Partial Autocorrelation Research Articles

Temporal dynamics and forecasting of aerosol optical depth in megacities Lahore and Karachi: Insights from the Indo-Gangetic Basin and southern Pakistan, and implications for Sustainable development

This scientific study investigates the temporal dynamics and forecasts aerosol optical depth (AOD) in Lahore and Karachi, Pakistan's two most populated cities. Lahore, in the center of the Indo-Gangetic Basin, and Karachi, on the southern coast, have issues from growing urbanization and significant aerosol emissions. Understanding AOD trends is critical for successful environmental management, public health planning, and climate change mitigation. Using the Box-Jenkins ARIMA models, this work systematically analyses monthly AOD fluctuations from July 2002 to May 2023 to confirm their predicting accuracy. The autocorrelation function (ACF) and partial autocorrelation function (PACF) have been employed to estimate the suitable model and identify significant lags to maintain prediction accuracy. The study concludes with a judgment that Model A is ideal for the ecology of Karachi and Model B for the ecology of Lahore. The forecast till January 2030 is available to look at several trends on AOD, namely, periods of seasonal solid fluctuations for both sites. This diversity emphasizes the need for specific actions, such as stricter environmental regulations, air quality monitoring, and providing greener transport solutions, which will result in blue skies. Utilizing the in-depth observations and forecast of the changing distribution of AOD values, the study helps develop approaches for reducing aerosol pollution. This is also one of the key contributions. We investigated critical environmental problems in the cities of Karachi and Lahore and provided means for such issues' resolution, enabling sustainable development and clean air.

Forecasting Analysis of the Hungarian CPI Based on the Arima Model

Since the twenty-first century, under the influence of economic system reform and economic globalization, Hungary's economic development has prospered, and the GDP index has increased significantly, however, while the country's economic development level has increased year by year, the consumer price index has also shown a year by year increasing trend. Consumer price index (CPI) is closely related to the quality of life, employment and economic stability. In this paper, the CPI in 2021 is taken as the base (100), and the data from 1990 to 2021 are statistically analyzed, and the ARIMA model is used to make time-series forecasts. Based on the ADF test, autocorrelation and partial autocorrelation plots for the determination of the series parameters, the ARIMA (1, 1, 0) model is obtained, and the final results are obtained for the ten data forecasts after 2021. The results show that the Hungarian consumer price index will still grow in the next ten years, but unlike the exponential growth after 2017, the growth rate slows down in the next ten years, indicating that the economic situation will stabilize in the future and price fluctuations will not be too high.

Air Quality and Public Health Risk Assessment: A Case of an Industrial Area in Haridwar City, Uttarakhand (India).

Air pollution is a significant issue for a developing country like India and the air quality index (AQI) forecasting helps to predict air quality levels in advance and allows individuals to take precautionary measures to protect their health. The study aimed to forecast the AQI for an industrial area (SIDCUL, Haridwar City) using a time series regression model. Three years of existing AQI data points (post-COVID-19) were collected from the Uttarakhand Pollution Control Board for the SIDCUL area of Haridwar City and tried to know the status of AQI values for the following 12 months. Trend and seasonality components were seen through the decomposition process. Further, the augmented Dickey-Fuller test was applied to check the stationarity of the series before finalizing the best-suited time series model for forecasting the AQI values. With the help of autocorrelation function (ACF)/partial ACF plots, a seasonal autoregressive integrated moving average (ARIMA) (0,1,0) (1,0,0)[12] model was selected with the minimum akaike information criterion (253.143) and mean absolute percentage error (17.42%). The AQI values have also been forecasted for this industrial area (SIDCUL) for the following year. The seasonal ARIMA (0,1,0) (1,0,0)[12] model may be helpful to forecast the AQI values for a nonstationary time series dataset. Research indicates that the air of the SIDCUL area will become moderately polluted and may cause breathing discomfort to asthma patients' health. The scientists might apply this model to other polluted regions of the country so that the public and the government can take preventive measures in advance.

Построение краткосрочного прогноза количества вагонов на станции и путях необщего пользования

Objective: collect raw data for building predictive models. Analyze the initial data, identify data outliers and outliers, divide the data into time intervals, calculate correlation coefficients, partial autocorrelation, cross-correlation, analyze the trend and seasonality of the obtained time series. Using autoregressive models, machine learning models, neuro-fuzzy models to build forecasts of time series and determine the quality of the obtained forecasts. Methods: point density, autocorrelation, partial autocorrelation, cross-correlation, Foster-Stewart test, Dickey-Fuller test, ARMA, MLP, Encoder-Decoder LTSM, TSK, Fuzzy-Partitions, SCRG, Transformers. Results: we obtained estimates of the prediction accuracy of the selected models, compared the results of the predictive models trained on different samples of initial data. Conclusions are made about the efficiency and methods of building predictive models. Practical significance: the 
 significance of building accurate predictive models for the key quantitative indicators of stations and nonpublic routes operation is shown. The factors influencing the accuracy of the obtained forecasts are analyzed.

Novel hybrid intelligence predictive model based on successive variational mode decomposition algorithm for monthly runoff series

A high-accuracy estimation of the runoff has always been an extremely relevant and challenging subject in hydrology science.Therefore, in the current research, a novel hybrid decomposition-integration-optimization based model is developed to enhance the estimation precision of the runoff. The suggested predictive model is a combination of successive variational mode decomposition (SVMD) technique and Multi-Layer Perceptron neural network (MLP) model integrated with particle swarm optimization (PSO) meta-heuristic algorithm (i.e., hybrid SVMD-MLP-PSO model). To test its performance, the mean monthly runoff data recorded from Sep 1986-Aug 2017 in Dez River basin (MRDRm), southwest of Iran, are used. The performance of the recommended model is also matched with other different hybrid and single models including MLP-PSO, SVMD-MLP, and MLP as the benchmark model. In all models, the sequence-to-one regression module of forecasting (i.e., without using meteorological parameters recorded in the study region) is utilized. In the SVMD based hybrid models, the optimal value of compactness of mode (α) for the original MRDRm time series is achieved at 100. Then, the PACF(partial autocorrelation function) diagram related to the lag length from each decomposed intrinsic mode function (IMF) sub-signals sequence generated is operated to select the ideal input variables. Performance evaluation metrics prove that the hybrid SVMD-MLP-PSO model under the best predictor and meta-parameters, outperformed with an R2 of 0.89, modified 2012 version of Kling-Gupta efficiency (KGEʹ) of 0.83, volumetric efficiency (VE) of 0.91, Nash–Sutcliffe efficiency (NSE) of 0.88, and RMSE of 13.91 m3/s. Comparatively, the standalone MLP as the benchmark model results in an R2 of 0.24, VE of 0.33, KGEʹ of 0.2, NSE of 0.29, and RMSE of 153.39 m3/s.

Time Series Model to Forecast Fresh Coconut Exports from Sri Lanka

Coconut accounts for approximately 12% of all agricultural produce in Sri Lanka with the total land area under cultivation covering 409, 244 hectares ranking second to rice production. The primary regions for coconut cultivation are the Puttalam and Kurunegala districts in North-Western Province and Gampaha district in the Western Province, forming what is known as the Coconut Triangle. This region accounts for 232,270 hectares (50.94%) of the overall coconut cultivation area. The remaining coconut cultivation areas are found in the Southern Province, specifically in the districts of Galle (13,833 hectares), Matara (14,946 hectares), and Hambantota (25,837 hectares), and in non-traditional regions of the Eastern and Northern provinces. The annual coconut production varies between 2,800 to 3,000 million nuts. Having advanced knowledge of exporting coconuts offers numerous advantages to Sri Lanka, particularly in terms of establishing forward contracts with other countries. Based on secondary data of annual fresh coconut exports from 1981 to 2020 obtained from the Coconut Development Authority (CDA) of Sri Lanka, the paper developed ARIMA (2,1,0) model to forecast export. The model was selected out of three parsimonious models which were identified from the Sample Autocorrelation Function (ACF) and Partial Autocorrelation Function (PACF) of the stationary series and a comparison of significant parameters and lowest values of Akaike Information Criterion (AIC), Schwarz Bayesian Information Criterion (SBIC) and Hannan-Quinn Information Criterion (HQIC). The errors of the fitted model were found to be random and constant variance. The model was validated using 2021 and 2022 data. The percentage errors for 2021 and 2022 are 20.23% and -29.57% respectively. The predictions for 2023 and 2024 are 14696 and 15052 respectively. The model can be used effectively by the Coconut Development Authority for decision-making. However, it is suggested to develop the model further to reduce the percentage error. Keywords: ARIMA model, Forecast, Fresh Coconut Exports and Validate

Forecasting of tilapia (Oreochromis niloticus) production in Bangladesh using ARIMA model

Tilapia farming has expanded rapidly in Bangladesh over the years thanks to a suitable climate for aquaculture and a consistently increasing demand for the fish rich in vitamins and minerals. A clear picture regarding the future trend of tilapia production in Bangladesh is still not available, however. The purpose of this study was to estimate parameters that fit into the Autoregressive Integrated Moving Average (ARIMA) model for forecasting tilapia production in Bangladesh. This was accomplished by calibrating and validating the ARIMA model taking into account the lowest values of the Akaike Information Criterion (AIC) and Bayesian Information Criteria (BIC), graphical arrangements of autocorrelation function (ACF) and partial autocorrelation function (PACF) plots. The best model derived was ARIMA (1, 1, 1), which showed an upward trend of tilapia production since 2006 to date and predicted a similar trend until the year 2040. If this trend continues, the yearly tilapia outturn in the country may reach 690,000 MT, with an upper limit of 1.15 million MT and lower limit of 0.23 million MT, reflecting a substantial increase of around 118% over that produced in 2021. The results of this study will serve as a valuable resource for researchers, decision-makers, academics, and tilapia entrepreneurs, enabling them to develop effective action plans to optimize tilapia production in Bangladesh and strategize for the future integration of tilapia within the country.

Monthly Streamflow Prediction of the Source Region of the Yellow River Based on Long Short-Term Memory Considering Different Lagged Months

Accurate and reliable monthly streamflow prediction plays a crucial role in the scientific allocation and efficient utilization of water resources. In this paper, we proposed a prediction framework that integrates the input variable selection method and Long Short-Term Memory (LSTM). The input selection methods, including autocorrelation function (ACF), partial autocorrelation function (PACF), and time lag cross-correlation (TLCC), were used to analyze the lagged time between variables. Then, the performance of the LSTM model was compared with three other traditional methods. The framework was used to predict monthly streamflow at the Jimai, Maqu, and Tangnaihai stations in the source area of the Yellow River. The results indicated that grid search and cross-validation can improve the efficiency of determining model parameters. The models incorporating ACF, PACF, and TLCC with lagged time are evidently superior to the models using the current variable as the model inputs. Furthermore, the LSTM model, which considers the lagged time, demonstrated better performance in predicting monthly streamflow. The coefficient of determination (R2) improved by an average of 17.46%, 33.94%, and 15.29% for each station, respectively. The integrated framework shows promise in enhancing the accuracy of monthly streamflow prediction, thereby aiding in strategic decision-making for water resources management.

A novel SARCIMA model based on central difference and its application in solar power generation of China

Due to the influence of exogenous factors such as weather, solar power generation shows the characteristics of instability and volatility, so the prediction of solar power generation has become especially important. In this paper, a new seasonal central difference autoregressive moving average model abbreviate as SARCIMA is proposed to accurately predict solar power generation. Firstly, the non-stationary time series is subjected to central difference until the difference series is stationary. Then, by analyzing autocorrelation images and partial autocorrelation images respectively, the number of the autoregressive term p and the moving average term q are obtained, so as to obtain the ARCIMA model. Next, the seasonal difference is combined with the ARCIMA model, thus establishing the SARCIMA model. Finally, the new model is applied to the prediction of solar power generation data exhibiting periodic characteristics and compared with five competing models. Mean absolute percentage error and residuals are separately calculated as indicators to evaluate the accuracy and stability of the models. In addition, the prediction of solar power generation in the next three months shows that the new model has better effectiveness, which provides a scientific basis for predicting solar power generation in the future.

Forecasting seasonal influenza activity in Canada-Comparing seasonal Auto-Regressive integrated moving average and artificial neural network approaches for public health preparedness.

Public health preparedness is based on timely and accurate information. Time series forecasting using disease surveillance data is an important aspect of preparedness. This study compared two approaches of time series forecasting: seasonal auto-regressive integrated moving average (SARIMA) modelling and the artificial neural network (ANN) algorithm. The goal was to model weekly seasonal influenza activity in Canada using SARIMA and compares its predictive accuracy, based on root mean square prediction error (RMSE) and mean absolute prediction error (MAE), to that of an ANN. An initial SARIMA model was fit using automated model selection by minimizing the Akaike information criterion (AIC). Further inspection of the autocorrelation function and partial autocorrelation function led to 'manual' model improvements. ANNs were trained iteratively, using an automated process to minimize the RMSE and MAE. A total of 378, 462 cases of influenza was reported in Canada from the 2010-2011 influenza season to the end of the 2019-2020 influenza season, with an average yearly incidence risk of 20.02 per 100,000 population. Automated SARIMA modelling was the better method in terms of forecasting accuracy (per RMSE and MAE). However, the ANN correctly predicted the peak week of disease incidence while the other models did not. Both the ANN and SARIMA models have shown to be capable tools in forecasting seasonal influenza activity in Canada. It was shown that applying both in tandem is beneficial, SARIMA better forecasted overall incidence while ANN correctly predicted the peak week.

Prediction and Classification Models of Wordle Data Set Based On ARMA, XGBoost

This study intends to use machine learning method to solve the problem of predicting the number of word guessing and the difficulty of word guessing in natural language. Firstly, this study smoothed the data according to the COF method. According to the images of the sample autocorrelation function and the sample partial autocorrelation function, the ARMA model is constructed and the coefficient of the AMRA model is calculated, and the number of word contest people on March 1, 2023 is predicted to drop to [18002,20622]. Second, based on the seven attributes of the word, the XGBoost classification model is used to predict the value of the first attempt, and then the XGBoost prediction model is used to predict the results of the other attempts. Eerie distribution of different attempts to {0,8.890, 17.650, 28.191, 32.451, 11.349, 1.483}. The average accuracy of the model on the test set is 79.4%.

The research of analysis lung, bronchus and trachea cancer death rate in US

This research delves into an analysis of lung, bronchus, and trachea cancer rates in the United States across genders. Employing the data spanning seven decades (1950-2020) sourced from the Our World in Data website, the study leverages time series modeling techniques, ARIMA and ETS models. The ARIMA methodology initiates with an assessment of data stationarity, followed by differencing procedures to transform the dataset into a non-stationary data. Subsequently, Autocorrelation Function (ACF) and Partial Autocorrelation Function (PACF) plots are examined. Last, the ARIMA model is fitted to dissect the mortality rates among males and females. Simultaneously, the ETS model is directly applied to the mortality data of both genders. The components of the ETS model and the check residuals for ETS are delineated. The outcomes reveal the trends: both genders exhibit a discernible decline in lung, bronchus, and trachea cancer death rates over the period. Despite this downward trajectory, the persistent mortality rates underscore the gravity of the issue. This paper advocates for a heightened focus on lung-related cancers. Understanding and addressing these mortality rates are imperative.

Research on Stock Price Prediction based on LSTM Modeling-A Stock Market as a Case Study

This research intends to predict the closing values of the Shanghai Stock Exchange 50 Index using an enhanced Long Short-Term Memory (LSTM) neural network approach. The investigation leverages a comprehensive data set from August 2013 to August 2023, encompassing various market conditions. Alongside the primary LSTM analysis, the study introduces supplementary methodologies, specifically the Auto-correlation Function (ACF) and Partial Auto-correlation Function (PACF), to validate and enrich the time-series analysis. This study verified the non-stationary of the original data and processed them with method. 80%of the data was allocated for training, while the subsequent 20% was reserved for testing, the LSTM model, with its intricate architecture, exhibits superior predictive capabilities, particularly in stable market conditions. However, its performance wanes during volatile market periods, suggesting further refinements are necessary. This research contributes to the existing literature by applying machine learning methodologies to the turbulent and complex A-share market, offering invaluable insights for both academic researchers and market investors.

A Modified LSTM Neural Network Based on Boosting and Sufficient Dimensionality Reduction

Stock price prediction is a common scenario in time series data forecasting, providing effective guidance for investment decisions. Long Short-Term Memory (LSTM) is a widely used model for stock price prediction, yet the selection of its hyperparameters remains an unresolved issue. In this paper, we address this challenge by employing model averaging instead of model selection. Specifically, we adaptively solve the hyperparameter selection problem by utilizing a distance covariance-weighted method, effectively balancing the bias and variance of the predictive model. Additionally, we propose an enhanced model that employs a boosting approach based on sufficiently reducing dimensionality through a multifactor model. This approach captures stock price sequence information beyond volatility. Practical data analysis demonstrates that the proposed method exhibits significant advantages over the original LSTM model in terms of mean square error or absolute error. Furthermore, the proposed framework can be applied to hyperparameter selection in other time series prediction models, such as autoregressive integrated moving averages (ARIMA), including the selection of autoregressive and partial autocorrelation orders.

PREDICTIVE ANALYSIS OF CLIMATE DISASTER DATA

In this paper, the Total deaths and Cost per Index (CPI) of worldwide climate disaster dataset has been modelled. The time period of the dataset is from 1900 to 2021. The Autoregressive Integrated Moving Average (ARIMA) has been applied to forecast the Total Deaths and CPI of the study area. The total of 75% of the train data is used for construction of the model and the remaining 25% dataset is used for testing the model. The ARIMA model is general provides more accurate projection especially interval forecast and is more reliable than other common statistical techniques. The best-fitted model is identified as ARIMA(2,0,1) and (2,1,2) for Cost per Index CPI and Total Deaths respectively, generated on the basis of minimum values of Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC) procedures. The accuracy parameter considered as Mean Absolute Error (MAE) and Root Mean Square Error (RMSE) both parameters shows the model is accurate respectively. There is a 7% difference between the auto and manual models for the CPI feature, similarly, there is a 4% difference for Total Deaths, indicating that CPI plays a significant impact in climatic disasters. In order to identify best fitted model, we applied the model manually and automatic processing. By means of Auto Correlation Function (ACF) and Partial Auto Correlation Function (PACF) plots, the most appropriate order of the ARIMA model are determine and evaluated. Accordingly the created model can help in determining future strategies related to climate disaster dataset of the world. From the forecast result it is found that the results seems to show an increasing trend in CPI values and the minimal decreasing in total death condition and economic activities of the world.

Forecasting carbon price using signal processing technology and extreme gradient boosting optimized by the whale optimization algorithm

AbstractPredicting carbon prices is crucial for the growth of China's carbon trading industry. This paper proposes a residual correction model that considers multiple influencing factors. First, the best historical data and main external factors input by the model are determined by using the partial autocorrelation function and Spearman correlation analysis, and the carbon price forecasting index system is constructed. Second, the whale optimization algorithm (WOA) is utilized to determine the optimal parameters of the extreme gradient boosting (XGBoost), and the WOA‐XGBoost model is built to perform preliminary carbon price forecasts and obtain the residual series. Finally, the carbon price residual series undergoes decomposition into multiple components utilizing the complete ensemble empirical mode decomposition for subsequent forecasting and the aggregation of outcomes. Experiments are conducted to predict two carbon trading markets in Hubei and Guangzhou, and a feature importance analysis is performed. The results indicate that the proposed hybrid model consistently outperforms the comparative models in terms of prediction accuracy. Furthermore, it is revealed that historical carbon prices and European Union carbon prices are the key factors influencing the prediction of carbon market prices.

МОДЕЛЬ ARIMA В МАШИННОМ ОБУЧЕНИИ: ПРОГНОЗИРОВАНИЕ ВРЕМЕННЫХ РЯДОВ

The paper considers the ARIMA method as a time series forecasting tool. Most often, its use is aimed at checking their stationarity. Usually, special tests of unit roots and the order of integration of the series are used. Then (when the order of integration exceeds zero), the series is transformed by searching for the difference in the required order. In the completed work, the process is illustrated by building on the example of the ticker of the OZON company. A graph of time series components, autocorrelation and partial autocorrelation functions were formed. The study resulted in forecasts for OZON, Alrosa and VTB, built with the help of ARIMA, as well as a comparison of these forecasts.

The usage of the autoregressive integrated moving average model for forecasting milk production in Egypt (2022-2025).

Milk is considered one of the most important capital goods and essential sources of animal protein in the diet of the Egyptian family, as well as an effective means to improve the economic condition of farmers, considering this important view, the policymakers need accurate and advance information regarding future supply for planning on the both short and long term. The study aims to forecast the production of milk in Egypt during the period from 2022 to 2025 using the Autoregressive Integrated Moving Average (ARIMA) model using time series data of milk production (MP) (1970-2021) obtained from the Central Agency for public mobilization and statistics (CAPMS). Augmented Dickey-Fullar Unit Root test, Partial autocorrelation function (PACF), and Autocorrelation function (ACF) of the time series sequence were used to judge the stationarity of the data. After confirming the stationarity of the data, the appropriate ARIMA model was selected based on certain statistical parameters like significant coefficients, values of adjusted R-squared, Akaike information criteria (AIC), Schwarz criterion (SC), and Standard Error of Regression. After the selection of the model based on the previous parameters, the verification of the model was employed by checking the residuals of the Correlogram-Q-Statistics test. The most fitted model to predict the future levels of MP in Egypt was ARIMA (1, 1, and 3). Using the ARIMA (1, 1, 3) model, it could be forecasted that the production of milk in Egypt would show an increasing trend from 6,152.606 thousand tons in 2022 to 6,360.829 thousand tons in 2025.

Time Series Data Analysis of Mindfulness Breathing Method Using Electroencephalogram.

Workers and students are often stressed and distressed by a variety of factors, including work and study. However, support for individual psychological stress is not yet well established. This study aimed to evaluate the effect of mindfulness breathing on the mental load of college students using an electroencephalogram (EEG). Twenty participants were randomly allocated into treatment or control groups, with 10 participants in each group. Mindfulness breathing was applied to participants in the treatment group, while those in the control group received no treatment. The regression equation was evaluated from the EEG, and time series analysis was performed based on autocorrelation and partial autocorrelation. In the After condition after mindfulness breathing exercises in the Mi group, the alpha wave content of the regression equation at eye closure after task performance showed an upward trend, and the autocorrelation coefficient showed repeated upward and downward fluctuations. It was suggested that alpha wave content may increase over time with mindfulness breathing exercises. The EEG after mindfulness breathing exercises was shown not to be constant and to have non-linear characteristics. This suggested that the effects of mindfulness breathing exercises could be evaluated using time series data.

Long-term trend prediction of surface water quality of two main river basins of China using Machine Learning Method

Rivers play a crucial role as sources of freshwater worldwide. The Yangtze and Yellow rivers, often regarded as the lifelines of China, significantly contribute to the nation's economy through their abundant water resources. Maintaining the quality of water in these river basins is essential for both human health and a thriving ecological system. This study intended to assess the historical water quality of China's two mother river basins including the Yangtze River, and the Yellow River. This assessment analyzes the historical dissolved oxygen, Ammonium nitrogen, and permanganate, and calculates comprehensive water quality identification (CWQII) values to find the trend and predict future values using a Machine learning model. To evaluate the stationarity of historical data, different tests and measures have been taken such as ADF and KSPP to test stationarity. Autocorrelation and partial autocorrelation also have been performed to understand the nature of the data. According to the SARIMA model, the Mean Absolute Percentage Error (MAPE) for the CWQII was 9.1% for the Yangtze and 13.3% for the Yellow River. In contrast, the LSTM model yielded MAPE values of 7% and 14%, respectively. For Dissolved Oxygen (DO) prediction, the SARIMA model showed MAPEs of 8.9% for the Yangtze and 9.87% for the Yellow River, while the LSTM model resulted in 8% and 16%, respectively. The current and future forecasting of CWQII values suggest that, based on model forecasts, the water quality in the Yellow River basin may be poorer compared to the Yangtze River basin This study might help the government, researchers, and other stakeholders to take proper steps to develop water pollution control strategy.