Stationary Time Series Data Research Articles

Could Regression of Stationary Series Be Spurious?

Spurious regression, commonly associated with independent and (nearly) non-stationary time series, has been extensively studied. However, the potential for spurious outcomes in regression involving stationary time series remains largely unexplored, representing a gap in the literature. To address this gap, we propose that regression of stationary time series may yield spurious outcomes and conduct a comprehensive investigation to verify this conjecture. Additionally, we present a remedy algorithm to mitigate spurious effects and improve model interpretability. Through extensive simulations, we validate our conjecture and demonstrate the efficacy of the proposed remedy. A numerical analysis further illustrates the practical utility of our approach. This study offers a fresh perspective on spurious regression and provides a practical solution to enhance the reliability of regression analyses involving stationary time series data.

Method to establish time-series building energy data inventory based on frequency for energy-sharing community planning

This study aims to establish a foundation for estimating energy demand according to building types by proposing a method to establish a time-series energy data inventory solely based on energy consumption in countries where typical models or benchmarking data by building types have not been developed. First, we presented the characteristics of energy consumption patterns that can be defined from the energy consumption itself based on frequency characteristics. Then, we defined a method to normalize and classify types of daily energy consumption patterns using this method and validated it with measured data. Finally, based on the results, a generalized method for establishing building time series energy data inventory was proposed. This method has a simple procedure and its result can be interpreted intuitively. It does not require data to be converted into stationary time-series data, unlike statistical methods, and it can avoid data distortion due to building operational errors. Moreover, it is easy to find the reasons for the results because the processes are easy to understand, unlike artificial intelligence methods. This study proposes a method to establish a time-series building energy data inventory by classifying types based solely on energy consumption. Furthermore, it suggests the possibility of its application in the early stages of planning an energy-sharing community.

The performance analysis of deep learning algorithms for modelling and forecasting the particulate matter (PM10) in the eastern part of Turkey

The main purpose of this study is to select the most reliable nonlinear computational model to predict the particulate matter (PM10) concentrations. Time series data of three years PM10 concentrations were used as input variable. For the prediction, three different types of dynamic nonlinear autoregressive models were built and compared. These models are the Levenberg-Marquardt algorithm, the Bayesian Regulization algorithm, and the Scaled Conjugate Gradient algorithm. For each of these algorythms, various settings were adopted with the subsequent statistical analysis. To analyse the model performance, we used mean prediction error, root mean square error, and correlation coefficient. The lowest root mean square errors were found for the Levenberg-Marquardt algorithm with 15 neurons, for the Bayesian Regularization and for the Scaled Conjugate Gradient algorithm with 20 neurons in hidden layer. In our study, we focused on the long-term forecast of stationary dynamic time series data and on the large amount of data, which is presented as a scientific novelty. Additionally, we determined the main model parameters that most improve quality in terms of training and network capacity. Therefore, the derived forecasting model can be used as a priori for air quality management and regulations aimed on the reducing of pollutant level.

Impact of climate change on dengue incidence in Singapore: time-series seasonal analysis

ABSTRACT This study aimed to identify the meteorological factors that contribute to dengue epidemics. The monthly incidence of dengue was used as the outcome variable, while maximum temperature, humidity, precipitation, and sunshine hours were used as independent variables. The results showed a consistent increase in monthly dengue cases from 2013 to 2021, with seasonal patterns observed in stationary time-series data. The ARIMA (2, 1, 3) × seasonal (0, 1, 2)12 model was used based on its lowest Akaike Information Criterion (AIC) values. The analysis revealed that a 1-unit increase in rainfall was positively correlated with a small 0.062-unit increase in dengue cases, whereas a 1-unit increase in humidity was negatively associated, leading to a substantial reduction of approximately 16.34 cases. This study highlights the importance of incorporating weather data into national dengue prevention programs to enhance public awareness and to promote recommended safety measures.

Forecasting EV Stock Trends Based on ARIMA Model Represented by Tesla and BYD

In recent years, an increasing number of people have turned their attention to renewable energy, and sales of electric vehicles have skyrocketed, making electric vehicles (EVs) a very popular topic. To better understand the development of the electric vehicle market and provide some insights for investors, this study forecasts EV stock trends of two leading companies in the Electric Vehicle industry, Tesla and BYD, by the Autoregressive Integrated Moving Average (ARIMA) model. The data in this research includes a daily time series of stock prices. ARIMA model is chosen in this research for its effectiveness in predicting stationary time series data, for its effectiveness in predicting stationary time series data, particularly suitable given the limited data available in the recently emerged EV industry. This research demonstrates that both Tesla and BYD’s stock closing prices are not stationary data. After differencing, for Tesla, the predicted result suggests a slightly increasing trend, while BYD's prices are predicted to remain at the same level and relatively stable in future 100 days. The study provides insights into the EV stock market, indicating a potential upward yet not pronounced trend in the future. But such a stable price might be a good choice for the investor low-risk takers.

Analisis Data Time Series Menggunakan Model Kernel: Pemodelan Data Harga Saham MDKA

<p>Classic time series data analysis techniques, such as autoregressive, model stationary data in which the values of prior observations influence the current observations through a process known as linear regression. There are several requirements for error assumptions in autoregressive, including independence, normal distribution with a zero mean and constant variance. It is frequently discovered that these assumptions are challenging to verify when modelling real data. Kernel time series regression is an alternative model that does not require error assumptions. Non-stationary time series data can be effectively modelled using the kernel time series method. Time series data that isn't yet stationary is made stationary first, then the data is modified by forming the current stationary time series data as the response variable and the previous period data as the predictor variable. Next, regression kernel modelling is carried out while applying kernel weight function and determining the optimal bandwidth. For development of science, the optimal bandwidth can be achieved by minimizing the MSE, CV, GCV, or UBR values. It is possible to use R<sup>2</sup> or MAPE as the kernel time series regression model's goodness metric. A strong model is generated while modelling MDKA stock price data using kernel regression utilizing the Gaussian kernel function and optimal bandwidth selection using GCV since R<sup>2</sup> is 0.9828372 more than 0.67 and MAPE is 1.985681% under 10%.</p><p><strong>Keywords</strong><strong>: </strong>3 time series; kernel regression; GCV; MDKA stock price.</p>

Predicting Tuberculosis Incidence and Its Trend in Tigray, Ethiopia: A Reality-Counterfactual Modeling Approach.

The Tigray region of Ethiopia, which has been affected by civil war from 2020 to 2022, is facing an increase in tuberculosis in the damaged health system. Our study employed mathematical modeling to predict the incidence of tuberculosis and its trends during the war and in the post-conflict setting of Tigray, Northern Ethiopia. We predicted the incidence of tuberculosis from 2020 to 2025 in Tigray using the SEIRD model in the context of the recent war and compared it with its counterfactual trend in the absence of war. The counterfactual trend was forecasted using an autoregressive integrated moving average (ARIMA) model for stationary time-series data. We performed rolling origin cross-validation for ARIMA and sensitivity analysis for the SEIRD model. The initial tuberculosis data and model parameters were obtained from the Institute for Health Metrics and Evaluation and the literature, respectively. Between 2000 and 2017, the incidence of tuberculosis in Tigray decreased at an annual rate of 3.0%. Shortly before the war, the incidence of tuberculosis in the region was 178 per 100,000 people. In a counterfactual scenario where there was no war, the incidence was projected to decrease to 144.3 in 2022 and 126.3 in 2025. However, owing to the war and siege, the SEIRD-projected incidence of tuberculosis would have increased to 965.5 (95% CI: 958.5-972.7) in 2022 and 372.4 (95% CI: 367.7-376.6) in 2025. Over 800 cases of tuberculosis per 100,000 people were attributed to the war in 2022. In the postwar period, the incidence is projected to decrease by 30% by 2023. The Tigray War reversed a two-decade decline in tuberculosis cases, causing a five-fold increase compared to the no-war scenario. Urgent interventions are needed to support tuberculosis prevention, testing, and treatment, particularly in key and vulnerable populations.

An Empirical Study on the Correction of Missing Data in Coastal Stationary Observation Time Series Data: Focusing on Jumunjin Observatory

An Empirical Study on the Correction of Missing Data in Coastal Stationary Observation Time Series Data: Focusing on Jumunjin Observatory

Setting the Initial Value for Single Exponential Smoothing and the Value of the Smoothing Constant for Forecasting Using Solver in Microsoft Excel

Although single exponential smoothing is a popular forecasting method for a wide range of applications involving stationary time series data, consistent rules about choosing the initial value and determining the value for the smoothing constant (α) are still required, because they directly impact the forecast accuracy. The purpose of this study is to mitigate these shortcomings. First, a new method for setting the initial value by weighting is derived, and its performance is compared with two other traditional methods. Second, the optimal (α) was automatically solved using Solver in Microsoft Excel, after which 𝛼 was determined by minimizing the mean squared error (MSE). This was accomplished by comparing the 𝛼 from Solver with step search by setting the smoothing constant by varying its value from 0.001 to 1 in increments of 0.001 and then choosing the optimal 𝛼 value from this range that has the lowest MSE. The experimental results show that 𝛼 from Solver and the optimal 𝛼 with step search are not different, and the initial value set by the proposed method outperformed the existing ones regarding the MSE.

Analysis and Prediction of the Contribution Rate of China's Tertiary Industry Based on ARIMA Model

In order to explore the evolution law and future state characteristics of China's tertiary industry contribution rate, this paper selects the contribution index data of China's tertiary industry to GDP from 1990 to 2020. It uses the ARIMA model to predict the future data of China's tertiary industry contribution index to GDP from 2021 to 2022. A stationary time series data is obtained through the stationary processing of time series, and finally, a prediction model of ARIMA (1,1,3) is established. The results show that the contribution index of China's tertiary industry to GDP shows a cyclical fluctuation of increase and decrease. The rising trend indicates that China's economic restructuring has achieved specific results. The validity of the predicted data is verified by using the actual tertiary industry contribution index data of GDP in 2020, proving the rationality of the predicted results. Furthermore, the predicted data in 2022 show a downward trend. On this basis, relevant suggestions are put forward to develop the tertiary industry vigorously and steadily promote the transformation and upgrading of economic structure.

Research on influencing factors and transmission mechanisms of green credit risk.

Controlling green credit risk is conducive to increasing the confidence of financial institutions, improving the enthusiasm of enterprises for green innovation, and promoting the sustainable development of green credit and the high-quality development of green economy. This paper puts government intervention, green technology innovation, and regulatory action into the same theoretical framework and puts forward the green credit risk transmission mechanisms which involve the transmission relationship and transmission path on the basis of the influencing factors. Then, this research uses stationary time series data (from the "China Statistical Yearbook," the "Statistical Yearbook" of various provinces, the annual reports of listed companies, etc.) to analyze the current situation of green credit risk in different regions. From the systematic perspective, this study verifies the transmission path of green credit risk and tests the rationality and effectiveness of the green credit risk transmission mechanisms. The research shows that the management of green credit risk requires the active actions of government departments, financial institutions, green enterprises, and regulatory departments.

Purchase and Analytics for Grace Marketing

In recent years development of computer systems were able to learn and adapt without following explicit instructions, by using algorithms and statistical models to analyze and draw inferences from patterns in data is known as machine learning.In this phase sales of different lubricants were predicted using a multivariate time series forecasting algorithm.Previously it showed that the model was accurate in predicting the engine oil sales for a particular time.Using Regressions the accuracy of sales prediction was less (74%) and the models like SVM and Random forest were showing signs of over fitting.The accuracy obtained in the multivariate time series forecasting was good than other algorithms.Time series algorithms are used extensively for forecasting time-based data.In time series ARIMA,SARIMA and SARIMAX are the common methods to forecast time based data.SARIMAX are efficient in forecasting data which has seasonality trends than ARIMA which are good in forecasting data which is stationary in nature Time series methods are extensively used for forecasting time based data.In time series ARIMA,SARIMA and SARIMAX are the common methods to forecast tie based data.ARIMA is the abbreviation of Auto Regressive Integrated Moving Average a model which explains a given time series model based on its lags and other values.SARIMAX is the abbreviation of Seasonal Auto Regressive Integrated Moving Average with Xegeneous variables. ARIMA model is best for forecasting stationary time series data and SARIMAX is used for forecasting values which is seasonal in nature.

Purchase and Analytics for Grace Marketing

In recent years development of computer systems were able to learn and adapt without following explicit instructions, by using algorithms and statistical models to analyze and draw inferences from patterns in data is known as machine learning.In this phase sales of different lubricants were predicted using a multivariate time series forecasting algorithm.Previously it showed that the model was accurate in predicting the engine oil sales for a particular time.Using Regressions the accuracy of sales prediction was less (74%) and the models like SVM and Random forest were showing signs of over fitting.The accuracy obtained in the multivariate time series forecasting was good than other algorithms.Time series algorithms are used extensively for forecasting time-based data.In time series ARIMA,SARIMA and SARIMAX are the common methods to forecast time based data.SARIMAX are efficient in forecasting data which has seasonality trends than ARIMA which are good in forecasting data which is stationary in nature Time series methods are extensively used for forecasting time based data.In time series ARIMA,SARIMA and SARIMAX are the common methods to forecast tie based data.ARIMA is the abbreviation of Auto Regressive Integrated Moving Average a model which explains a given time series model based on its lags and other values.SARIMAX is the abbreviation of Seasonal Auto Regressive Integrated Moving Average with Xegeneous variables. ARIMA model is best for forecasting stationary time series data and SARIMAX is used for forecasting values which is seasonal in nature.

The impact of world oil and food price shocks on the interdependence of Brazil and Russia: SVAR-DCC-GARCH model

This study seeks to identify the extent to which global oil and food price volatilities affected the interdependence of the Brazilian and Russian economies in the period from 1996 to 2021. The ARCH/GARCH framework was used to model the volatility of oil and food prices. The Structural Vector Autoregressive (SVAR) approach was used to ascertain the sensitivity of key economic indicators to oil and food shocks. The Impulse Response Function (IRF) was used to trace short-term effects over a period of 12 months. Subsequently, the multivariate dynamic conditional correlation DCC-GARCH model, created by Engle & Sheppard (2001), was used to model time-varying correlations of paired macroeconomic variables. This study contributes to the empirical literature in two fundamental ways. Firstly, it pairs the two largest oil and food producers in the BRICS bloc. Secondly, unlike some earlier studies, the applied methodology ensures the effectiveness of the results by using stationary time series data. The results show that Brazil and Russia have long-run spillover effects for all macroeconomic variables in response to both oil and food price shocks. Furthermore, money supply and exchange rate variables exhibited declining positive correlation coefficients during the global financial crisis of 2008–2009, but peaked in early 2020 due to the Covid-19 pandemic. As a corollary of the main findings, the researchers recommend that investors should diversify their portfolios beyond these two economies in order to minimize the risk of contagion during severe global crises.

Measuring Dispersion and Serial Dependence in Ordinal Time Series Based on the Cumulative Paired ϕ-Entropy

The family of cumulative paired -entropies offers a wide variety of ordinal dispersion measures, covering many well-known dispersion measures as a special case. After a comprehensive analysis of this family of entropies, we consider the corresponding sample versions and derive their asymptotic distributions for stationary ordinal time series data. Based on an investigation of their asymptotic bias, we propose a family of signed serial dependence measures, which can be understood as weighted types of Cohen’s , with the weights being related to the actual choice of . Again, the asymptotic distribution of the corresponding sample is derived and applied to test for serial dependence in ordinal time series. Using numerical computations and simulations, the practical relevance of the dispersion and dependence measures is investigated. We conclude with an environmental data example, where the novel -entropy-related measures are applied to an ordinal time series on the daily level of air quality.

The Stock Index Prediction Based on SVR Model with Bat Optimization Algorithm

Accurate stock market prediction models can provide investors with convenient tools to make better data-based decisions and judgments. Moreover, retail investors and institutional investors could reduce their investment risk by selecting the optimal stock index with the help of these models. Predicting stock index price is one of the most effective tools for risk management and portfolio diversification. The continuous improvement of the accuracy of stock index price forecasts can promote the improvement and maturity of China’s capital market supervision and investment. It is also an important guarantee for China to further accelerate structural reforms and manufacturing transformation and upgrading. In response to this problem, this paper introduces the bat algorithm to optimize the three free parameters of the SVR machine learning model, constructs the BA-SVR hybrid model, and forecasts the closing prices of 18 stock indexes in Chinese stock market. The total sample comes from 15 January 2016 (the 10th trading day in 2016) to 31 December 2020. We select the last 20, 60, and 250 days of whole sample data as test sets for short-term, mid-term, and long-term forecast, respectively. The empirical results show that the BA-SVR model outperforms the polynomial kernel SVR model and sigmoid kernel SVR model without optimized initial parameters. In the robustness test part, we use the stationary time series data after the first-order difference of six selected characteristics to re-predict. Compared with the random forest model and ANN model, the prediction performance of the BA-SVR model is still significant. This paper also provides a new perspective on the methods of stock index forecasting and the application of bat algorithms in the financial field.

Studying Changes on Stock Market Transactions Using Different Techniques for Multivariate Time Series

There are many studies dealt with univariate time series data, but the analysis of multivariate time series are rarely discussed. This article discusses the theoretical and numerical aspects of different techniques that analyze the multivariate time series data. These techniques are ANN, ARIMA, GLM and VARS models. All techniques are used to analyze the data that obtained from Egypt Stock Exchange Market. R program with many packages are used. These packages are the "neuralnet, nnet, forecast, MTS and vars". The process of measuring the accuracy of forecasting are investigated using the measures ME, ACF, MAE, MPE, RMSE, MASE, and MAPE. This is done for seasonal and non-seasonal time series data. Best ARIMA model with minimum error is constructed and tested. The lags order of the model are identified. Granger test for causality indicated that Exchange rate is useful for forecasting another time series. Also, the Instant test indicated that there is instantaneous causality between Exchange rate and other time series. For non-seasonal data, the NNAR() model is equivalent to ARIMA() model. Also, for seasonal data, the NNAR(p,P,0)[m] model is equivalent to an ARIMA(p,0,0)(P,0,0)[m] model. For these data, we concluded that the ANN and GLMs of fitting multivariate seasonal time series is better than multivariate non-seasonal time series. The transactions of Finance, Household and Chemicals sectors are significant for Exchange rate in non-seasonal time series case. The forecasts that based on stationary time series data are more smooth and accurate. VARS model is more accurate rather than VAR model for ARIMA (0,0,1). Forecasts of VAR values are predicted over short horizon, because the prediction over long horizon becomes unreliable or uniform.

On Order and Regime Determination of SETAR Model in Modelling Nonlinear Stationary Time Series Data Structure: Application to Lafia Rainfall Data, Nasarawa State, Nigeria

The linear time series model refers to the class of models for which fixed correlation parameters can fully explain the dependency between two random variables, but many real-life circumstances, such as monthly unemployment results, supplies and demands, interest rate, exchange rate, share prices, rainfall, etc., violate the assumption of linearity. For fitting and forecasting of nonlinear time series data, the self-exiting threshold autoregressive (SETAR) model was suggested. Using R to generate random nonlinear autoregressive data, a Monte Carlo simulation was performed, the SETAR model was fitted to the simulated data and Lafia rainfall data, Nasarawa State, Nigeria to determine the best regime orders and/or scheme number to make future forecast. Using Mean Square Error (MSE) and Akaike Information Criteria (AIC), the relative performance of models was examined. At a specific autoregressive order, regime order, sample size and step ahead, the model with minimum criteria was considered as the best. The results show that the best autoregressive and regime orders to be chosen are 3rd and 2nd [SETAR (3, 2)] respectively for fitting and forecasting nonlinear autoregressive time series data with small and moderate sample sizes. As the sample size increases, the output of the four models increases. Finally, it is shown that when sample size and number of steps forward are increased, the efficiency and forecasting capacity of the four models improves.

Parallel genetic algorithms for optimizing the SARIMA model for better forecasting of the NCDC weather data

Autoregressive Integrated Moving Average (ARIMA) and seasonal ARIMA (SARIMA) models are common techniques that are widely used in analysing and forecasting stationary and seasonal time series data. The three essential steps involved to construct ARIMA are identification, estimation, and checking the validity of the model. The most critical step followed in constructing the ARIMA model is model identification. However, overcoming the difficult local optima problem for both ARIMA and SARIMA is still challenging as there is no appropriate method to solve it. In this paper, the proposed parallel GA-SARIMA model is used to solve the problem of local optima, where the genetic algorithm (GA) is used at the initial stage to identify the order and estimation of the parameters for SARIMA. The National Climate Data Centre (NCDC) time series dataset is used for testing the efficiency of the final parallel GA-SARIMA model to forecast the mean temperature of India from 2000 to 2017. The GA algorithm is successfully implemented to solve the optimization problems by introducing better solutions suitable for SARIMA models. The results of the study showed that the implementation of the combined approach of parallel GA and SARIMA enhances the prediction accuracy of the model. The parallel GA-SARIMA method is particularly robust, faster and performs better than sequential SARIMA models in terms of running time and cost function values.

Empirical analysis of energy consumption and economic growth in Tanzania: based on Engel and Granger tests

Purpose - This article aims to investigate the effect of energy consumption on economic growth in Tanzania. It is a quantitative investigation that is structured by the time series data from the World Bank (WB) database which started from 1990 to 2019. The article uses variables of Energy consumption (EC) and Economic growth (GDP). The variables are measured in GDP (Constant US$) and EC (MTOE). Methodology – To obtain the significant estimated results, this study uses econometric tools for both theoretical and empirical analysis such Augmented Dickey-Fuller (ADF) test for identifying stationary and nonstationary time series data, Engel and Granger test for determination of the existence or absence of cointegration relationship, Vector Error Correction Model (VECM) for determining the speed of adjustment (ECT) and Classical Granger-causality test for a causal relationship between economic growth and consumption. Findings- The core findings from the study are; the cointegration relationship between Energy consumption (EC) and Economic growth (GDP), a bidirectional causal relationship between energy consumption (EC) and Economic growth (GDP) in Tanzania. Therefore, the study accepts the energy feedback hypothesis that revealed to exist both a long-run effect and short-run effect between the energy consumption and economic growth in Tanzania. Conclusion- The estimated results of this study provide the information to Tanzanian policymakers with a new dimensional approach to Tanzanian economic growth through an increase in energy consumption use. Although Tanzanian government has a huge and long term sustainable project of increasing energy power by adding 2115megawatts to Tanzanian national grid using the Stigler gorge or Julius Nyerere Hydroelectric power at Rufiji River but also Tanzania should invest to the short energy projects consumptions that can facilitate and improve the economic development of domestic hoods.