Ljung Box Research Articles

SARIMA Model Forecasting Performance of the COVID-19 Daily Statistics in Thailand during the Omicron Variant Epidemic.

This study aims to identify and evaluate a robust and replicable public health predictive model that can be applied to the COVID-19 time-series dataset, and to compare the model performance after performing the 7-day, 14-day, and 28-day forecast interval. The seasonal autoregressive integrated moving average (SARIMA) model was developed and validated using a Thailand COVID-19 open dataset from 1 December 2021 to 30 April 2022, during the Omicron variant outbreak. The SARIMA model with a non-statistically significant p-value of the Ljung–Box test, the lowest AIC, and the lowest RMSE was selected from the top five candidates for model validation. The selected models were validated using the 7-day, 14-day, and 28-day forward-chaining cross validation method. The model performance matrix for each forecast interval was evaluated and compared. The case fatality rate and mortality rate of the COVID-19 Omicron variant were estimated from the best performance model. The study points out the importance of different time interval forecasting that affects the model performance.

Application of the ARIMA Model in Forecasting the Incidence of Tuberculosis in Anhui During COVID-19 Pandemic from 2021 to 2022.

ObjectiveForecasting the seasonality and trend of pulmonary tuberculosis is important for the rational allocation of health resources. In this study, we predict the incidence of pulmonary tuberculosis by establishing the autoregressive integrated moving average (ARIMA) model and providing support for pulmonary tuberculosis prevention and control during COVID-19 pandemic.MethodsRegistered tuberculosis(TB) cases from January 2013 to December 2020 in Anhui province were analysed using traditional descriptive epidemiological methods. Then we used the monthly incidence rate of TB from January 2013 through June 2020 to construct ARIMA model, and used the incidence rate from July 2020 to December 2020 to evaluate the forecasting accuracy. Ljung Box test, Akaike's information criterion(AICc), Bayesian information criterion(BIC) and Realtive error were used to evaluate the model fitting and forecasting effect, Finally, the optimal model was used to forecast the expected monthly incidence of tuberculosis for 2021 and 2022 to learn about the incidence trend.ResultsA total of 255,656 TB cases were registered. The reported rate of tuberculosis was highest in 2013 and lowest in 2020. The peak incidence was in March, Tongling (71.97/100,000), Chizhou (59.93/100,000), and Huainan (58.36/100,000) had the highest number of cases. The ratio of male to female incidence was 2.59:1, with the largest proportion of people being between 66 and 75 years old. The main occupation of patients was farmer. ARIMA (0, 1, 1) (0, 1, 1)12 model was the optimal model to forecast the incidence trend of TB.ConclusionTongling, Chizhou, and Huainan should strengthen measures for TB. In particular, the government should pay more attention on elderly people to prevent tuberculosis infections. The rate of TB patient registration and reporting has decreased under the pandemic of COVID-19. The ARIMA model can be a useful tool for predicting future TB cases.

The SARIMA model-based monthly rainfall forecasting for the Turksvygbult Station at the Magoebaskloof Dam in South Africa

Rainfall forecast information is important for the planning and management of water resources and agricultural activities. Turksvygbult rainfall near the Magoebaskloof Dam (South Africa) has never been modelled and forecasted. Hence, the objective of this study was to forecast its monthly rainfall using the SARIMA model. GReTL and automatic XLSTAT software were used for forecasting. The trend of the long-term rainfall time series (TS) was tested by Mann–Kendall and its stationarity was proved by various unit root tests. The TS data from Oct 1976 to Sept 2015 were used for model training and the remaining data (Oct 2015 to Sept 2018) for validation. Then, all TS (Oct 1976 to Sept 2018) were used for out of sample forecasting. Several SARIMA models were identified using correlograms that were derived from seasonally differentiated TS. Model parameters were derived by the maximum likelihood method. Residual correlogram and Ljung–Box Q tests were used to check the forecast accuracy. Based on minimum Akaike information criteria (AI) value of 5642.69, SARIMA (2, 0, 3) (3, 1, 3) 12 model was developed using GReTL as the best of all models. SARIMA (1, 0, 1) (3, 1, 3) 12, with minimum AI value of 5647.79, was the second-best model among GReTl models. This second model was also the first best automatically selected model by XLSTAT. In conclusion, these two best models can be used by managers for rainfall forecasting and management of water resources and agriculture, and thereby it can contribute to economic growth in the study area. Hence, the developed SARIMA forecasting procedure can be used for forecasting of rainfall and other time series in different areas.

RF eigenfingerprints, an Efficient RF Fingerprinting Method in IoT Context.

In IoT networks, authentication of nodes is primordial and RF fingerprinting is one of the candidates as a non-cryptographic method. RF fingerprinting is a physical-layer security method consisting of authenticated wireless devices using their components’ impairments. In this paper, we propose the RF eigenfingerprints method, inspired by face recognition works called eigenfaces. Our method automatically learns important features using singular value decomposition (SVD), selects important ones using Ljung–Box test, and performs authentication based on a statistical model. We also propose simulation, real-world experiment, and FPGA implementation to highlight the performance of the method. Particularly, we propose a novel RF fingerprinting impairments model for simulation. The end of the paper is dedicated to a discussion about good properties of RF fingerprinting in IoT context, giving our method as an example. Indeed, RF eigenfingerprint has interesting properties such as good scalability, low complexity, and high explainability, making it a good candidate for implementation in IoT context.

Wild bootstrap Ljung–Box test for residuals of ARMA models robust to variance change

Wild bootstrap Ljung–Box test for residuals of ARMA models robust to variance change

A procedure for testing the hypothesis of weak efficiency in financial markets: a Monte Carlo simulation

The weak form of the efficient market hypothesis is identified with the conditions established by different types of random walks (1–3) on the returns associated with the prices of a financial asset. The methods traditionally applied for testing weak efficiency in a financial market as stated by the random walk model test only some necessary, but not sufficient, condition of this model. Thus, a procedure is proposed to detect if a return series associated with a given price index follows a random walk and, if so, what type it is. The procedure combines methods that test only a necessary, but not sufficient, condition for the fulfilment of the random walk hypothesis and methods that directly test a particular type of random walk. The proposed procedure is evaluated by means of a Monte Carlo experiment, and the results show that this procedure performs better (more powerful) against linear correlation-only alternatives when starting from the Ljung–Box test. On the other hand, against the random walk type 3 alternative, the procedure is more powerful when it is initiated from the BDS test.

Data Driven Mathematical Models for Forecast of Covid-19 Disease in Nigeria

In this research, two mathematical models are proposed for investigation of laboratory confirmed daily COVID-19 disease incidence and total active daily infectious COVID-19 cases using data obtained from Nigeria Centre for Disease Control. Due to the observed patterns in the raw data, Autoregressive Integrated Moving Average(ARIMA) method is used on the data which covered a period of 521 days (27 February, 2020- 1st August 2021). While diagnostic check of ARIMA(11,1,0) indicate Ljung-Box Q(18) statistics value of 12.544 with p-value of 0.084, diagnostic check of ARIMA(1, 1, 1) indicate Ljung Box Q(18) statistics value of 22.420 with p-value of 0.130. Furthermore, stationary R- squared values are 0.803 and 0.858 at 95% confidence bound for ARIMA (11, 1, 0) and ARIMA (1, 1, 1) respectively which are indicative of good models. Results from ARIMA (11, 1, 0) forecast show a slightly moderate upward trend in confirmed daily COVID-19 incidence in Nigeria and results from ARIMA(1, 1, 1) indicate significant upward trend in total active daily infectious COVID-19 cases in Nigerian population. Therefore, the developed models can be adopted by presidential taskforce and other agencies in health sector regarding future vaccination towards prevention of the spread of COVID-19 disease in Nigeria provided that the present general prevailing conditions of disease spread remain fairly the same.

Mathematical Modeling to Predict COVID-19 Infection and Vaccination Trends.

Background: COVID-19 caused by the Severe Acute Respiratory Syndrome Coronavirus 2 placed the health systems around the entire world in a battle against the clock. While most of the existing studies aimed at forecasting the infections trends, our study focuses on vaccination trend(s). Material and methods: Based on these considerations, we used standard analyses and ARIMA modeling to predict possible scenarios in Romania, the second-lowest country regarding vaccinations from the entire European Union. Results: With approximately 16 million doses of vaccine against COVID-19 administered, 7,791,250 individuals had completed the vaccination scheme. From the total, 5,058,908 choose Pfizer–BioNTech, 399,327 Moderna, 419,037 AstraZeneca, and 1,913,978 Johnson & Johnson. With a cumulative 2147 local and 17,542 general adverse reactions, the most numerous were reported in recipients of Pfizer–BioNTech (1581 vs. 8451), followed by AstraZeneca (138 vs. 6033), Moderna (332 vs. 1936), and Johnson & Johnson (96 vs. 1122). On three distinct occasions have been reported >50,000 individuals who received the first or second dose of a vaccine and >30,000 of a booster dose in a single day. Due to high reactogenicity in case of AZD1222, and time of launching between the Pfizer–BioNTech and Moderna vaccine could be explained differences in terms doses administered. Furthermore, ARIMA(1,1,0), ARIMA(1,1,1), ARIMA(0,2,0), ARIMA(2,1,0), ARIMA(1,2,2), ARI-MA(2,2,2), ARIMA(0,2,2), ARIMA(2,2,2), ARIMA(1,1,2), ARIMA(2,2,2), ARIMA(2,1,1), ARIMA(2,2,1), and ARIMA (2,0,2) for all twelve months and in total fitted the best models. These were regarded according to the lowest MAPE, p-value (p < 0.05, p < 0.01, and p < 0.001) and through the Ljung–Box test (p < 0.05, p < 0.01, and p < 0.001) for autocorrelations. Conclusions: Statistical modeling and mathematical analyses are suitable not only for forecasting the infection trends but the course of a vaccination rate as well.

Comparison of Stationarity on Ljung Box Test Statistics for Forecasting

The movements in Asset prices are very complex, therefore seem to be unpredictable. However, one of the main challenges of the econometric models is to get the best data for forecasting in order to present accurate results. This paper investigates the performance of stationary and non-stationary data on Ljung Box test statistics, to check the fitness of the data for forecasting. In the paper three assets (Groundnut, sorghum and soya bean) are used, tests are conducted for Ljung box statistics; Correlogram, Histogram Normality and Heteroscedasticity test. It is observed that stationary data are better for forecasting than non-stationary data in this research.

Optimal Stochastic Forecast Models of Rainfall in South-West Region of Nigeria

Rainfall estimates are important components of water resources applications, especially in agriculture, transport constructing irrigation and drainage systems. This paper aims to stochastically model and forecast the rainfall trend and pattern for a city, each purposively selected in five states of the South-Western Region of Nigeria. The data collected from Nigerian Meteorological Agency (NIMET) website are captured with fractional autoregressive integrated moving average (ARFIMA) and seasonal autoregressive integrated moving average (SARIMA) models. The autocorrelation function (ACF) and partial autocorrelation function (PACF) are used for model identification, the models selected are subjected to diagnostic checks for the models adequacy. Several tests: Augmented Dickey Fuller (ADF), Ljung Box and Jarque Bera tests are used for investigating unit root, serial autocorrelation and normality of residuals, respectively; the mean square error, root mean square error and mean absolute error are employed in validating the optimal stochastic model for each city in all states, in which the model with the lowest error of forecasting of all competing models is suggested as the best. The analyses and findings suggest SARIMA(1,0,1)(1,1,0) [12], SARIMA(3,0,2)(1,0,0) [12], SARIMA(1,0,0)(1,1,0) [12], SARIMA(2,0,2)(2,1,0) [12] and SARIMA(0,0,1)(1,1,0) [12] for (Ibadan) Oyo State, (Ikorodu) Lagos State, (Osogbo) Osun State, (Abeokuta) Ogun State and (Akure) Ondo state, respectively. The seasonal ARIMA (SARIMA) model was proven to be the best optimal stochastic forecast model for forecasting rainfall in the selected cities. The SARIMA model was, therefore, recommended as a veritable technique that will assist decision makers (Government, Farmers, and Policymakers) to establish better strategies “aprior” on the management of rainfall against upcoming weather changes to ensure increase in agricultural yields for the betterment of the citizenry and general economic growth.

Point and interval forecasts of electricity demand with Reg-SARMA models

This paper deals especially with a two-stage approach to forecasting hourly electricity demand by using a linear regression model with serially correlated residuals. Firstly, ordinary least squares are applied to estimate a linear regression model based on purely deterministic predictors (essentially, polynomials in time and calendar dummy variables). In the case wherein the regression residuals are not a white noise series, a SARMA (seasonal autoregressive moving average) process is applied to the estimated regression residuals. After examining a vast set of potential representations, the stationary and invertible process associated with the smaller Akaike information criterion and the smaller Ljung–Box statistic is selected. Secondly, two sets of instrumental predictors are added to the current model: the estimated residuals of the first regression model plus the estimated errors of the chosen SARMA process. The new regression model is estimated by again using ordinary least squares, but taking advantage of the fact that the new regressors eliminate serial correlation. Practical issues in points and interval forecasting are illustrated with reference to nine-day ahead prediction performance for short-term electric loads in Italy.

Rainfall prediction using optimally pruned extreme learning machines

Rainfall impacts local water quantity and quality. Accurate and timely prediction of rainfall is highly desirable in water management and hydrogeologic hazards mitigation, which is critical for the environmentally sustainable development. Previous rainfall prediction processes are complex and computationally costly for its intrinsic high uncertainty and variability. In this paper, a data-driven approach is applied to predict the rainfall based on historic data via time-series modeling and optimally pruned extreme learning machine (OP-ELM). The rainfall datasets collected from six counties within Three Georges Reservoir are utilized as case studies in this research, first, the rainfall data is pre-processed with outlier removal and missing value imputation, and the monthly ahead difference is computed based on the instant average of monthly rainfall. Next, the autocorrelation function and partial autocorrelation function were computed and the Ljung–Box test statistic is utilized to explore the significance of the historic lagged-series. All the statistically significant historic lags are selected as inputs for prediction algorithms. Last, an OP-ELM algorithm is developed to predict the monthly rainfall with tenfold cross validation. Four activation functions: the sigmoid, sine, hardlim, and radial basis function, are considered in the OP-ELM. The prediction performance is evaluated with metrics including mean absolute error, mean absolute percentage error, root mean square error, and max error rate. Overall, the computational results indicate the proposed framework outperforms the other benchmarking machine learning algorithms through six case studies in Three Gorges Reservoir, China.

Transformer Winding Faults Detection Based on Time Series Analysis

Monitoring of winding faults is of great significance for the assessment of the transformer maintenance status. In this study, the time series analysis is combined with frequency response analysis (FRA) for better interpretation and analysis of FRA results. Here, healthy baseline residual data are modeled using the time series analysis for faults detection of the transformer winding. Different statistical software, such as R 4.0.2 and ITSM2000, are used to analyze measured data. To detect the transformer’s winding faults, various analyses, such as the autocorrelation and partial autocorrelation functions plot, the Box–Pierce test, the Ljung–Box test, the McLeod–Li test, the turning points test, the Wallis and Moore phase–frequency test, and the Jarque–Bera test, and the order of minimum corrected Akaike’s information criteria are used. The simulation results show that the suggested method is able to classify and discriminate mechanical and electrical faults of the transformer’s winding with good accuracy.

Private Label and Macroeconomic Indicators: Europe and USA

In this study, we have analyzed the impact and evolution of some of the most important macroeconomic indices on the market share and value of private brands. The originality and objective of this work is the linkage of macroeconomic variables in European countries and the USA with the evolution of private labels in these countries. A sample of 19 European countries and all states within the USA has been collected over a 10-year period, including data on private labels and macroeconomic indices. The analysis of the panel data has been applied using the SPSS software through the Ljung–Box test. The most significant data from the sample study is that for GDP; we advised national brand managers to make a special communication effort in nations that offer a lower GDP within Europe for their volume and in value for the US. On the other hand, it was found that when the unemployment rate increases, the value of private label market share decreases for the US, but increases for Europe, in addition to other findings that will help organizations make different business decisions.

ROBUST TESTS FOR WHITE NOISE AND CROSS-CORRELATION

Commonly used tests to assess evidence for the absence of autocorrelation in a univariate time series or serial cross-correlation between time series rely on procedures whose validity holds for i.i.d. data. When the series are not i.i.d., the size of correlogram and cumulative Ljung–Box tests can be significantly distorted. This paper adapts standard correlogram and portmanteau tests to accommodate hidden dependence and nonstationarities involving heteroskedasticity, thereby uncoupling these tests from limiting assumptions that reduce their applicability in empirical work. To enhance the Ljung–Box test for non-i.i.d. data, a new cumulative test is introduced. Asymptotic size of these tests is unaffected by hidden dependence and heteroskedasticity in the series. Related extensions are provided for testing cross-correlation at various lags in bivariate time series. Tests for the i.i.d. property of a time series are also developed. An extensive Monte Carlo study confirms good performance in both size and power for the new tests. Applications to real data reveal that standard tests frequently produce spurious evidence of serial correlation.

Global autocorrelation test based on the Monte Carlo method and impacts of eliminating nonstationary components on the global autocorrelation test

Autocorrelation and non-stationarity are always concerned in analysis of meteorological and hydrological time series. Current commonly used methods, such as the Box-Pierce (BP) test and Ljung-Box (LB) test, always preset the maximum order for the autocorrelation significance test without considering the existence of high-order autocorrelation coefficient(s), and also neglect a fact that the sum of sample autocorrelation function is a constant value. Moreover, the impacts of autocorrelation on the significance test of nonstationary components of sample time series have drawn much attention, but less attention is paid to the impacts of eliminating nonstationary components on the global autocorrelation significance test. These issues are addressed in the paper. Based on the Monte Carlo method, a global autocorrelation test method, the quadratic sum (QS) test, is presented for judging the existence of high-order autocorrelation coefficient(s) of a sample time series. Besides, two nonparametric trend estimators (nonlinear and linear trend estimators) are employed to investigate the impacts of eliminating nonstationary components on the global autocorrelation test. The results show that (i) the QS test method is more robust than the BP test and LB test in verifying the existence of significant high-order autocorrelation coefficient(s); and (ii) eliminating a linear trend has less damage on the original global autocorrelation structure of sample time series by comparing with eliminating a nonlinear trend. Therefore, it is recommended to initially eliminate the linear trend from a sample time series, and then judge the existence of high-order autocorrelation coefficients of the time series based on the QS test.

Predictive Modeling of Wildfire Occurrence and Damage in a Tropical Savanna Ecosystem of West Africa

Wildfires are a major environmental, economic, and social threat. In Central Côte d’Ivoire, they are among the biggest environmental and forestry problems during the dry season. National authorities do not have tools and methods to predict spatial and temporal fire proneness over large areas. This study, based on the use of satellite historical data, aims to develop an appropriate model to forecast wildfire occurrence and burnt areas in each ecoregion of the N’Zi River Watershed. We used an autoregressive integrated moving average (ARIMA) model to simulate and forecast the number of wildfires and burnt area time series in each ecoregion. Nineteen years of monthly datasets were trained and tested. The model performance assessment combined Ljung–Box statistics, residuals, and autocorrelation analysis coupled with cross-validation using three forecast errors—namely, root mean square error, mean absolute error, and mean absolute scaled error—and observed–simulated data analysis. The results showed that the ARIMA models yielded accurate forecasts of the test dataset in all ecoregions and highlighted the effectiveness of the ARIMA models to forecast the total number of wildfires and total burnt area estimation in the future. The forecasts of possible wildfire occurrence and extent of damages in the next four years will help decision-makers and wildfire managers to take actions to reduce the exposure and the vulnerability of ecosystems and local populations to current and future pyro-climatic hazards.

A novel validation framework to enhance deep learning models in time-series forecasting

Time-series analysis and forecasting is generally considered as one of the most challenging problems in data mining. During the last decade, powerful deep learning methodologies have been efficiently applied for time-series forecasting; however, they cannot guarantee the development of reliable prediction models. In this work, we introduce a novel framework for supporting deep learning in enhancing accurate, efficient and reliable time-series models. The major novelty of our proposed methodology is that it ensures a time-series to be “suitable” for fitting a deep learning model by performing a series of transformations in order to satisfy the stationarity property. The enforcement of stationarity is performed by the application of Augmented Dickey–Fuller test and transformations based on first differences or returns, without the loss of any embedded information. The reliability of the deep learning model’s predictions is guaranteed by rejecting the hypothesis of autocorrelation in the model’s errors, which is demonstrated by autocorrelation function plots and Ljung–Box Q test. Our numerical experiments were performed utilizing time-series from three real-world application domains (financial market, energy sector, cryptocurrency area), which incorporate most of global research interest. The performance of all forecasting models was compared on both problems of forecasting time-series price (regression) and time-series directional movements (classification). Additionally, the reliability of the models’ forecasts was evaluated by examining the existence of autocorrelation in the errors. Our numerical experiments indicate that our proposed methodology considerably improves the forecasting performance of a deep learning model, in terms of efficiency, accuracy and reliability.

SARIMA Approach to Generating Synthetic Monthly Rainfall in the Sinú River Watershed in Colombia

Seasonal Auto Regressive Integrative Moving Average models (SARIMA) were developed for monthly rainfall time series. Normality of the rainfall time series was achieved by using the Box Cox transformation. The best SARIMA models were selected based on their autocorrelation function (ACF), partial autocorrelation function (PACF), and the minimum values of the Akaike Information Criterion (AIC). The result of the Ljung–Box statistical test shows the randomness and homogeneity of each model residuals. The performance and validation of the SARIMA models were evaluated based on various statistical measures, among these, the Student’s t-test. It is possible to obtain synthetic records that preserve the statistical characteristics of the historical record through the SARIMA models. Finally, the results obtained can be applied to various hydrological and water resources management studies. This will certainly assist policy and decision-makers to establish strategies, priorities, and the proper use of water resources in the Sinú river watershed.

Power Comparisons of Five Most Commonly Used Autocorrelation Tests

In regression analysis, autocorrelation of the error terms violates the ordinary least squares assumption that the error terms are uncorrelated. The consequence is that the estimates of coefficients and their standard errors will be wrong if the autocorrelation is ignored. There are many tests for autocorrelation, we want to know which test is more powerful. We use Monte Carlo methods to compare the power of five most commonly used tests for autocorrlation, namely Durbin-Watson, Breusch-Godfrey, Box–Pierce, Ljung Box, and Runs tests in two different linear regression models. The results indicate the Durbin-Watson test performs better in the regression model without lagged dependent variable, although the advantage over the other tests reduce with increasing autocorrelation and sample sizes. For the model with lagged dependent variable, the Breusch-Godfrey test is generally superior to the other tests.R code for Power Comparison of the Five Autocorrelation Tests is provided.