, particularly in rainfed agricultural systems. This study employs the Autoregressive Integrated Moving Average (ARIMA) technique, a data mining approach commonly used for time series analysis and future forecasting. Given the increasing importance of climate change forecasting in averting unexpected natural hazards such as floods, frost, forest fires, and droughts, accurate weather data forecasting becomes imperative. The objective of this study was to develop a Seasonal Auto-Regressive Integrative Moving Average (SARIMA) model for forecasting weekly rainfall in Junagadh Station, Gujarat. Utilizing 53 years of historical data (1963 to 2016), the SARIMA model predicts weekly rainfall for the subsequent five years (2018 to 2022). Through comprehensive evaluation using ACF and PACF plots, AIC, SBC, MAPE, and MAE values, the study identifies SARIMA (0,0,4)(0,1,1)52 as the optimal model, offering the most accurate prediction. The robust results affirm that the SARIMA model provides reliable and satisfactory weekly rainfall predictions. This research contributes valuable insights into the precision and efficacy of SARIMA models for rainfall forecasting, aiding in strategic water resource management in the Junagadh region.

Profiling Temporal Pattern of Particulate Matter (PM10) and Meteorological Parameters in Jakarta Province during 2020-2021

Introduction: Jakarta has recorded heightened air pollution for years, and particulate matter (PM10) is one of the pollutants that could bring health burden in population. This study described the distribution of PM10 as well as analysed the correlation with meteorological parameters during 2020–2021 in Jakarta Province. Methods: Air quality standard index daily data from January 1st 2020 to March 31st 2021 was retrieved from the official data portal (https://data.jakarta.go.id/). The Spearman Rank correlation was employed to understand the correlation between PM10 Index with meteorological factors. Autoregressive Integrative Moving Average (ARIMA) model was constructed and Akaike Information Criterion (AIC) selected the model. Cross-correlation analysis explored the association between PM10 with meteorological parameters at multiple time lags. Results and Discussion: PM10 Index started to increase in April 2020 and reached its peak in August 2020. PM10 was positively correlated with temperature (p-value <0.05, R2: 0.134), but it was negatively correlated with humidity and wind speed (p-value <0.05, R2: -0.392 and -0.129). The high cross-correlation coefficients were found between PM10 and temperature at lag 0, humidity at lag 1 and wind speed at lag 1 (rho: 0.42, -0.38 and -0.24). The time series model ARIMA with parameter (p,d,q) (1,1,1) describes the fluctuation of PM10 index data with AIC 3552.75. Conclusion: PM10 concentration in Jakarta is significantly correlated with meteorological factors. The implementation of social restriction in Jakarta need to be supported by pollution control in the neighbouring areas in order to be able to reduce PM10 pollution level.

Data Forecasting Model to Know the Social Impact of Poverty in the Era of Globalization in West Java Province, Indonesia

Globalization has a social impact in the form of poverty. Meanwhile, poverty data in West Java Province, Indonesia, will increase in 2021 by 999,960 people. In addition to education, a country's poverty level shows its citizens' welfare. Therefore the poverty level in that country must be considered. In the Sustainable Development Goals, poverty is the priority scale to be considered. Therefore, forecasting is quite crucial in planning to know in advance what will happen. ARIMA (Auto Regressive Integrative Moving Average) is a modeling approach that can calculate the probability of a future value between two specified limits. This study predicts the number of poor people in West Java Province, Indonesia, from 2022 to 2025. The data used are 15 years from 2007 to 2021 and are processed with the Eviews computer program to see patterns and results in the ARIMA model. The modeling stage starts from data stationarity testing, model identification, model estimation, and model verification to forecasting. Based on the results of this study, the prediction results of the number of poor people in 2022 are 3,618,866; in 2023, it will be 3,512,758; in 2024, there will be 3,406,651, and in 2025 it will be 3,300,543 people. This forecasting uses the ARIMA (Auto Regressive Integrative Moving Average) model (1, 2, 1) as the most accurate method with MAD (Mean Absolute Deviation) error parameters of 1,751,747, MSE (Mean Square Error) of 6,977,202,252. 995 and MAPE (Mean Absolute Percentage Error) of 8%.

Forecasting the Number of Vehicles in Indonesia Using Auto Regressive Integrative Moving Average (ARIMA) Method

The number of vehicles in Indonesia increases significantly from year to year. This has an impact on various aspects such as traffic jams, air pollution, traffic accidents etc. The purpose of this study is to obtain the best model for forecast the number of cars and the number of motorcycles in the next 11 years. For the purpose, ARIMA method was used. Using the historical data of the number of cars and the number of motorcycles from 2001 to 2019, the best model for forecasting the number of cars and the number of motorcycles is ARIMA (1,1,0) and ARIMA (2,1,2), respectively. The models have MAPE of 7.01% and 7.24% for cars and motorcycles, respectively.

A Quantitative Study on Crucial Food Supplies after the 2011 Tohoku Earthquake Based on Time Series Analysis.

Awareness of the requested quantity and characteristics of emergency supplies is crucial for facilitating an efficient relief operation. With the aim of focusing on the quantitative study of immediate food supplies, this article estimates the numerical autoregressive integrative moving average (ARIMA) model based on the actual data of 14 key commodities in the Sendai City of Japan during the 2011 Tohoku earthquake. Although the temporal patterns of key food commodity groups are qualitatively similar, the results show that they follow different ARIMA processes, with different autoregressive moving averages and difference order patterns. A key finding is that 3 of the 14 items are significantly related to the number of temporary residents in shelters, revealing that the relatively low number of different items makes it easier to deploy these key supplies or develop regional purchase agreements so as to promptly obtain them from distributors.

The Effect of Maximum Daily Temperature on Outdoor Violence

Although temperature aggression theory maintains that a high temperature engenders more aggressive behavior by irritating individuals, routine activity theory asserts that violent crime increases as temperature rises because of enhanced interaction among the public in outdoor settings. We investigate the effect of maximum daily temperature on whether crime victims are physically injured during the commission of an outdoor criminal offense in Cleveland, Ohio. We focus on violent crimes occurring outdoors because most U.S. households have central air-conditioning or room air conditioners. Two autoregressive integrative moving average (ARIMA) analyses provide support for routine activity theory because although maximum daily temperature has a strong positive effect on the frequency of violent crimes occurring outdoors, it has little influence on the physical injury of crime victims.

Evaluation of the relationship between slow-waves of intracranial pressure, mean arterial pressure and brain tissue oxygen in TBI: a CENTER-TBI exploratory analysis

Brain tissue oxygen (PbtO2) monitoring in traumatic brain injury (TBI) has demonstrated strong associations with global outcome. Additionally, PbtO2 signals have been used to derive indices thought to be associated with cerebrovascular reactivity in TBI. However, their true relationship to slow-wave vasogenic fluctuations associated with cerebral autoregulation remains unclear. The goal of this study was to investigate the relationship between slow-wave fluctuations of intracranial pressure (ICP), mean arterial pressure (MAP) and PbtO2 over time. Using the Collaborative European NeuroTrauma Effectiveness Research in Traumatic Brain Injury (CENTER-TBI) high resolution ICU sub-study cohort, we evaluated those patients with recorded high-frequency digital intra-parenchymal ICP and PbtO2 monitoring data of a minimum of 6 h in duration. Digital physiologic signals were processed for ICP, MAP, and PbtO2 slow-waves using a moving average filter to decimate the high-frequency signal. The first 5 days of recording were analyzed. The relationship between ICP, MAP and PbtO2 slow-waves over time were assessed using autoregressive integrative moving average (ARIMA) and vector autoregressive integrative moving average (VARIMA) modelling, as well as Granger causality testing. A total of 47 patients were included. The ARIMA structure of ICP and MAP were similar in time, where PbtO2 displayed different optimal structure. VARIMA modelling and IRF plots confirmed the strong directional relationship between MAP and ICP, demonstrating an ICP response to MAP impulse. PbtO2 slow-waves, however, failed to demonstrate a definite response to ICP and MAP slow-wave impulses. These results raise questions as to the utility of PbtO2 in the derivation of cerebrovascular reactivity measures in TBI. There is a reproducible relationship between slow-wave fluctuations of ICP and MAP, as demonstrated across various time-series analytic techniques. PbtO2 does not appear to reliably respond in time to slow-wave fluctuations in MAP, as demonstrated on various VARIMA models across all patients. These findings suggest that PbtO2 should not be utilized in the derivation of cerebrovascular reactivity metrics in TBI, as it does not appear to be responsive to changes in MAP in the slow-waves. These findings corroborate previous results regarding PbtO2 based cerebrovascular reactivity indices.

Institutional Arrangement for Food Price Stabilization and Market Distribution System: Study of Chili Commodity in Banyuwangi Regency

The fluctuating development of chili prices implies that the maintained supply of chili is very important to maintaining the stability of food prices. The value chain integration of the chili commodity from upstream to downstream supported by the availability of adequate infrastructure and institutions is the main prerequisite in increasing the productivity of chili commodities. The purpose of this study is (1) to give a description of the chili commodity marketing chain in Banyuwangi Regency; (2) analyze the determinants of structure, conduct, and performance of the chili commodity market in Banyuwangi Regency. The analytical method used consists of the Autoregressive Integrative Moving Average (ARIMA) and Structure Conduct Performance (SCP) models.The results of the study show that price determination was based on market mechanisms and collective agreements for farmers who partner with collectors and food processing industries. However, the lack of price and knowledge information in market analysis and projections of price movements and the absence of special institutions that deal with chili governance and limited use of technology have led to the emergence of asymmetrical information from chili businesses and the growth of new players in the trade system that dominates the chili trade. The chili market structure tends to oligopsony, which has the power to influence market prices and is concentrated, causing little competition between chili traders in Banyuwangi Regency.

Comparison of high versus low frequency cerebral physiology for cerebrovascular reactivity assessment in traumatic brain injury: a multi-center pilot study

Current accepted cerebrovascular reactivity indices suffer from the need of high frequency data capture and export for post-acquisition processing. The role for minute-by-minute data in cerebrovascular reactivity monitoring remains uncertain. The goal was to explore the statistical time-series relationships between intra-cranial pressure (ICP), mean arterial pressure (MAP) and pressure reactivity index (PRx) using both 10-s and minute data update frequency in TBI. Prospective data from 31 patients from 3 centers with moderate/severe TBI and high-frequency archived physiology were reviewed. Both 10-s by 10-s and minute-by-minute mean values were derived for ICP and MAP for each patient. Similarly, PRx was derived using 30 consecutive 10-s data points, updated every minute. While long-PRx (L-PRx) was derived via similar methodology using minute-by-minute data, with L-PRx derived using various window lengths (5, 10, 20, 30, 40, and 60 min; denoted L-PRx_5, etc.). Time-series autoregressive integrative moving average (ARIMA) and vector autoregressive integrative moving average (VARIMA) models were created to analyze the relationship of these parameters over time. ARIMA modelling, Granger causality testing and VARIMA impulse response function (IRF) plotting demonstrated that similar information is carried in minute mean ICP and MAP data, compared to 10-s mean slow-wave ICP and MAP data. Shorter window L-PRx variants, such as L-PRx_5, appear to have a similar ARIMA structure, have a linear association with PRx and display moderate-to-strong correlations (r ~ 0.700, p < 0.0001 for each patient). Thus, these particular L-PRx variants appear closest in nature to standard PRx. ICP and MAP derived via 10-s or minute based averaging display similar statistical time-series structure and co-variance patterns. PRx and L-PRx based on shorter windows also behave similarly over time. These results imply certain L-PRx variants may carry similar information to PRx in TBI.

Water Demand Prediction for Housing Apartments Using Time Series Analysis

Water management has always been a topic of serious discussion since infrastructure, rural, and industrial development flourished. Due to the depleting water resources, this is now even a bigger challenge. So, here is developed an IoT-based water management system where ultrasonic sensors are employed for predicting the depth of water in the tank and accordingly pumping the water to the sub tank of the apartment. In addition, the time series analysis Auto Regressive Integrative Moving Average (ARIMA) and Least Square Linear Regression (LSLR) algorithms were employed and compared for predicting the water demand for next six months based on the historical water consumption record of the main reservoir/tank. The information on the amount of water consumed from the main reservoir is pushed to the cloud and to the mobile application developed for utilities. The purpose is to access the water consumption pattern and predict water demand for the next six months from the cloud.

Non-Invasive Pressure Reactivity Index Using Doppler Systolic Flow Parameters: A Pilot Analysis.

The goal was to predict pressure reactivity index (PRx) using non-invasive transcranial Doppler (TCD) based indices of cerebrovascular reactivity, systolic flow index (Sx_a), and mean flow index (Mx_a). Continuous extended duration time series recordings of middle cerebral artery cerebral blood flow velocity (CBFV) were obtained using robotic TCD in parallel with direct intracranial pressure (ICP). PRx, Sx_a, and Mx_a were derived from high frequency archived signals. Using time-series techniques, autoregressive integrative moving average (ARIMA) structure of PRx was determined and embedded in the following linear mixed effects (LME) models of PRx: PRx ∼ Sx_a and PRx ∼ Sx_a + Mx_a. Using 80% of the recorded patient data, the LME models were created and trained. Model superiority was assessed via Akaike information criterion (AIC), Bayesian information criterion (BIC), and log-likelihood (LL). The superior two models were then used to predict PRx using the remaining 20% of the signal data. Predicted and observed PRx were compared via Pearson correlation, linear models, and Bland-Altman (BA) analysis. Ten patients had 3-4 h of continuous uninterrupted ICP and TCD data and were used for this pilot analysis. Optimal ARIMA structure for PRx was determined to be (2,0,2), and this was embedded in all LME models. The top two LME models of PRx were determined to be: PRx ∼ Sx_a and PRx ∼ Sx_a + Mx_a. Estimated and observed PRx values from both models were strongly correlated (r > 0.9; p < 0.0001 for both), with acceptable agreement on BA analysis. Predicted PRx using these two models was also moderately correlated with observed PRx, with acceptable agreement (r = 0.797, p = 0.006; r = 0.763, p = 0.011; respectively). With application of ARIMA and LME modeling, it is possible to predict PRx using non-invasive TCD measures. These are the first and as well as being preliminary attempts at doing so. Much further work is required.

Estimating Pressure Reactivity Using Noninvasive Doppler-Based Systolic Flow Index.

The study objective was to derive models that estimate the pressure reactivity index (PRx) using the noninvasive transcranial Doppler (TCD) based systolic flow index (Sx_a) and mean flow index (Mx_a), both based on mean arterial pressure, in traumatic brain injury (TBI). Using a retrospective database of 347 patients with TBI with intracranial pressure and TCD time series recordings, we derived PRx, Sx_a, and Mx_a. We first derived the autocorrelative structure of PRx based on: (A) autoregressive integrative moving average (ARIMA) modeling in representative patients, and (B) within sequential linear mixed effects (LME) models with various embedded ARIMA error structures for PRx for the entire population. Finally, we performed sequential LME models with embedded PRx ARIMA modeling to find the best model for estimating PRx using Sx_a and Mx_a. Model adequacy was assessed via normally distributed residual density. Model superiority was assessed via Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC), log likelihood (LL), and analysis of variance testing between models. The most appropriate ARIMA structure for PRx in this population was (2,0,2). This was applied in sequential LME modeling. Two models were superior (employing random effects in the independent variables and intercept): (A) PRx ∼ Sx_a, and (B) PRx ∼ Sx_a + Mx_a. Correlation between observed and estimated PRx with these two models was: (A) 0.794 (p < 0.0001, 95% confidence interval (CI) = 0.788-0.799), and (B) 0.814 (p < 0.0001, 95% CI = 0.809-0.819), with acceptable agreement on Bland-Altman analysis. Through using linear mixed effects modeling and accounting for the ARIMA structure of PRx, one can estimate PRx using noninvasive TCD-based indices. We have described our first attempts at such modeling and PRx estimation, establishing the strong link between two aspects of cerebral autoregulation: measures of cerebral blood flow and those of pulsatile cerebral blood volume. Further work is required to validate.

Examining Dense-Array Electroencephalographic Networks during Sleep – Partial or Non-Partial Correlations?

Both partial and non-partial correlation methods have been utilized by researchers to construct dense-array electroencephalographic (dEEG) networks. Similarly, researchers have been using different protocols to preprocess data and minimize spurious correlations. This methodological study examined the extent to which the dEEG connectivity networks computed by the non-partial, first-order partial, and (N-2)-order/254th-order partial correlation methods resemble each other, with two autoregressive integrative moving average (ARIMA) preprocessing models and three sample lengths being taken into consideration. Data were collected from two volunteers during the last 60 seconds of the second and fourth rapid-eye-movement epochs using a 256-channel electroencephalographic system and prior to correlation analyses, were preprocessed by either ARIMA (40, 1, 1) or ARIMA (20, 1, 1) transformation. The analyses demonstrate that the partial method, even at the first-order level, can substantially suppress the overall degree of connectivity in a network. Nevertheless, the moderate-to-large rank-order correlation values comparing the similarities between the three network-construction methods casts doubt on the supposition that a network built upon partial correlations is fundamentally distinguished from that derived from nonpartial correlations.

A Hunter’s Moon: the Effect of Moon Illumination on Outdoor Crime

We use National Incident-Based Reporting System (NIBRS) data and an AutoRegressive Integrative Moving Average (ARIMA) study design to investigate the effect of moon illumination on reported crime occurring outdoors between the hours of 10 pm to 2 am in 13 U.S. states and the District of Columbia. Prior research analyzed a confounded dependent variable that amalgamated indoor and outdoor crimes. This situation is problematic in that there is little reason to speculate a relationship between moon illumination and indoor crime because artificial illumination is used within dwellings. Findings show that while moon illumination has little influence on total crime and indoor crime, the intensity of moonlight does have a substantive positive effect on outdoor criminal activity. As moon illumination intensifies, outdoor crime increases markedly. Plausible explanations for this relationship are discussed.

Does Targeted Capture Reduce Terrorism?

From January 1979 to December 2009, the Maoist insurgent Shining Path committed a total of 9,034 violent acts in a concerted attempt to topple the Peruvian government. These acts of violence included bombings, armed assaults, and assassinations. The Shining Path's leader Abimael Guzmán was captured by the Peruvian government on 12 September 1992. Using quarterly data and an interrupted times-series AutoRegressive Integrative Moving Average (ARIMA) study design, we investigated the effect of Abimael Guzmán's capture on the ability of the Shining Path to wage its war against the Peruvian government. Maximum-likelihood results revealed that the frequency of terrorist acts committed by the Shining Path dropped by 143 incidents per quarter a short time after Guzmán was captured. The analysis also evinced a positive relationship between the lethality of attacks and the frequency of the Shining Path's terrorist activity. We conclude that targeted capture shows some promise as an effective counterterrorism strategy, at least for terrorist groups such as the Shining Path that have a top-down type of organizational structure.

Synchronous neural interactions assessed by magnetoencephalography: a functional biomarker for brain disorders**Contribution by the authors: Designed research (APG); acquired data (AAA, IGK, FJPL, ACL, SML, JJS); analyzed data (APG, EK, ACL, JKL); wrote the paper (APG, EK, ACL, SML); contributed subjects (AAA, ZA, AFC, AG, LSH, IGK, FJPL, SML, JRM, SEM, JVP, PJP, GJP, SJR, BMS, SRS, MS, JJS, JJW);

We report on a test to assess the dynamic brain function at high temporal resolution using magnetoencephalography (MEG). The essence of the test is the measurement of the dynamic synchronous neural interactions, an essential aspect of the brain function. MEG signals were recorded from 248 axial gradiometers while 142 human subjects fixated a spot of light for 45–60 s. After fitting an autoregressive integrative moving average (ARIMA) model and taking the stationary residuals, all pairwise, zero-lag, partial cross-correlations (PCCij0) and their z-transforms (zij0) between i and j sensors were calculated, providing estimates of the strength and sign (positive, negative) of direct synchronous coupling at 1 ms temporal resolution. We found that subsets of zij0 successfully classified individual subjects to their respective groups (multiple sclerosis, Alzheimer's disease, schizophrenia, Sjögren's syndrome, chronic alcoholism, facial pain, healthy controls) and gave excellent external cross-validation results.

Time series analysis of magnetoencephalographic data during copying

We used standard time series modeling to analyze magnetoencephalographic (MEG) data acquired during three tasks. Each task lasted 45 s, for a total data acquisition period of 135 s. Ten healthy human subjects fixated their eyes on a central blue point for 45 s (fixation only, "F" task). Then a pentagon (visual template) appeared surrounding the fixation point which simultaneously became red (fixation + template, "FT" task). After 45 s, the fixation point changed to green, which was the "go" signal for the subjects to begin continuously copying the pentagon for 45 s using a joystick and without visual feedback of their movement trajectory (fixation + template + copying, "FTC" task). MEG data were acquired continuously from 248 axial gradiometers at a sampling rate of 1017.25 Hz. After removal of cardiac artifacts and rejection of records with eyeblink artifacts, a Box-Jenkins autoregressive integrative moving average (ARIMA) analysis was applied to the unsmoothed, unaveraged MEG time series for model identification and estimation within 25 time lags (approximately 25 ms). We found that an ARIMA model of 25th order autoregressive, first order differencing, and first order moving average (p=25, d=1, q=1) adequately modeled the series and yielded residuals practically stationary with respect to their mean, variance, and autocorrelation structure. These "prewhitened" residuals were then used for assessing pairwise associations between series using crosscorrelation analysis with +/-25 time lags (approximately +/-25 ms). The cross-correlograms thus obtained revealed rich and consistent patterns of interactions between series with respect to positive and/or negative correlations. The overall prevalence of these patterns was very similar in the three tasks used, and, for particular sensor pairs, they tended to be preserved across tasks.

Diversification Strategy as a Determinant of the Earnings Persistence of U.S. Multinational Firms

This study tests the relationship between diversification strategy and earnings persistence provided by Autoregressive, Integrative, Moving Average (ARIMA) models. When higher-order ARIMA models are used, this study shows the earnings persistence of U.S. Multinational firms to be positively related to size, related diversification and vertical integration, and negatively related to unrelated diversification.