Time Series Forecasting Using Wavelet Denoising an Application to Saudi Stock Index

Time series modeling and analysis provides means of predicting the future and has been widely used in a variety of fields ranging from seismology for predicting earthquake and volcanic eruption, to finance for risk assessment, and to quantum information processing. The conventional integer order models can only capture short-range dependence; for example, Poisson processes, Markov processes, autoregressive (AR), moving average (MA), autoregressive moving average (ARMA) and autoregressive integrated moving average (ARIMA) processes. In time series analysis, one of the conventional assumptions is that the coupling between values at different time instants decreases rapidly as the time difference or distance increases. However, there are situations where strong coupling between values at different times exhibit properties of long range dependence which cannot be processed by the conventional time series analysis. Typical examples of long range dependence signals include financial time series, underwater noise, electroencephalography (EEG) signal, etc. ARFIMA, a fractional order signal processing technique, is the generalization of the conventional integer order techniques, namely, ARIMA and ARMA methods. Hence, it is capable of capturing both short-range dependence and long-range dependence in signals. Compared to conventional integer order models, the ARFIMA model gives a better fit and result when dealing with the data which possess the long range dependence property. In this paper, we investigate the application of the ARFIMA as well as AR methods to model EEG signals obtained from different brain channels. We analyze the resulting correlations for comparison the benefits of ARFIMA over AR on the EEG data exhibiting the long range dependency property. The results showed that the prediction results have a better performance compared to the conventional ARMA models.

A result of a real-life driving test observation usually consists of data that contains high irregularity. As a result, the shape of data trends from observations becomes difficult to know. Therefore, data that contain high irregularity in time series analysis are processed using the data smoothing method. In this study, a dataset of real-life driving tests observation of an electric vehicle is processed using the Simple Moving Average (SMA), Single Exponential Smoothing (SES), and Double Exponential Smoothing (DES) methods. Furthermore, the evaluation of each data smoothing results using Mean Arctangent Absolute Percentage Error (MAAPE). The results of data smoothing show that the lowest MAAPE is 0.252, which is generated through the SES method with data smoothing constant of 0.9. This indicates that SES with data smoothing constant of 0.9 produces data smoothing that is closest to the original data or has the smallest deviation with the original data, but data trends are difficult to know because they still contain high irregularity. Conversely, the data trend is clearly visible by the results of SMA data smoothing with a period constant of 250 with a MAAPE value of 0.793, despite having the greatest deviation with the original data. For the purpose of knowing trends in this study, SMA with a period constant of 250 shows the best results. For related studies, this trend from data smoothing could be used as a standard cycle (driving cycle in certain environments) on components and electric vehicles test.

The application of time series analysis to describe the dynamic movements of suspension bridges

The quarterly electricity consumption curve shows certain regularity due to factors such as temperature and holidays. The ARMA(Autoregressive Moving Average) model has a good fitting ability for such time series, but the quarterly electricity consumption is also affected by economic growth. It is an ascending time series, which is a nonstationary time series. It cannot be directly predicted by ARMA model. Therefore, it is necessary to make finite difference processing to the original time series to stationary time series. The original time series is suitable for ARIMA(Autoregressive Integrated Moving Average) model. Any prediction model can not avoid the generation of residuals. The K-means clustering algorithm is used to divide the residual sequence state. By exploring the relationship between states at different moments, the transition matrix is established to predict the probability distribution of the residual state at the next moment. The predicted state is restored to the residual prediction value, and the prediction of the residual is completed to implement the correction of the original prediction value. That is, by predicting the residual by establishing a Markov model, the predicted value of the ARIMA model is corrected, and the prediction accuracy is improved.

Fuel is an important part of vehicles and machinery where sales demand is very high and has various fluctuations. The uncertainty in these fuel sales patterns poses serious problems in inventory management and fuel distribution planning in Indonesia, which can result in excess stock or fuel scarcity in various regions. Additionally, changing trends in vehicle usage and the impact of the COVID-19 pandemic have made accurate sales predictions increasingly difficult. Therefore, this research aims to understand the current and future sales patterns and trends of fuel sales in Indonesia. Careful analysis of prices and other factors such as data processing and other variables is required. This study uses time series analysis methods and compares four models, namely Long Short-Term Memory (LSTM), FB Prophet, Simple Moving Average (SMA), and Exponential Moving Average (EMA). By comparing the results using statistics such as Root Mean Square Error (RMSE) and Mean Absolute Percentage Error (MAPE) over various prediction time frames, we assessed the patterns of each model. The results of the analysis show that the LSTM model outperformed all other methods with the lowest MAPE for the prediction of gasoline in the next 31 days, which is 17.11%, while the FB Prophet outperformed all other methods with the lowest MAPE for the prediction of diesel in the next 31 days, which is 18.32%. Although the LSTM model generally outperformed all other algorithms, the FB Prophet model can be used to predict future trends, such as increased use of diesel and decreased use of gasoline which are expected to last within one year. This analysis also provides insights for choosing the right model for a time series problem, including the characteristics of the data to be predicted and analyzed, as well as the assumptions of stationarity and normality of the data. The results of this study indicate that machine learning algorithms can improve the accuracy of time series predictions significantly compared to traditional statistical methods.

The stock index is an important indicator to measure stock market fluctuation, with a guiding role for investors’ decision-making, thus being the object of much research. However, the stock market is affected by uncertainty and volatility, making accurate prediction a challenging task. We propose a new stock index forecasting model based on time series decomposition and a hybrid model. Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN) decomposes the stock index into a series of Intrinsic Mode Functions (IMFs) with different feature scales and trend term. The Augmented Dickey Fuller (ADF) method judges the stability of each IMFs and trend term. The Autoregressive Moving Average (ARMA) model is used on stationary time series, and a Long Short-Term Memory (LSTM) model extracts abstract features of unstable time series. The predicted results of each time sequence are reconstructed to obtain the final predicted value. Experiments are conducted on four stock index time series, and the results show that the prediction of the proposed model is closer to the real value than that of seven reference models, and has a good quantitative investment reference value.

Univariate time-series analyses were conducted on stable carbon isotope ratios obtained from tree-ring cellulose. We looked for the presence and structure of autocorrelation. Significant autocorrelation violates the statistical independence assumption and biases hypothesis tests. Its presence would indicate the existence of lagged physiological effects that persist for longer than the current year. We analyzed data from 28 trees (60-85 years old; mean = 73 years) of western white pine (Pinus monticola Dougl.), ponderosa pine (Pinus ponderosa Laws.), and Douglas-fir (Pseudotsuga menziesii (Mirb.) Franco var. glauca) growing in northern Idaho. Material was obtained by the stem analysis method from rings laid down in the upper portion of the crown throughout each tree's life. The sampling protocol minimized variation caused by changing light regimes within each tree. Autoregressive moving average (ARMA) models were used to describe the autocorrelation structure over time. Three time series were analyzed for each tree: the stable carbon isotope ratio (delta(13)C); discrimination (delta); and the difference between ambient and internal CO(2) concentrations (c(a) - c(i)). The effect of converting from ring cellulose to whole-leaf tissue did not affect the analysis because it was almost completely removed by the detrending that precedes time-series analysis. A simple linear or quadratic model adequately described the time trend. The residuals from the trend had a constant mean and variance, thus ensuring stationarity, a requirement for autocorrelation analysis. The trend over time for c(a) - c(i) was particularly strong (R(2) = 0.29-0.84). Autoregressive moving average analyses of the residuals from these trends indicated that two-thirds of the individual tree series contained significant autocorrelation, whereas the remaining third were random (white noise) over time. We were unable to distinguish between individuals with and without significant autocorrelation beforehand. Significant ARMA models were all of low order, with either first- or second-order (i.e., lagged 1 or 2 years, respectively) models performing well. A simple autoregressive (AR(1)), model was the most common. The most useful generalization was that the same ARMA model holds for each of the three series (delta(13)C, delta, c(a) - c(i)) for an individual tree, if the time trend has been properly removed for each series. The mean series for the two pine species were described by first-order ARMA models (1-year lags), whereas the Douglas-fir mean series were described by second-order models (2-year lags) with negligible first-order effects. Apparently, the process of constructing a mean time series for a species preserves an underlying signal related to delta(13)C while canceling some of the random individual tree variation. Furthermore, the best model for the overall mean series (e.g., for a species) cannot be inferred from a consensus of the individual tree model forms, nor can its parameters be estimated reliably from the mean of the individual tree parameters. Because two-thirds of the individual tree time series contained significant autocorrelation, the normal assumption of a random structure over time is unwarranted, even after accounting for the time trend. The residuals of an appropriate ARMA model satisfy the independence assumption, and can be used to make hypothesis tests.

The Stochastic Oscillator which is one of the leading indicators has the disadvantage of opening the gap for false signals. To minimize false signals, the smoothing process is carried out using the Moving Average. Stochastic Oscillator is usually combined with SMA (Simple Moving Average). But SMA has the disadvantage of giving the same weight to all data, even though in reality the data that best reflects the next value is the last data. This makes the basis of weighting the WMA (Weighted Moving Average) method.This study aims to test the combination of Stochastic Oscillator with SMA and WMA and use the best combination to predict the trends that will occur and trading decisions taken from the results of these predictions. The research samples were ANTM, BBRI, and GIAA stocks from November 9 2015 to November 9, 2018.The results show a combination of Stochastic Oscillator and WMA is a better combination of predictions than Stochastic Oscillator and SMA because it has a smaller MSE value. Based on the comparison of signal accuracy based on Overbought and Oversold, the best period of combination of Stochastic Oscillator and WMA is period 25. From the predicted trend that will occur with a combination of Stochastic Oscillator and WMA period 25 a decision is made to buy shares for ANTM shares, sell shares for BBRI shares, and waiting for a buy signal for GIAA shares.Keywords: Stochastic Oscillator, SMA, WMA, Predictions, Trends

Background/Objective: To provide an efficient predictive technique to foresee future workload as well as to handle the resources efficiently by performing hybrid auto scaling for Cloud applications. Cloud applications might expertise completely different workload at different times, automatic provisioning has to work with efficiency at any point of time. Auto scaling is a feature of cloud computing that potentially scale the resources in line on demand. Considering this expectation, they are generally categorized into Reactive scaling which adds or reduces resources based on a fixed threshold value. The predictive scaling is used provide necessary scaling actions beforehand. Methods/Statistical Analysis: To perform the hybrid auto scaling (reactive plus predictive auto scaling), a time series technique should be used. Auto-regressive Moving Average (ARMA) model, the Exponential Smoothing (ES) model, the Autoregressive model (AR), the Moving Average model (MA) and the Trend- Adjusted Exponential Smoothing (TAES), Auto Regressive Integrated Moving Average (ARIMA) Time-series model, Naïve bayes algorithm, Recurrent Neural Network- Long Short Term Memory (RNN-LSTM), Independent Recurrent Neural Network (IndRNN) are time series techniques used to foresee the future workload. To find the effectiveness of predictive techniques, Mean Absolute Error (MAE), Mean Squared Error (MSE) and Mean Absolute Percentage Error (MAPE) performance metrics are evaluated. Findings: Based on the evaluation, IndRNN gives the minimum error rate. IndRNN is used to predict the future resource requisites in order to ascertain adequate resource are available ahead of time. Application: The predicted result from IndRNN method is integrated on private cloud to autoscale the resources for cloud applications. Keywords: Cloud Applications, Hybrid Autoscaling, Independent Recurrent Neural Network (IndRNN), Private Cloud, Workload

Three important parametric models for describing the correlation functions and spectra of stationary stochastic processes are the autoregressive (AR), moving average (MA), and autoregressive-moving average (ARMA) models. Quite recently, the MATLAB toolbox “ARMASA” has been made publicly available. This toolbox provides state-of-the-art algorithms to perform automatic identification and selection between the models based on the estimated prediction error. ARMASA works on a single segment of data, whereas in some applications, the data are available as multiple segments. We could process each segment independently and average the estimated autocorrelation functions or spectra afterward. Better performance, however, can be expected when all segments are processed simultaneously, for two reasons. Initially, the bias in the estimated model parameters depends on the number of observations in a segment. Averaging models from segments does not reduce this bias, in contrast to identification from all the data at once. In either case, the variance of the estimated model parameters will decrease. By considering all the data at once this variance reduction can be considered in the order selection stage, decreasing the selection bias. In this paper, we extend the parameter estimation algorithms of the ARMASA toolbox to the case of multiple segments. AR parameter estimation from segments has been considered before, but not for the MA and ARMA models. In addition, in the AR case, model order selection can be done easily when the segments are independent. But, in the application we are primarily interested in, the segments are formed by lines of scanning transmission electron microscopy (STEM) images, which can be correlated with each other. Because the correlation among data segments influences the effective number of independent observations available it becomes necessary to estimate that number. This is not an easy problem in general. For observations from a stochastic process with an isotropic 2-D autocorrelation function we can, however, formulate an accurate estimator in terms of the line autocorrelation function. This situation arises, for example, in STEM images of amorphous specimens. From the AR model identification for segments, the extension to the MA and ARMA models is rather straightforward because MA and ARMA algorithms are based on Durbin's methods, whose first step is the estimation of a long AR model. We compare the segment-based algorithms to conventional ARMASA with simulations of stationary stochastic processes. An illustrative example involving simulated STEM images shows large potential benefits.

This research focuses on optimizing a neural network model for stock price prediction using Particle Swarm Optimization (PSO), considering the inherent risks and potential high returns associated with stock investment. Given the challenges posed by stock price volatility, this study combines Moving Average (MA) a fundamental statistical technique in stock market analysis with advanced data mining approaches, specifically neural networks and PSO, to enhance prediction accuracy. The primary objective is to improve the efficiency of neural networks by minimizing error rates and equipping investors with more reliable tools for financial decision-making. The proposed methodology involves converting historical stock price data into a Simple Moving Average (SMA) over a 5-day period, followed by optimizing a neural network model using PSO. This optimization process fine-tunes key parameters, particularly the weight distributions of various stock market indicators, including Open SMA, High SMA, Low SMA, and Close SMA. Model performance is evaluated using Root Mean Square Error (RMSE) as a validation metric. The findings indicate a significant enhancement in the predictive accuracy of the neural network model after PSO optimization. The optimal configuration is identified in a two-layer neural network with a specific node arrangement. This optimized model not only improves stock price forecasting precision but also has practical implications for investors and financial analysts in risk management and profit maximization.

Introducción. Las Enfermedades Transmitidas por Alimentos ( ETA), constituyen un problema de salud pública de relevancia mundial, siendo motivo de vigilancia epidemiológica y son el resultado del consumo de alimentos que contienen toxinas o microorganismos patógenos vivos. El objetivo de este estudio es analizar las series temporales de Salmonella spp. para el periodo 2014-2022 en Chile y desarrollar un modelo predictivo de Media Móvil Autorregresiva (ARIMA). Métodos. Se realizó una descomposición de la serie para estudiar tendencia y estacionalidad. Se utilizó la prueba de Dickey-Fuller para estacionalidad y Kruskall-Wallis para comparación de grupos. Se aplicó el modelo ARIMA para realizar una predicción de casos en un año adelante. Resultados. La serie de estudio para Salmonella spp. tuvo un comportamiento estacional sin diferencias significativas entre grupos (periodos). El modelo ARIMA tuvo un buen desempeño para predecir casos en una serie continua. Conclusiones. El análisis de series temporales en epidemiología es una herramienta valiosa para prever futuros brotes o epidemias en el territorio nacional. El modelo ARIMA tiene un buen desempeño en la serie estacional analizada para Salmonella spp en muestras de deposición.

Index of stocks listed on the Indonesia Stock Exchange (IDX) there are conventional that one of them is the Composite Stock Price Index (CSPI) and the index of stocks that are sharia is the Jakarta Islamic Index (JII). In its movement, the value of CSPI and JII often increases and decreases that are influenced by several factors, one of which is the world oil price of Brent Crude Oil . To see the value of CSPI and JII conditions during the period of the next few months it takes the model equations. Because the third such data included in the time series data, we used time series analysis with the appropriate method is the Vector Autoregressive Exogenous (VARX). VARX( p , q ) is a model of multivariate time series that consists of several endogenous variable of the time series order p with q adding exogenous variables. The purpose of this study is to obtain an appropriate VARX models and forecasting for data CSPI and JII. The model to predict CSPI and JII with exogenous variables that influence the world oil prices of Brent Crude Oil is VARX(1,1). Test parameters for exogenous variables in the model VARX(1,1) not significant at significance level α = 5%, but this result could be ignored and continues to testing residual assumptions. Residual model VARX(1,1) satisfies the assumption of white noise and multivariate normal distribution, in order to obtain results as very good forecast that with each MAPE value for CSPI and JII forecast of 2,71% and 3,63%. Keywords : CPSI, JII, Brent Crude Oil , VARX, MAPE.

This article presents a comprehensive study of sales predictions using time series analysis, focusing on a case study of Walmart sales data. The aim of this study is to evaluate the effectiveness of various time series forecasting techniques in predicting weekly sales data for Walmart stores. Leveraging a dataset from Kaggle comprising weekly sales data from various Walmart stores around the United States, this study explores the effectiveness of time series analysis in forecasting future sales trends. Various time series analysis techniques, including Auto Regressive Integrated Moving Average (ARIMA), Seasonal Auto Regressive Integrated Moving Average (SARIMA), Prophet, Exponential Smoothing, and Gaussian Processes, are applied to model and forecast Walmart sales data. By comparing the performance of these models, the study seeks to identify the most accurate and reliable methods for forecasting retail sales, thereby providing valuable insights for improving sales predictions in the retail sector. The study includes an extensive exploratory data analysis (EDA) phase to preprocess the data, detect outliers, and visualize sales trends over time. Additionally, the article discusses the partitioning of data into training and testing sets for model evaluation. Performance metrics such as Root Mean Squared Error (RMSE) and Mean Absolute Error (MAE) are utilized to compare the accuracy of different time series models. The results indicate that Gaussian Processes outperform other models in terms of accuracy, with an RMSE of 34,116.09 and an MAE of 25,495.72, significantly lower than the other models evaluated. For comparison, ARIMA and SARIMA models both yielded an RMSE of 555,502.2 and an MAE of 462,767.3, while the Prophet model showed an RMSE of 567,509.2 and an MAE of 474,990.8. Exponential Smoothing also performed well with an RMSE of 555,081.7 and an MAE of 464,110.5. These findings suggest the potential of Gaussian Processes for accurate sales forecasting. However, the study also highlights the strengths and weaknesses of each forecasting methodology, emphasizing the need for further research to refine existing techniques and explore novel modeling approaches. Overall, this study contributes to the understanding of time series analysis in retail sales forecasting and provides insights for improving future forecasting endeavors.

Comparison of the ARMA, ARIMA, and the autoregressive artificial neural network models in forecasting the monthly inflow of Dez dam reservoir