ARIMA Errors Research Articles

Research on the relationship between global oil prices and economic indicators based on linear regression and ARIMAX models

This report aims to analyze the relationship between global oil prices and various economic indexes by using linear regression and ARIMAX models. This study will predict global oil prices accurately and establish a reasonable system for regulating oil prices. The research uses the statistical approach to predict oil prices based on historical data (including independent variables and dependent variable). The study uses monthly average data of WTI crude oil prices from January 2000 to March 2023 and contains the analysis of various economic indicators such as Consumer Price Index (CPI), Personal Consumption Expenditures (PCE), Employment, Population, and Oil Price. The findings indicate that the linear regression model can explain about 40.89% of the variation in log oil price, with significant negative effects of log_PCE, log_EMPLOYMENT, and log_POPULATION, and a significant positive effect of CPI on log_price. However, there exists the probability that some other factors have impact on oil prices. In this study, the author employ the ARIMAX model with ARIMA(4,1,1) errors, which can describe a relatively good fit and small errors in training set measures. Overall, while the linear regression model partially explains the variability in global oil prices, further analysis on residuals is necessary. The study concludes that the ARIMAX model provides a better approach to capture the time-series nature of the data.

EVALUATING TIME SERIES PREDICTION MODELS: EGG PRICES IN MEXICO

Mexico is the world’s largest consumer of eggs, producing 3.05 million Mg in 2021. The high variation in wholesale prices is a feature of the egg production system, which is important to producers and government institutions that need to forecast future prices for activity planning. As a result, it is necessary to propose tools that can reliably predict egg prices. The goal of this paper was to compare the performance of various statistical models by analyzing the time series of egg prices using the Akaike index and forecast error to determine which model best predicts the wholesale price of white eggs. The models evaluated were the autoregressive integrated moving average model (ARIMA), ARIMA with interventions, ARIMA with transfers, and regression with ARIMA errors. Two time series were used: the wholesale price of white eggs, constructed with data from the National System of Information and Market Integration (SNIIM) and the Agrifood and Fisheries Information Service (SIAP), and egg imports, calculated with data from the Economic Information System. The latter was used as an exogenous variable to explain the price of eggs. Both cover the period from January 2006 to December 2021. According to the Akaike index, the model with the best adjustment was ARIMA (0,1,1)(1,0,1)[12] with interventions. In the evaluation of forecast error, the best models were the regression models with ARIMA (1,1,0)(1,0,1)[12] and ARIMA (1,1,0)(1,0,1)[12] errors with transfer.

Influence of temperature and precipitation on dengue incidence in Campinas, São Paulo State, Brazil (2013-2022).

Global dengue cases are rising, notably in Brazil. By using monthly data, we estimated linear regressions with ARIMA errors to measure the influence of temperature and precipitation on dengue incidence in the city of Campinas, São Paulo State, Brazil. Findings suggest that a 1°C increase in mean temperature can lead to a cumulative increase of up to 40% in dengue incidence within 2 months. Precipitation shows no significant impact. Results highlight the importance of temperature on the spread of dengue and potentially other mosquito-borne diseases.

Forecasting the US Dollar/Euro Exchange Rate Based on ARIMA Model

The exchange rate is an important indicator for investors and governments as well as a verdict on economic prospects. The euro reached its lowest point in 20 years on August 22, 2022, falling below parity with the dollar and terminating a one-to-one exchange rate with the American currency. The event's great significance provides paramount motivation for us to construct a suitable model capable to forecast it. Numerous modeling methods are proposed to predict and analysis the exchange rate. This paper discussed the applicability of a univariate ARIMA model. Moreover, a multivariable ARIMA model, i.e., four macroeconomic variables supposed influential to the change of exchange rate, were introduced in the AR part of the ARIMA model. For the training set, data is gathered on a monthly basis from January 1999 to December 2021, while the period forecasted is the plunge event from January to August, in 2022. Their 8-month long forecasting experiments reveal that the univariate ARIMA model has no ability to forecast the trend of the exchange rate. In general, the multivariate regression model with ARIMA errors is capable of forecasting the historical change of the USD/EURO spot exchange rate. However, its performance totally depends on the quality of the predicted predictors, which are the four macro-economic variables in this study.

Forecasting the daily demand for emergency medical ambulances in England and Wales: a benchmark model and external validation

BackgroundWe aimed to select and externally validate a benchmark method for emergency ambulance services to use to forecast the daily number of calls that result in the dispatch of one or more ambulances.MethodsThe study was conducted using standard methods known to the UK’s NHS to aid implementation in practice. We selected our benchmark model from a naive benchmark and 14 standard forecasting methods. Mean absolute scaled error and 80 and 95% prediction interval coverage over a 84 day horizon were evaluated using time series cross validation across eight time series from the South West of England. External validation was conducted by time series cross validation across 13 time series from London, Yorkshire and Welsh Ambulance Services.ResultsA model combining a simple average of Facebook’s prophet and regression with ARIMA errors (1, 1, 3)(1, 0, 1, 7) was selected. Benchmark MASE, 80 and 95% prediction intervals were 0.68 (95% CI 0.67 - 0.69), 0.847 (95% CI 0.843 - 0.851), and 0.965 (95% CI 0.949 - 0.977), respectively. Performance in the validation set was within expected ranges for MASE, 0.73 (95% CI 0.72 - 0.74) 80% coverage (0.833; 95% CI 0.828-0.838), and 95% coverage (0.965; 95% CI 0.963-0.967).ConclusionsWe provide a robust externally validated benchmark for future ambulance demand forecasting studies to improve on. Our benchmark forecasting model is high quality and usable by ambulance services. We provide a simple python framework to aid its implementation in practice. The results of this study were implemented in the South West of England.

Examining how social activities influence pertussis. An application of random forest regression

Relatively few epidemiological studies have utilized Random Forests (RF), possibly because the time series data often encountered in this discipline are perceived as unsuitable for supervised learning methods. We show RF can be used for such data, and demonstrate an example examining which social activities influence pertussis. Results are compared with regression with ARIMA errors modelling. Pertussis continues to be perceived as a childhood condition, despite recent incidence increases in older ages. COVID-19 provided a unique situation; social restrictions were implemented and the number of pertussis cases declined. This meant the influence of different activities on transmission could be gauged. Data detailing restrictions was used from the Oxford 'COVID-19 Government Response Tracker' (OxCGRT). The number of cases of pertussis and OxGCRT variables were lagged then embedded into a matrix, before being fitted into a RF regression model. Based on VIMP, this identified ‘international travel’ ‘public events’ and ‘workplace’ as the most important variables, suggesting adult based activities may be of most importance. An ARIMA(1,0,1), using OxCGRT categories as external regressors, similarly indicated that adult social activities better accounted for the number of cases of pertussis.

Impact of the COVID-19 Pandemic on Retail Sales of Health and Personal Care Stores in the United States

In recent years, as a result of the Covid-19 pandemic, the health and personal care stores have been remarkably affected in a wide range of aspects. This became one of the reasons why medical staff felt pressure, leading to quite a number of staffs resigning, and meanwhile the management pattern of medical employees changes and seems to be more strict. Furthermore, the prevalence of Covid-19 pandemic also causes some mental diseases such as sleeping disturbance, anxiety as well as skin problems whether for adults or younger people. As a consequence, the health and personal care industry has been brought to light. This industry has become high in demand like never before. Therefore, complemented by daily and monthly U.S. coronavirus cases, retail sales of health and personal care stores in the USA is a time series worth analyzing. Best-fit ARIMA model for the retail sales is determined to be ARIMA (2, 2, 3) to forecast future health and personal care retail sales in hope of supporting the industry prepare for the ongoing pandemic and in case of another crisis. Regression models are built to find correlations between health and personal care retail sales and coronavirus cases. Additionally, this paper extended ARIMA by employing dynamic regression model which generates a more accurate forecast from regression with ARIMA (0, 1, 1) errors.

Time Series Analysis and Prediction of COVID-19 Pandemic Using Dynamic Harmonic Regression Models

Rapidly spreading COVID-19 virus and its variants, especially in metropolitan areas around the world, became a major health public concern. The tendency of COVID-19 pandemic and statistical modelling represents an urgent challenge in the United States for which there are few solutions. In this paper, we demonstrate combining Fourier terms for capturing seasonality with ARIMA errors and other dynamics in the data. Therefore, we have analyzed 156 weeks COVID-19 dataset on national level using Dynamic Harmonic Regression model, including simulation analysis and accuracy improvement from 2020 to 2023. Most importantly, we provide new advanced pathways which may serve as targets for developing new solutions and approaches.

A Time-Series Analysis on the Covid-19 Mortality, PM2.5 Levels, and Weather Variables in Denpasar City, Indonesia

The objective of this study is to explore the relationship between Covid-19 mortality cases and environmental variables, namely PM2.5 concentration and weather variables, in Denpasar City, Indonesia. Regression models were used. The response variable was the monthly Covid-19 mortality from March 2020 to December 2021 and the predictor variables were the mean concentration of PM2.5, temperature, wind speed, rainfall and duration of sunshine. All data analyzed were provided by the Indonesian Government. Simple linear regression (SLR) and dynamic regression with ARIMA error models were used. Further, of the 22 monthly data, the first 19 months data were used to train the models and the remaining data were used as the test data. It is found that both wind speed and the interaction between PM2.5 concentration and wind speed have statistically significant relationships with Covid-19 mortality. The estimates of SLR and ARIMA (0,1,1) with interaction models show that on average, in case of 0.5 m/s wind speed, an increase of 1 \U0001d707g/m3 in the monthly mean of daily PM2.5 concentrations associates with 17.4 and 16.3 increase in the monthly Covid-19 mortality case, respectively. Although this study is observational, its findings suggest the importance of controlling PM2.5 concentration.

DETERMINING FACTORS FOR 10-YEAR LOCAL CURRENCY SOVEREIGN BONDS YIELD WITH DYNAMIC REGRESSION MODEL

Sovereign bonds, particularly Local Currency Bonds (LCB) of 10-year tenure, had a strategic role in economy, thus understanding factors affecting its yield’s movement would help government to maintain economic stability.
 This paper empirically study Indonesia’s 10-year LCB and its relationship with several factors; US Treasury (UST) yield, credit default swap (CDS), foreign ownership, central bank's policy rate (policy rate), exchange rate, volatility index (VIX) and primary dealers' trading behavior. The relationship was modelled using Dynamic Regression Model (DRM), with ARIMA errors to absorb the dynamics. Evaluation on the model's performance was conducted by making prediction on the real LCB yield’s movement during 2021.
 The best model containing 10y-UST yield and its lag-1, 5y-CDS and its lag-1, exchange rate, policy rate and ARIMA errors of AR(1) and AR(2) could perform well in predicting the real yield. This study confirmed that 10y-UST and its lag-1 are the main drivers for the LCB yield’s movement, along with compelling influence of the exchange rate.

Modelling Customs Revenue in Ghana Using Novel Time Series Methods

Governments across the world rely on their Customs Administration to provide functions that include border security, intellectual property rights protection, environmental protection, and revenue mobilisation amongst others. Analyzing the trends in revenue being collected from Customs is necessary to direct government policies and decisions. Models that can capture the trends being purported from the nominal (nonreal) tax values with respect to the trade volumes (value) over the period are indispensable. Predominant amongst the existing models are the econometric models (the GDP-based model, the monthly receipts model, and the microsimulation model), which are laborious and sometimes unreliable when studying trends in time series data. In this study, we modelled monthly revenue data obtained from the Ghana Revenue Authority-Customs Division (GRA-CD) for the period January 2010 to December 2019 using two traditional time series models, ARIMA model and ARIMA Error Regression Model (ARIMAX), and two machine learning time series models, Bayesian Structural Time Series (BSTS) model and a Neural Network Autoregression model. The Neural Network Autoregression model of the form NNAR (1, 3) provided the best forecasts with the least Mean Squared Error (MSE) of 53.87 and relatively lower Mean Absolute Percentage Error (MAPE) of 0.08. Generally, the machine learning models (NNAR (1, 3) and BSTS) outperformed the traditional time series models (ARIMA and ARIMAX models). The forecast values from the NNAR (1, 3) indicated a potential decline in revenue and this emphasizes the need for relevant authorities to institute measures to improve revenue generation in the immediate future.

Forecasting SARS-CoV-2 Incidence in Ontario Municipalities with Statistical and Algorithmic Modeling and Ensembles

PurposeIn this study, a variety of statistical and algorithmic models were applied to forecast Covid-19 incidence in two Canadian cities, Wellington-Dufferin-Guelph (WDG) and Toronto, Ontario. The purpose of forecasting incidence in the two cities was to explore and compare the predictive capacity of each approach in two regions where daily incidences differ due to population sizes, thus requiring different analytical approaches to inform public health.Methods & MaterialsThe dataset consisted of daily Covid-19 incidence within WDG and Toronto, Ontario. Data was split into training data (March 13, 2020, to June 17, 2021) and validation data (June 18, 2021, to July 8, 2021). Models fitted to the training data were assessed on validation data. Additionally, the effective reproductive number (Re), holidays, type of variant (i.e., Alpha, Beta, Gamma, Delta), mutation common to a variant detected or no mutation detected as well as the cumulative number of first and second vaccination doses were included as predictors.Statistical models employed were General Linear Autoregressive Moving Average (GLARMA), Seasonal Autoregressive Integrated Moving Average (SARIMA) and Regression with ARIMA errors. The two machine learning algorithms were Neural Network Autoregression (NNAR) and Random Forest (RF). A hybrid model combining the statistical and algorithmic approaches (ARIMA-Boosted) was also explored. Ensembles combining several of the models were then generated to investigate improvement in predictive performance. Performance was assessed via Root Mean Square Prediction Error (RMSE) and Mean Absolute Scale Prediction Error (MASE).ResultsIn WDG, regression with ARIMA achieved respectable forecast accuracy (RMSE = 3.50, MASE = 0.71). Ensembles provided a marginal gain in forecast accuracy (RMSE = 3.48, MASE = 0.67) In Toronto, SARIMA modeling had the superior forecasts (RMSE = 8.14, MASE = 0.52), whereas ensembles did not improve accuracy (RMSE = 8.57, MASE = 0.58).ConclusionModels based on observed associations (i.e., statistical modeling) provided more accurate forecasts than data driven algorithmic modeling (i.e., machine learning) for forecasting epidemic/pandemic trajectory. This finding was consistent in both WDG and Toronto, Ontario. While ensemble forecasts may slightly improve the forecast accuracy, the computational expense did not justify its application in the current examples.

Restrictive and stimulative impacts of COVID-19 policies on activity trends: A case study of Kyoto

This paper employs regression with ARIMA errors (RegARIMA) to quantify the impacts of multiple non-pharmaceutical interventions, daily new cases, seasonal and calendar effects, and other factors on activity trends across the timeline of the ongoing COVID-19 pandemic in Japan. The discussion focuses on two controversial policy sets imposed by the Japanese government that aim to contain the pandemic and to stimulate the recovery of the economy. The containing effect was achieved by stay-at-home requests and declaring a “State of Emergency” in the combat against the first waves of infectious cases. After observing reduced cases, Go-to-travel and Go-to-eat campaigns were launched in July 2020 to encourage recreational travel and to revive the economy. To better understand the impact of the policies we utilize “Google trends” which measure how much these policies are looked up online. We suggest this reflects how much they are part of the public discussion. A case study is conducted in Kyoto, a city famous for tourism. The proposed RegARIMA model is compared with linear regression and time series models. The outperformances in measuring the magnitude of intervention impacts and forecasting the future trends are confirmed by using a total of twelve activity and mobility indices as the dependent variable. Nine indices are released by Google and Apple and three are obtained from local Wi-Fi packet sensors. The effect of the State of Emergency declaration is found to erode at the second implementation, and the second stage of the Go-to-travel campaign successfully stimulated travel demand in the autumn sighting season of 2020.

Regression with ARIMA Error Model for Government Expenditure in Sri Lanka

Regression with ARIMA Error Model for Government Expenditure in Sri Lanka

Crime and COVID-19: effect of changes in routine activities in Mexico City

This study aimed to determine whether crime patterns in Mexico City changed due to the COVID-19 pandemic, and to test whether any changes observed were associated with the disruption of routine activities, as measured by changes in public transport passenger numbers. The first objective was assessed by comparing the observed incidence of crime after the COVID-19 pandemic was detected in the country with that expected based on ARIMA forecasts based on the pre-pandemic trends. The second objective was assessed by examining the association between crime incidence and the number of passengers on public transport using regressions with ARIMA errors. Results indicated that most crime categories decreased significantly after the pandemic was detected in the country or after a national lockdown was instituted. Furthermore, the study found that some of the declines observed were associated with the reductions seen in public transport passenger numbers. However, the findings suggested that the changes in mobility explain part of the declines observed, with important variations per crime type. The findings contribute to the global evaluation of the effects of COVID-19 on crime and propose a robust method to explicitly test whether the changes observed are associated with changes in routine activities.

Forecasting emergency admissions in the city of Milan to predict overflow: a 2-day warning system

BackgroundThe emergency department (ED) is one of the most critical area in any hospitals. In Italy, the mean waiting time is increasing causing potentially ED overflow and a detrimental effect on quality of care.MethodsWe collected total daily ED visits between 2014 and 2019 in the five major hospitals of Milan. To predict daily volumes, we used a regression model with ARIMA errors. Predictors included were weekly and yearly periodicity, meteorological and environmental variables, information on influenza epidemics and festivities. Parameters have been calibrated on training datasets (2014-2018) and successively validated on 2019, accuracy of prediction have been evaluated with the Mean Absolute Percentage Error (MAPE). Finally, we evaluated the impact of the COVID-19 outbreak calculating the proportion of ED accesses by triage levels, before and after the outbreak.ResultsBetween 2014 and 2019 there have been 2 million of ED visits in the hospitals of Milan. We found different patterns of ED visits across age and days: children (0-14 years) tended to visit ED more likely on weekends while adults and senior people on Mondays. Results confirmed the role of meteorological and environmental variables, and the presence of yearly and weekly pattern. We found high correlation between observed and predicted value with a MAPE globally smaller than 8.1%. During the COVID-19 outbreak, the number of white triage ED accesses was reduced up to 71%.ConclusionsResults permitted to develop a 2-day ED warning system combining forecast data provided by ARPA Lombardia. This is crucial in a system where inappropriate emergency admissions are still high where the analysis conducted during the COVID-19 pandemic period suggested a dramatic reduction in the number of daily ED access of lower triages.Key messages The ability to forecast future demands would be a valuable support in a system of limited resources, which must therefore be used in the best way.Environmental and meteorological variable have a moderate effect on emergency admissions.

Improving Flood Forecasting in Karnali River Basin of Nepal Using Rainfall-Runoff Model and Complementary Error Model

Accuracy of flood forecast is important to take appropriate preparedness measures for saving lives and livelihoods of people residing in the floodplains. Predictions from flood forecasting models are usually uncertain which can be improved by complementing the hydrological model with an error model that can capture the information which the operational hydrological model lacks. This paper presents the application of this approach for improving daily flow forecasts for flood warning in Karnali River Basin of Nepal. A conceptual rainfall-runoff model, TUWmodel has been developed to model the rainfall-runoff processes and to predict the runoff at the outlet of the basin at Chisapani. The model has been calibrated for the period 2008-2011 with Nash-Sutcliffe Efficiency (NSE) 0.91 and percent bias (PBIAS) -0.7% and validated for the period 2012-2014 with NSE 0.88 and PBIAS -9.1% using observed temperature, precipitation and discharge data. A complementary ARIMA error model was developed from the error series for calibration set using automatic procedure and the predicted discharges were corrected using the error predictions from the error model. After error corrections, NSE and PBIAS were 0.95 and 0.1% respectively for calibration and 0.92 and 0.1% respectively for validation indicating significant improvements in the skill of forecasts.

Regression and Arima to measure the wave length effect on percentage adsorbed on Stronsium Titanate

Strontium titanate (SrTiO3) which belongs to the ferroelectric material is very sensitive to wavelength. Therefore research on the effect of wavelengths on light absorbed by strontium titanate is very important.The results showed that the wavelength affected to the percentage adsorbed by the Strontium Titanate Trioxide linearly at various levels of concentration of Rudenium Oxide. The addition of the ARIMA Error model can improve the accuracy of the model.

Multivariate Analysis of the Effect of Climate Conditions on Gold Production in Ghana

The change in climatic conditions and its catastrophic effect on mining activities has become a source of worry for mining industries and therefore needs due attention. This study examined the effect some climate factors have on gold production in Ghana. First, a direct Multiple Linear Regression was applied on the climate factors with the aim of determining the relative effect of each factor on gold production which exhibited a time series structure. The consequence is that, the estimates of the coefficients and their standard errors will be wrongly estimated if the time series structure of the errors is ignored. In order to eliminate these deficiencies and better understand the effect of these climate factors on gold production, regression with ARIMA errors technique was employed after its appropriateness has been tested. The model was then compared in terms of prediction accuracy which resulted a MAPE of 9.78%. It was concluded that, gold production in Ghana is positively related to Temperature whilst negatively to Rainfall and Precipitate. It was recommended that mine operators in Ghana could base on this analysis to optimise their production planning and scheduling. Keywords: Gold Production, Climate, Multicollinearity, VIF, Regression Models with ARIMA Errors

Forecasting Emergency Department Admissions for Pneumonia in Tropical Singapore

ObjectiveTo develop a forecasting model for weekly emergency department admissions due to pneumonia using information from hospital-based, community-based and laboratory-based surveillance systems.IntroductionPneumonia, an infection of the lung due to bacterial, viral or fungal pathogens, is a significant cause of morbidity and mortality worldwide. In the past few decades, the threat of emerging pathogens presenting as pneumonia, such as Severe Acute Respiratory Syndrome, avian influenza A(H5N1) and A(H7N9), and Middle East Respiratory Syndrome coronavirus has emphasised the importance of the surveillance of pneumonia and other severe respiratory infections. An unexpected increase in the number of hospital admissions for pneumonia or severe respiratory infections could be a signal of a change in the virulence of the influenza viruses or other respiratory pathogens circulating in the community, or an alert of an emerging pathogen which warrants further public health investigation.The purpose of this study was to develop a forecasting model to prospectively forecast the number of emergency department (ED) admissions due to pneumonia in Singapore, a tropical country. We hypothesise that there is complementary information between hospital-based and community-based surveillance systems. The clinical spectrum of many respiratory pathogens causing pneumonia ranges from asymptomatic or subclinical infection to severe or fatal pneumonia, and it is usually difficult to distinguish between the different pathogens in the absence of a laboratory test. Infected persons could present with varying degrees of severity of the infection, and seek treatment at different healthcare facilities. Hospital-based surveillance captures the more severe manifestation of the infection while community-based surveillance captures the less severe manifestation of the infection and enables earlier detection of the infection. Thus, the integration of information from the two surveillance systems should improve the prospective forecasting of ED admissions due to pneumonia. We also investigate if the inclusion of influenza data from the laboratory surveillance system would improve the forecasting model, since influenza circulates all-year round in Singapore and is a common aetiology for pneumonia.MethodsThis was a retrospective study using aggregated national surveillance data and meteorological data during the period 3 January 2011 to 1 January 2017.We compared the performance of autoregressive integrated moving average model (ARIMA) with multiple linear regression models with ARIMA errors, with and without the inclusion of influenza predictors at forecast horizons of 2, 4, 6 and 8 weeks in advance. Weekly data between the study period of 3 January 2011 and 1 January 2017 were split into training and validation sets, with the first three years of data used as the base training set. Time series cross validation was used to estimate the models’ accuracy and out-of-sample forecast accuracy was based on the calculation of the mean absolute error (MAE) and mean absolute percent forecast error (MAPE).ResultsThe multiple linear regression model with ARIMA errors that included influenza predictors was the best performing model while the basic ARIMA model was the worst performing model for all forecast horizons. The two multiple linear regression models with ARIMA errors had a MAPE of less than 10% for all forecast horizons.ConclusionsData from different multiple surveillance systems and the inclusion of influenza trends can be used to improve the forecast of ED admissions due to pneumonia in a tropical setting, despite the absence of large differences between seasons. Accurate forecasting at the national level can prepare healthcare facilities for an impending surge.