Search results for: time series

Authors: Hisyam Hidayatullah

Abstract:

This world events consciously or not realize everything has a pattern, until the events of the universe according to the Big Bang theory of the solar system which makes so regular in the rotation. The author would like to create a results curve area between the quadratic function y=kx2 and line y=ka2 using GeoGebra application version 4.2. This paper can provide a series that is no less interesting with Fourier series, so that will add new material about the series can be calculated with sigma notation. In addition, the ranks of the unique natural numbers of extensive changes in established areas. Finally, this paper provides analytical and geometric proof of the vast area in between the lines and curves that give the area is formed by y=ka2 dan kurva y=kx2, x-axis, line x=√a and x=-√a make a series of numbers for k=1 and a ∈ original numbers. ∑_(i=0)^n=(4n√n)/3=0+4/3+(8√2)/3+4√3+⋯+(4n√n)/3. The author calls the series “H154M”.

Keywords: sequence, series, sigma notation, application GeoGebra

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Authors: Ali Ben Abbes, Imed Riadh Farah

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Due to the considerable advances in Multi-Temporal Satellite Images (MTSI), remote sensing application became more accurate. Recently, many advances in modeling MTSI are developed using various models. The purpose of this article is to present an overview of studies using Hidden Markov Model (HMM). First of all, we provide a background of using HMM and their applications in this context. A comparison of the different works is discussed, and possible areas and challenges are highlighted. Secondly, we discussed the difference on vegetation monitoring as well as urban growth. Nevertheless, most research efforts have been used only stationary data. From another point of view, in this paper, we describe a new non-stationarity HMM, that is defined with a set of parts of the time series e.g. seasonal, trend and random. In addition, a new approach giving more accurate results and improve the applicability of the HMM in modeling a non-stationary data series. In order to assess the performance of the HMM, different experiments are carried out using Moderate Resolution Imaging Spectroradiometer (MODIS) NDVI time series of the northwestern region of Tunisia and Landsat time series of tres Cantos-Madrid in Spain.

Keywords: multi-temporal satellite image, HMM , nonstationarity, vegetation, urban

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Authors: Budi Nurani Ruchjana, Atje Setiawan Abdullah, I. Gede Nyoman Mindra Jaya, Eddy Hermawan

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In this paper, we propose the application package to estimate parameters of spatiotemporal model based on the multivariate time series analysis using the R open-source software. We build packages mainly to estimate the parameters of the Generalized Space Time Autoregressive (GSTAR) model. GSTAR is a combination of time series and spatial models that have parameters vary per location. We use the method of Ordinary Least Squares (OLS) and use the Mean Average Percentage Error (MAPE) to fit the model to spatiotemporal real phenomenon. For case study, we use oil production data from volcanic layer at Jatibarang Indonesia or climate data such as rainfall in Indonesia. Software R is very user-friendly and it is making calculation easier, processing the data is accurate and faster. Limitations R script for the estimation of model parameters spatiotemporal GSTAR built is still limited to a stationary time series model. Therefore, the R program under windows can be developed either for theoretical studies and application.

Keywords: GSTAR Model, MAPE, OLS method, oil production, R software

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Authors: Karim Hamidi Machekposhti, Hossein Sedghi, Abdolrasoul Telvari, Hossein Babazadeh

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Rainfall and runoff phenomenon is a chaotic and complex outcome of nature which requires sophisticated modelling and simulation methods for explanation and use. Time Series modelling allows runoff data analysis and can be used as forecasting tool. In the paper attempt is made to model river runoff data and predict the future behavioural pattern of river based on annual past observations of annual river runoff. The river runoff analysis and predict are done using ARIMA model. For evaluating the efficiency of prediction to hydrological events such as rainfall, runoff and etc., we use the statistical formulae applicable. The good agreement between predicted and observation river runoff coefficient of determination (R²) display that the ARIMA (4,1,1) is the suitable model for predicting Karkheh River runoff at Iran.

Keywords: time series modelling, ARIMA model, river runoff, Karkheh River, CLS method

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Authors: Cheng-yu Hsieh, Bo Zhang, Ahmed Hambaba

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Stock market prediction has long been an area of interest for both expert analysts and investors, driven by its complexity and the noisy, volatile conditions it operates under. This research examines the efficacy of combining the Patch Time Series Transformer (PatchTST) with wavelet transforms, specifically focusing on Haar and Daubechies wavelets, in forecasting the adjusted closing price of the S&P 500 index for the following day. By comparing the performance of the augmented PatchTST models with traditional predictive models such as Recurrent Neural Networks (RNNs), Convolutional Neural Networks (CNNs), Long Short-Term Memory (LSTM) networks, and Transformers, this study highlights significant enhancements in prediction accuracy. The integration of the Daubechies wavelet with PatchTST notably excels, surpassing other configurations and conventional models in terms of Mean Absolute Error (MAE) and Mean Squared Error (MSE). The success of the PatchTST model paired with Daubechies wavelet is attributed to its superior capability in extracting detailed signal information and eliminating irrelevant noise, thus proving to be an effective approach for financial time series forecasting.

Keywords: deep learning, financial forecasting, stock market prediction, patch time series transformer, wavelet transform

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Authors: Himayatullah Khan, Alena Fedorova

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The present paper analyses the income-consumption relationships in Pakistan using annual time series data from 1980-81 to 2010-1. The paper uses the Augmented Dickey-Fuller test to check the unit root and stationarity in these two time series. The paper finds that the two time series are nonstationary but stationary at their first difference levels. The Augmented Engle-Granger test and the Cointegrating Regression Durbin-Watson test imply that the two time series of consumption and income are cointegrated and that long-run marginal propensity to consume is 0.88 which is given by the estimated (static) equilibrium relation. The paper also used the error correction mechanism to find out to model dynamic relationship. The purpose of the ECM is to indicate the speed of adjustment from the short-run equilibrium to the long-run equilibrium state. The results show that MPC is equal to 0.93 and is highly significant. The coefficient of Engle-Granger residuals is negative but insignificant. Statistically, the equilibrium error term is zero, which suggests that consumption adjusts to changes in GDP in the same period. The short-run changes in GDP have a positive impact on short-run changes in consumption. The paper concludes that we may interpret 0.93 as the short-run MPC. The pair-wise Granger Causality test shows that both GDP and consumption Granger cause each other.

Keywords: cointegrating regression, Augmented Dickey Fuller test, Augmented Engle-Granger test, Granger causality, error correction mechanism

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Authors: Harold P. Villota, Alejandro Osorio B.

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The energy meteorology is an area for study energy complementarity and the use of renewable sources in interconnected systems. Due to diversify the energy matrix in Colombia with wind sources, is necessary to know the data bases about this one. However, the time series given by 260 automatic weather stations have empty, and no apply data, so the purpose is to fill the time series selecting two years to characterize, impute and use like base to complete the data between 2005 and 2020.

Keywords: complementarity, wind speed, renewable, colombia, characteri, characterization, imputation

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Authors: Akinbo Razak Yinka, Adesanya Kehinde Kazeem, Oladokun Oluwagbenga Peter

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Time series data are sequences of observations collected over a period of time. Such data can be used to predict health outcomes, such as disease progression, mortality, hospitalization, etc. The Statistical approach is based on mathematical models that capture the patterns and trends of the data, such as autocorrelation, seasonality, and noise, while Neural methods are based on artificial neural networks, which are computational models that mimic the structure and function of biological neurons. This paper compared both parametric and non-parametric time series models of patients treated for malaria in Maternal and Child Health Centres in Lagos State, Nigeria. The forecast methods considered linear regression, Integrated Moving Average, ARIMA and SARIMA Modeling for the parametric approach, while Multilayer Perceptron (MLP) and Long Short-Term Memory (LSTM) Network were used for the non-parametric model. The performance of each method is evaluated using the Mean Absolute Error (MAE), R-squared (R2) and Root Mean Square Error (RMSE) as criteria to determine the accuracy of each model. The study revealed that the best performance in terms of error was found in MLP, followed by the LSTM and ARIMA models. In addition, the Bootstrap Aggregating technique was used to make robust forecasts when there are uncertainties in the data.

Keywords: ARIMA, bootstrap aggregation, MLP, LSTM, SARIMA, time-series analysis

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Authors: Monika Chuchro

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This paper presents a preliminary attempt to apply classification of time series using meta-clusters in order to improve the quality of regression models. In this case, clustering was performed as a method to obtain a subgroups of time series data with normal distribution from inflow into waste water treatment plant data which Composed of several groups differing by mean value. Two simple algorithms: K-mean and EM were chosen as a clustering method. The rand index was used to measure the similarity. After simple meta-clustering, regression model was performed for each subgroups. The final model was a sum of subgroups models. The quality of obtained model was compared with the regression model made using the same explanatory variables but with no clustering of data. Results were compared by determination coefficient (R2), measure of prediction accuracy mean absolute percentage error (MAPE) and comparison on linear chart. Preliminary results allows to foresee the potential of the presented technique.

Keywords: clustering, data analysis, data mining, predictive models

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Authors: Ilaria Lucrezia Amerise

Abstract:

Electricity markets throughout the world have undergone substantial changes. Accurate, reliable, clear and comprehensible modeling and forecasting of different variables (loads and prices in the first instance) have achieved increasing importance. In this paper, we describe the actual state of the art focusing on reg-SARMA methods, which have proven to be flexible enough to accommodate the electricity price/load behavior satisfactory. More specifically, we will discuss: 1) The dichotomy between point and interval forecasts; 2) The difficult choice between stochastic (e.g. climatic variation) and non-deterministic predictors (e.g. calendar variables); 3) The confrontation between modelling a single aggregate time series or creating separated and potentially different models of sub-series. The noteworthy point that we would like to make it emerge is that prices and loads require different approaches that appear irreconcilable even though must be made reconcilable for the interests and activities of energy companies.

Keywords: interval forecasts, time series, electricity prices, reg-SARIMA methods

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Authors: Wiem Gadri

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This study delves into the intriguing properties of Pisot and Salem numbers within the framework of formal Laurent series over finite fields, a domain where these numbers’ spectral charac-teristics, Λm(β) and lm(β), have yet to be fully explored. Utilizing a methodological approach that combines algebraic number theory with the analysis of power series, we extend the foundational work of Erdos, Joo, and Komornik to this new setting. Our research uncovers bounds for lm(β), revealing how these depend on the degree of the minimal polynomial of β and thus offering a novel characterization of Pisot and Salem formal power series. The findings significantly contribute to our understanding of these numbers, highlighting their distribution and properties in the context of formal power series. This investigation not only bridges number theory with formal power series analysis but also sets the stage for further interdisciplinary research in these areas.

Keywords: Pisot numbers, Salem numbers, formal power series, over a finite field

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Authors: Tehreem Fatima, Enjun Xia

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The research investigates the relationship between total oil consumption and transport oil consumption, GDP, oil price, and oil reserve in order to forecast future oil demand in China. Annual time series data is used over the period of 1980 to 2015, and for this purpose, an oil demand function is estimated by applying structural time series model (STSM). The technique also uncovers the Underline energy demand trend (UEDT) for China oil demand and GDP, oil reserve, oil price and UEDT are considering important drivers of China oil demand. The long-run elasticity of total oil consumption with respect to GDP and price are (0.5, -0.04) respectively while GDP, oil reserve, and price remain (0.17; 0.23; -0.05) respectively. Moreover, the Estimated results of long-run elasticity of transport oil consumption with respect to GDP and price are (0.5, -0.00) respectively long-run estimates remain (0.28; 37.76;-37.8) for GDP, oil reserve, and price respectively. For both model estimated underline energy demand trend (UEDT) remains nonlinear and stochastic and with an increasing trend of (UEDT) and based on estimated equations, it is predicted that China total oil demand somewhere will be 9.9 thousand barrel per day by 2025 as compare to 9.4 thousand barrel per day in 2015, while transport oil demand predicting value is 9.0 thousand barrel per day by 2020 as compare to 8.8 thousand barrel per day in 2015.

Keywords: china, forecasting, oil, structural time series model (STSM), underline energy demand trend (UEDT)

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Authors: Sandeep Kaur Chouhan, Jatinderdeep Kaur, S. S. Bhatia

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The existence of sine and cosine series as a Fourier series, their L1-convergence seems to be one of the difficult question in theory of convergence of trigonometric series in L1-metric norm. In the literature so far available, various authors have studied the L1-convergence of cosine and sine trigonometric series with special coefficients. In this paper, we present a modified cosine and sine sums and criterion for L1-convergence of these modified sums is obtained. Also, a necessary and sufficient condition for the L1-convergence of the cosine and sine series is deduced as corollaries.

Keywords: conjugate Dirichlet kernel, Dirichlet kernel, L1-convergence, modified sums

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Authors: Yaxin Bi

Abstract:

Accurate prediction and understanding of the evolution mechanisms of earthquakes remain challenging in the fields of geology, geophysics, and seismology. This study leverages Long Short-Term Memory (LSTM) networks and Generative Adversarial Networks (GANs), a generative model tailored to time-series data, for generating synthetic time series data based on Swarm satellite data, which will be used for detecting seismic anomalies. LSTMs demonstrated commendable predictive performance in generating synthetic data across multiple countries. In contrast, the GAN models struggled to generate synthetic data, often producing non-informative values, although they were able to capture the data distribution of the time series. These findings highlight both the promise and challenges associated with applying deep learning techniques to generate synthetic data, underscoring the potential of deep learning in generating synthetic electromagnetic satellite data.

Keywords: LSTM, GAN, earthquake, synthetic data, generative AI, seismic precursors

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Authors: Mahdi Daghmhehci Firoozjaei, Minchang Kim, Dima Alhadidi

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In this paper, we present a power profiling model for smart grid consumers based on real time load data acquired smart meters. It profiles consumers’ power consumption behaviour using the dynamic time warping (DTW) clustering algorithm. Due to the invariability of signal warping of this algorithm, time-disordered load data can be profiled and consumption features be extracted. Two load types are defined and the related load patterns are extracted for classifying consumption behaviour by DTW. The classification methodology is discussed in detail. To evaluate the performance of the method, we analyze the time-series load data measured by a smart meter in a real case. The results verify the effectiveness of the proposed profiling method with 90.91% true positive rate for load type clustering in the best case.

Keywords: power profiling, user privacy, dynamic time warping, smart grid

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Authors: A. Buruzs, M. F. Hatwágner, A. Torma, L. T. Kóczy

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The development, operation and maintenance of Integrated Waste Management Systems (IWMS) affects essentially the sustainable concern of every region. The features of such systems have great influence on all of the components of sustainability. In order to reach the optimal way of processes, a comprehensive mapping of the variables affecting the future efficiency of the system is needed such as analysis of the interconnections among the components and modelling of their interactions. The planning of a IWMS is based fundamentally on technical and economical opportunities and the legal framework. Modelling the sustainability and operation effectiveness of a certain IWMS is not in the scope of the present research. The complexity of the systems and the large number of the variables require the utilization of a complex approach to model the outcomes and future risks. This complex method should be able to evaluate the logical framework of the factors composing the system and the interconnections between them. The authors of this paper studied the usability of the Fuzzy Cognitive Map (FCM) approach modelling the future operation of IWMS’s. The approach requires two input data set. One is the connection matrix containing all the factors affecting the system in focus with all the interconnections. The other input data set is the time series, a retrospective reconstruction of the weights and roles of the factors. This paper introduces a novel method to develop time series by content analysis.

Keywords: content analysis, factors, integrated waste management system, time series

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Authors: Farhad Asadi, Mohammad Javad Mollakazemi, Aref Ghafouri

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Recent research in neural networks science and neuroscience for modeling complex time series data and statistical learning has focused mostly on learning from high input space and signals. Local linear models are a strong choice for modeling local nonlinearity in data series. Locally weighted projection regression is a flexible and powerful algorithm for nonlinear approximation in high dimensional signal spaces. In this paper, different learning scenario of one and two dimensional data series with different distributions are investigated for simulation and further noise is inputted to data distribution for making different disordered distribution in time series data and for evaluation of algorithm in locality prediction of nonlinearity. Then, the performance of this algorithm is simulated and also when the distribution of data is high or when the number of data is less the sensitivity of this approach to data distribution and influence of important parameter of local validity in this algorithm with different data distribution is explained.

Keywords: local nonlinear estimation, LWPR algorithm, online training method, locally weighted projection regression method

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Authors: K. Subbaiah

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Friction stir welding is a solid state welding process. Friction stir welding process eliminates the defects found in fusion welding processes. It is environmentally friend process. 5000 and 6000 series aluminum alloys are widely used in the transportation industries. The Al-Mg-Mn (5000) and Al-Mg-Si (6000) alloys are preferably offer best combination of use in Marine construction. The medium strength and high corrosion resistant 5000 series alloys are the aluminum alloys, which are found maximum utility in the world. In this review, the tool pin profile, process parameters such as hardness, yield strength and tensile strength, and microstructural evolution of friction stir welding of Al-Mg alloys 5000 Series and 6000 series have been discussed.

Keywords: 5000 series and 6000 series Al alloys, friction stir welding, tool pin profile, microstructure and properties

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Authors: Houda Najeh, Stéphane Ploix, Mahendra Pratap Singh, Karim Chabir, Mohamed Naceur Abdelkrim

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Building systems are highly vulnerable to different kinds of faults and failures. In fact, various faults, failures and human behaviors could affect the building performance. This paper tackles the detection of unreliable sensors in buildings. Different literature surveys on diagnosis techniques for sensor grids in buildings have been published but all of them treat only bias and outliers. Occurences of data gaps have also not been given an adequate span of attention in the academia. The proposed methodology comprises the automatic thresholding for data gap detection for a set of heterogeneous sensors in instrumented buildings. Sensor measurements are considered to be regular time series. However, in reality, sensor values are not uniformly sampled. So, the issue to solve is from which delay each sensor become faulty? The use of time series is required for detection of abnormalities on the delays. The efficiency of the method is evaluated on measurements obtained from a real power plant: an office at Grenoble Institute of technology equipped by 30 sensors.

Keywords: building system, time series, diagnosis, outliers, delay, data gap

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Authors: Jatinderdeep Kaur

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In this paper, the results of Kano from one-dimensional cosine and sine series are extended to two-dimensional cosine and sine series. To extend these results, some classes of coefficient sequences such as the class of semi convexity and class R are extended from one dimension to two dimensions. Under these extended classes, I have checked the function f(x,y) is two dimensional Fourier Cosine and Sine series or equivalently it represents an integrable function. Further, some results are obtained which are the generalization of Moricz's results.

Keywords: conjugate dirichlet kernel, conjugate fejer kernel, fourier series, semi-convexity

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Authors: Slobodan B. Tričković

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We present the results concerned with trigonometric series that include sine and cosine functions with a parameter appearing in the denominator. We derive two types of closed-form formulas for trigonometric series. At first, for some integer values, as we know that Riemann’s ζ function and Dirichlet η, λ equal zero at negative even integers, whereas Dirichlet’s β function equals zero at negative odd integers, after a certain number of members, the rest of the series vanishes. Thus, a trigonometric series becomes a polynomial with coefficients involving Riemann’s ζ function and Dirichlet η, λ, β functions. On the other hand, in some cases, one cannot immediately replace the parameter with any positive integer because we shall encounter singularities. So it is necessary to take a limit, so in the process, we apply L’Hospital’s rule and, after a series of rearrangements, we bring a trigonometric series to a form suitable for the application of Choi-Srivastava’s theorem dealing with Hurwitz’s zeta function and Harmonic numbers. In this way, we express a trigonometric series as a polynomial over Hurwitz’s zeta function derivative.

Keywords: Dirichlet eta lambda beta functions, Riemann's zeta function, Hurwitz zeta function, Harmonic numbers

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Authors: Hossein Jafari, Xiangfang Li, Lijun Qian, Alexander Aved, Timothy Kroecker

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Traditionally in sensor networks and recently in the Internet of Things, numerous heterogeneous sensors are deployed in distributed manner to monitor a phenomenon that often can be model by an underlying stochastic process. The big time-series data collected by the sensors must be analyzed to detect change in the stochastic process as quickly as possible with tolerable false alarm rate. However, sensors may have different accuracy and sensitivity range, and they decay along time. As a result, the big time-series data collected by the sensors will contain uncertainties and sometimes they are conflicting. In this study, we present a framework to take advantage of Evidence Theory (a.k.a. Dempster-Shafer and Dezert-Smarandache Theories) capabilities of representing and managing uncertainty and conflict to fast change detection and effectively deal with complementary hypotheses. Specifically, Kullback-Leibler divergence is used as the similarity metric to calculate the distances between the estimated current distribution with the pre- and post-change distributions. Then mass functions are calculated and related combination rules are applied to combine the mass values among all sensors. Furthermore, we applied the method to estimate the minimum number of sensors needed to combine, so computational efficiency could be improved. Cumulative sum test is then applied on the ratio of pignistic probability to detect and declare the change for decision making purpose. Simulation results using both synthetic data and real data from experimental setup demonstrate the effectiveness of the presented schemes.

Keywords: CUSUM, evidence theory, kl divergence, quickest change detection, time series data

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Authors: Shalaka Kadam, Dinesh Apte, Sagar Mainkar

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The life cycle of products is becoming shorter and shorter due to increased competition in market, shorter product development time and increased product diversity. Short life cycles are normal in retail industry, style business, entertainment media, and telecom and semiconductor industry. The subject of accurate forecasting for demand of short lifecycle products is of special enthusiasm for many researchers and organizations. Due to short life cycle of products the amount of historical data that is available for forecasting is very minimal or even absent when new or modified products are launched in market. The companies dealing with such products want to increase the accuracy in demand forecasting so that they can utilize the full potential of the market at the same time do not oversupply. This provides the challenge to develop a forecasting model that can forecast accurately while handling large variations in data and consider the complex relationships between various parameters of data. Many statistical models have been proposed in literature for forecasting time series data. Traditional time series forecasting models do not work well for short life cycles due to lack of historical data. Also artificial neural networks (ANN) models are very time consuming to perform forecasting. We have studied the existing models that are used for forecasting and their limitations. This work proposes an effective and powerful forecasting approach for short life cycle time series forecasting. We have proposed an approach which takes into consideration different scenarios related to data availability for short lifecycle products. We then suggest a methodology which combines statistical analysis with structured judgement. Also the defined approach can be applied across domains. We then describe the method of creating a profile from analogous products. This profile can then be used for forecasting products with historical data of analogous products. We have designed an application which combines data, analytics and domain knowledge using point-and-click technology. The forecasting results generated are compared using MAPE, MSE and RMSE error scores. Conclusion: Based on the results it is observed that no one approach is sufficient for short life-cycle forecasting and we need to combine two or more approaches for achieving the desired accuracy.

Keywords: forecast, short life cycle product, structured judgement, time series

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Authors: Evren Şar İşbilen

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As it is known, the movies and tv series are occupying a large part in the daily lives of adults and children in our era. In this connection, in the present study, the most popular historical TV series of recent years in Turkey, “Muhteşem Yüzyıl” (The Magnificent Century), was selected as the sample for the data collection in order to explore the perception of history of university students’. The data collected was analyzed bothqualitatively and quantitatively. The findings discussed in relation to the possible educative effects of historical non-educational TV series and movies on students' perceptions related to history. Additionally, suggestions were made regarding to the utilization of non-educational TV series or movies in education in a positive way.

Keywords: education, history, movies, teacher candidates

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Authors: Manit Pollar

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Identifying the dengue epidemic periods early would be helpful to take necessary actions to prevent the dengue outbreaks. Providing an accurate prediction on dengue epidemic seasons will allow sufficient time to take the necessary decisions and actions to safeguard the situation for local authorities. This study aimed to develop a forecasting model on number of dengue incidences in Nakhon Si Thammarat Province, Southern Thailand using time series analysis. We develop Seasonal Autoregressive Moving Average (SARIMA) models on the monthly data collected between 2003-2011 and validated the models using data collected between January-September 2012. The result of this study revealed that the SARIMA(1,1,0)(1,2,1)12 model closely described the trends and seasons of dengue incidence and confirmed the existence of dengue fever cases in Nakhon Si Thammarat for the years between 2003-2011. The study showed that the one-step approach for predicting dengue incidences provided significantly more accurate predictions than the twelve-step approach. The model, even if based purely on statistical data analysis, can provide a useful basis for allocation of resources for disease prevention.

Keywords: SARIMA, time series model, dengue cases, Thailand

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Authors: Karim Hamidi Machekposhti, Hossein Sedghi

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This study was designed to find the best stochastic model (using of time series analysis) for annual extreme streamflow (peak and maximum streamflow) of Karkheh River at Iran. The Auto-regressive Integrated Moving Average (ARIMA) model used to simulate these series and forecast those in future. For the analysis, annual extreme streamflow data of Jelogir Majin station (above of Karkheh dam reservoir) for the years 1958–2005 were used. A visual inspection of the time plot gives a little increasing trend; therefore, series is not stationary. The stationarity observed in Auto-Correlation Function (ACF) and Partial Auto-Correlation Function (PACF) plots of annual extreme streamflow was removed using first order differencing (d=1) in order to the development of the ARIMA model. Interestingly, the ARIMA(4,1,1) model developed was found to be most suitable for simulating annual extreme streamflow for Karkheh River. The model was found to be appropriate to forecast ten years of annual extreme streamflow and assist decision makers to establish priorities for water demand. The Statistical Analysis System (SAS) and Statistical Package for the Social Sciences (SPSS) codes were used to determinate of the best model for this series.

Keywords: stochastic models, ARIMA, extreme streamflow, Karkheh river

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Authors: Anthony Usoro

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In this paper, two classes of bilinear time series model are obtained under certain conditions from the general bilinear autoregressive moving average model. Bilinear Autoregressive (BAR) and Bilinear Moving Average (BMA) Models have been identified. From the general bilinear model, BAR and BMA models have been proved to exist for q = Q = 0, => j = 0, and p = P = 0, => i = 0 respectively. These models are found useful in modelling most of the economic and financial data.

Keywords: autoregressive model, bilinear autoregressive model, bilinear moving average model, moving average model

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Authors: Nazima Ellahi, Danish Ramzan

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There is a growing trend among development economists regarding the importance of financial sector for economic development and growth activities. The development thus introduced, helps to promote welfare effects and poverty alleviation. This study is an attempt to find the nature of link between Islamic banking financing and development of output growth for Pakistan. Time series data set has been utilized for a time period ranging from 1990 to 2010. Following the Phillip Perron (PP) and Augmented Dicky Fuller (ADF) test of unit root this study applied Ordinary Least Squares (OLS) method of estimation and found encouraging results in favor of promoting the Islamic banking practices in Pakistan.

Keywords: Islamic finance, poverty alleviation, economic growth, finance, commerce

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Authors: Vaidehi Iyer, Konstantin Borozdin

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Time series prediction problems have many important practical applications, but are notoriously difficult for statistical modeling. Recently, machine learning methods have been attracted significant interest as a practical tool applied to a variety of problems, even though developments in this field tend to be semi-empirical. This paper explores application of Long Short Term Memory based Recurrent Neural Networks to the one-step prediction of time series for both trend and stochastic components. Two types of data are analyzed - daily stock prices, that are often considered to be a typical example of a random walk, - and weather patterns dominated by seasonal variations. Results from both analyses are compared, and reinforced learning framework is used to select more efficient between Recurrent Neural Networks and more traditional auto regression methods. It is shown that both methods are able to follow long-term trends and seasonal variations closely, but have difficulties with reproducing day-to-day variability. Future research directions and potential real world applications are briefly discussed.

Keywords: long short term memory, prediction methods, recurrent neural networks, reinforcement learning

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Authors: Salako Rotimi, Oshungade Stephen, Ojewoye Opeyemi

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The maintenance of price stability is one of the macroeconomic challenges facing Nigeria as a nation. This paper attempts to build a co-integration multivariate time series model for inflation movement in Nigeria using data extracted from the abstract of statistics of the Central Bank of Nigeria (CBN) from 2008 to 2017. The Johansen cointegration test suggests at least one co-integration vector describing the long run relationship between Consumer Price Index (CPI), Food Price Index (FPI) and Non-Food Price Index (NFPI). All three series show increasing pattern, which indicates a sign of non-stationary in each of the series. Furthermore, model predictability was established with root-mean-square-error, mean absolute error, mean average percentage error, and Theil’s unbiased statistics for n-step forecasting. The result depicts that the long run coefficient of a consumer price index (CPI) has a positive long-run relationship with the food price index (FPI) and non-food price index (NFPI).

Keywords: economic, inflation, model, series

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