Search results for: autoregressive models

Authors: Usoro Anthony E., Udoh Emediong

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Diagonal Vector Autoregressive Models are special classes of the general vector autoregressive models identified under certain conditions, where parameters are restricted to the diagonal elements in the coefficient matrices. Variance, autocovariance, and autocorrelation properties of the upper and lower diagonal VAR models are derived. The new set of VAR models is verified with empirical data and is found to perform favourably with the general VAR models. The advantage of the diagonal models over the existing models is that the new models are parsimonious, given the reduction in the interactive coefficients of the general VAR models.

Keywords: VAR models, diagonal VAR models, variance, autocovariance, autocorrelations

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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: Navid Daryasafar, Nima Farshidfar

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In this article, we make attempt to hide error in video with an emphasis on the time-wise use of autoregressive (AR) models. To resolve this problem, we assume that all information in one or more video frames is lost. Then, lost frames are estimated using analogous Pixels time information in successive frames. Accordingly, after presenting autoregressive models and how they are applied to estimate lost frames, two general methods are presented for using these models. The first method which is the same standard method of autoregressive models estimates lost frame in unidirectional form. Usually, in such condition, previous frames information is used for estimating lost frame. Yet, in the second method, information from the previous and next frames is used for estimating the lost frame. As a result, this method is known as bidirectional estimation. Then, carrying out a series of tests, performance of each method is assessed in different modes. And, results are compared.

Keywords: error steganography, unidirectional estimation, bidirectional estimation, AR linear estimation

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Authors: Panudet Saengseedam, Nanthachai Kantanantha

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This paper proposes a linear mixed model (LMM) with spatial effects to forecast rice and cassava yields in Thailand at the same time. A multivariate conditional autoregressive (MCAR) model is assumed to present the spatial effects. A Bayesian method is used for parameter estimation via Gibbs sampling Markov Chain Monte Carlo (MCMC). The model is applied to the rice and cassava yields monthly data which have been extracted from the Office of Agricultural Economics, Ministry of Agriculture and Cooperatives of Thailand. The results show that the proposed model has better performance in most provinces in both fitting part and validation part compared to the simple exponential smoothing and conditional auto regressive models (CAR) from our previous study.

Keywords: Bayesian method, linear mixed model, multivariate conditional autoregressive model, spatial time series

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Authors: Daniel Fulus Fom, Gau Patrick Damulak

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In this study, the Autoregressive Fractional Integrated Moving Average (ARFIMA) and Jordan Recurrent Neural Network (JRNN) models were employed to model the forecasting performance of the daily turbidity flow of White Clay Creek (WCC). The two methods were applied to the log difference series of the daily turbidity flow series of WCC. The measurements of error employed to investigate the forecasting performance of the ARFIMA and JRNN models are the Root Mean Square Error (RMSE) and the Mean Absolute Error (MAE). The outcome of the investigation revealed that the forecasting performance of the JRNN technique is better than the forecasting performance of the ARFIMA technique in the mean square error sense. The results of the ARFIMA and JRNN models were obtained by the simulation of the models using MATLAB version 8.03. The significance of using the log difference series rather than the difference series is that the log difference series stabilizes the turbidity flow series than the difference series on the ARFIMA and JRNN.

Keywords: auto regressive, mean absolute error, neural network, root square mean error

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Authors: Niya Chen, Jennifer Chan

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In the financial market, risk management helps to minimize potential loss and maximize profit. There are two ways to assess risks; the first way is to calculate the risk directly based on the volatility. The most common risk measurements are Value at Risk (VaR), sharp ratio, and beta. Alternatively, we could look at the quantile of the return to assess the risk. Popular return models such as GARCH and stochastic volatility (SV) focus on modeling the mean of the return distribution via capturing the volatility dynamics; however, the quantile/expectile method will give us an idea of the distribution with the extreme return value. It will allow us to forecast VaR using return which is direct information. The advantage of using these non-parametric methods is that it is not bounded by the distribution assumptions from the parametric method. But the difference between them is that expectile uses a second-order loss function while quantile regression uses a first-order loss function. We consider several quantile functions, different volatility measures, and estimates from some volatility models. To estimate the expectile of the model, we use Realized Conditional Autoregressive Expectile (CARE) model with the bayesian method to achieve this. We would like to see if our proposed models outperform existing models in cryptocurrency, and we will test it by using Bitcoin mainly as well as Ethereum.

Keywords: expectile, CARE Model, CARR Model, quantile, cryptocurrency, Value at Risk

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Authors: Shay Kee Tan, Kok Haur Ng, Jennifer So-Kuen Chan

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This paper extends the conditional autoregressive range (CARR) model to multivariate CARR (MCARR) model and further to the two-stage MCARR-return model to model and forecast volatilities, correlations and returns of multiple financial assets. The first stage model fits the scaled realised Parkinson volatility measures using individual series and their pairwise sums of indices to the MCARR model to obtain in-sample estimates and forecasts of volatilities for these individual and pairwise sum series. Then covariances are calculated to construct the fitted variance-covariance matrix of returns which are imputed into the stage-two return model to capture the heteroskedasticity of assets’ returns. We investigate different choices of mean functions to describe the volatility dynamics. Empirical applications are based on the Standard and Poor 500, Dow Jones Industrial Average and Dow Jones United States Financial Service Indices. Results show that the stage-one MCARR models using asymmetric mean functions give better in-sample model fits than those based on symmetric mean functions. They also provide better out-of-sample volatility forecasts than those using CARR models based on two robust loss functions with the scaled realised open-to-close volatility measure as the proxy for the unobserved true volatility. We also find that the stage-two return models with constant means and multivariate Student-t errors give better in-sample fits than the Baba, Engle, Kraft, and Kroner type of generalized autoregressive conditional heteroskedasticity (BEKK-GARCH) models. The estimates and forecasts of value-at-risk (VaR) and conditional VaR based on the best MCARR-return models for each asset are provided and tested using Kupiec test to confirm the accuracy of the VaR forecasts.

Keywords: range-based volatility, correlation, multivariate CARR-return model, value-at-risk, conditional value-at-risk

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Authors: Boukari Nassim

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This paper describes the use of odd pair autoregressive coefficients (Yule _Walker and Burg) for the feature extraction of electroencephalogram (EEG) signals. In the classification: the radial basis function neural network neural network (RBFNN) is employed. The RBFNN is described by his architecture and his characteristics: as the RBF is defined by the spread which is modified for improving the results of the classification. Five types of EEG signals are defined for this work: Set A, Set B for normal signals, Set C, Set D for interictal signals, set E for ictal signal (we can found that in Bonn university). In outputs, two classes are given (AC, AD, AE, BC, BD, BE, CE, DE), the best accuracy is calculated at 99% for the combined odd pair autoregressive coefficients. Our method is very effective for the diagnosis of epileptic EEG signals.

Keywords: epilepsy, EEG signals classification, combined odd pair autoregressive coefficients, radial basis function neural network

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Authors: Chiung-Ju Huang

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This study examines whether the Taiwan’s public debt is sustainable utilizing an unrestricted two-regime threshold autoregressive (TAR) model with an autoregressive unit root. The empirical results show that Taiwan’s public debt appears as a nonlinear series and is stationary in regime 1 but not in regime 2. This result implies that while Taiwan’s public debt was mostly sustainable over the 1996 to 2013 period examined in the study, it may no longer be sustainable in the most recent two years as the public debt ratio has increased cumulatively to 3.618%.

Keywords: nonlinearity, public debt, sustainability, threshold autoregressive model

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Authors: Suparman Suparman

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A white noise in autoregressive (AR) model is often assumed to be normally distributed. In application, the white noise usually do not follows a normal distribution. This paper aims to estimate a parameter of AR model that has a exponential white noise. A Bayesian method is adopted. A prior distribution of the parameter of AR model is selected and then this prior distribution is combined with a likelihood function of data to get a posterior distribution. Based on this posterior distribution, a Bayesian estimator for the parameter of AR model is estimated. Because the order of AR model is considered a parameter, this Bayesian estimator cannot be explicitly calculated. To resolve this problem, a method of reversible jump Markov Chain Monte Carlo (MCMC) is adopted. A result is a estimation of the parameter AR model can be simultaneously calculated.

Keywords: autoregressive (AR) model, exponential white Noise, bayesian, reversible jump Markov Chain Monte Carlo (MCMC)

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Authors: Bernur Acikgoz

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The purpose of this paper is to investigate the effects of public spending on economic growth and examine the sources of economic growth in developed countries since the 1990s. This paper analyses whether public spending effect on economic growth based on Cobb-Douglas Production Function with the two econometric models with Autoregressive Distributed Lag (ARDL) and Dynamic Fixed Effect (DFE) for 21 developed countries (high-income OECD countries), over the period 1990-2013. Our models results are parallel to each other and the models support that public spending has an important role for economic growth. This result is accurate with theories and previous empirical studies.

Keywords: public spending, economic growth, panel data, ARDL models

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Authors: Davies Obaromi, Qin Yongsong, James Ndege, Azeez Adeboye, Akinwumi Odeyemi

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The basic model usually used in disease mapping, is the Besag, York and Mollie (BYM) model and which combines the spatially structured and spatially unstructured priors as random effects. Bayesian Conditional Autoregressive (CAR) model is a disease mapping method that is commonly used for smoothening the relative risk of any disease as used in the Besag, York and Mollie (BYM) model. This model (CAR), which is also usually assigned as a prior to one of the spatial random effects in the BYM model, successfully uses information from adjacent sites to improve estimates for individual sites. To our knowledge, there are some unrealistic or counter-intuitive consequences on the posterior covariance matrix of the CAR prior for the spatial random effects. In the conventional BYM (Besag, York and Mollie) model, the spatially structured and the unstructured random components cannot be seen independently, and which challenges the prior definitions for the hyperparameters of the two random effects. Therefore, the main objective of this study is to construct and utilize an extended Bayesian spatial CAR model for studying tuberculosis patterns in the Eastern Cape Province of South Africa, and then compare for flexibility with some existing CAR models. The results of the study revealed the flexibility and robustness of this alternative extended CAR to the commonly used CAR models by comparison, using the deviance information criteria. The extended Bayesian spatial CAR model is proved to be a useful and robust tool for disease modeling and as a prior for the structured spatial random effects because of the inclusion of an extra hyperparameter.

Keywords: Besag2, CAR models, disease mapping, INLA, spatial models

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Authors: Nicola Rubino

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This paper presents an analysis of a group of commodity exporting countries' nominal exchange rate movements in relationship to the US dollar. Using a series of Unrestricted Self-exciting Threshold Autoregressive models (SETAR), we model and evaluate sixteen national CPI price differentials relative to the US dollar CPI. Out-of-sample forecast accuracy is evaluated through calculation of mean absolute error measures on the basis of two-hundred and fifty-three months rolling window forecasts and extended to three additional models, namely a logistic smooth transition regression (LSTAR), an additive non linear autoregressive model (AAR) and a simple linear Neural Network model (NNET). Our preliminary results confirm presence of some form of TAR non linearity in the majority of the countries analyzed, with a relatively higher goodness of fit, with respect to the linear AR(1) benchmark, in five countries out of sixteen considered. Although no model appears to statistically prevail over the other, our final out-of-sample forecast exercise shows that SETAR models tend to have quite poor relative forecasting performance, especially when compared to alternative non-linear specifications. Finally, by analyzing the implied half-lives of the > coefficients, our results confirms the presence, in the spirit of arbitrage band adjustment, of band convergence with an inner unit root behaviour in five of the sixteen countries analyzed.

Keywords: transition regression model, real exchange rate, nonlinearities, price differentials, PPP, commodity points

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Authors: Giriraj Achari, Malay Bhattacharyya

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In this paper, the effectiveness of Copula Markov Switching Multifractal (MSM) models at forecasting Value-at-Risk of a two-stock portfolio is studied. The innovations are allowed to be drawn from distributions that can capture skewness and leptokurtosis, which are well documented empirical characteristics observed in financial returns. The candidate distributions considered for this purpose are Johnson-SU, Pearson Type-IV and α-Stable distributions. The two univariate marginal distributions are combined using the Student-t copula. The estimation of all parameters is performed by Maximum Likelihood Estimation. Finally, the models are compared in terms of accurate Value-at-Risk (VaR) forecasts using tests of unconditional coverage and independence. It is found that Copula-MSM-models with leptokurtic innovation distributions perform slightly better than Copula-MSM model with Normal innovations. Copula-MSM models, in general, produce better VaR forecasts as compared to traditional methods like Historical Simulation method, Variance-Covariance approach and Copula-Generalized Autoregressive Conditional Heteroscedasticity (Copula-GARCH) models.

Keywords: Copula, Markov Switching, multifractal, value-at-risk

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Authors: Raymond K. Dziwornu

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Lending rate of agriculture loan has persistently been high and attributed to risk in the sector. This study examined how food inflation and agriculture lending rate react to each other in Ghana using vector autoregressive approach. Quarterly data from 2006 to 2018 was obtained from the Bank of Ghana quarterly bulletin and the Ghana Statistical Service reports. The study found that a positive standard deviation shock to food inflation causes lending rate of agriculture loan to react negatively in the short run, but positively and steadily in the long run. This suggests the need to direct appropriate policy measures to reduce food inflation and consequently, the cost of credit to the agricultural sector for its growth.

Keywords: food inflation, agriculture, lending rate, vector autoregressive, Ghana

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Authors: Wong Hock Tsen

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This study aims to investigate the impact of exchange rate volatility on real export in Malaysia. The moving standard deviation with order three (MSD(3)) is used for the measurement of exchange rate volatility. The conventional and partially asymmetric autoregressive distributed lag (ARDL) models are used in the estimations. This study finds exchange rate volatility to have significant impact on real total export and some sub-categories of real total export. Moreover, this study finds that the positive or negative exchange rate volatility tends to have positive or negative impact on real export. Exchange rate volatility can be harmful to export of Malaysia.

Keywords: exchange rate volatility, autoregressive distributed lag, export, Malaysia

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Authors: Diteboho Xaba, Kolentino Mpeta, Tlotliso Qejoe

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This paper assesses the in-sample forecasting of the South African exchange rates comparing a linear ARIMA model and a SETAR model. The study uses a monthly adjusted data of South African exchange rates with 420 observations. Akaike information criterion (AIC) and the Schwarz information criteria (SIC) are used for model selection. Mean absolute error (MAE), root mean squared error (RMSE) and mean absolute percentage error (MAPE) are error metrics used to evaluate forecast capability of the models. The Diebold –Mariano (DM) test is employed in the study to check forecast accuracy in order to distinguish the forecasting performance between the two models (ARIMA and SETAR). The results indicate that both models perform well when modelling and forecasting the exchange rates, but SETAR seemed to outperform ARIMA.

Keywords: ARIMA, error metrices, model selection, SETAR

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Authors: Yuzhi Cai

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In this paper, we discuss a Bayesian approach to quantile autoregressive (QAR) time series model estimation and forecasting. Together with a combining forecasts technique, we then predict USD to GBP currency exchange rates. Combined forecasts contain all the information captured by the fitted QAR models at different quantile levels and are therefore better than those obtained from individual models. Our results show that an unequally weighted combining method performs better than other forecasting methodology. We found that a median AR model can perform well in point forecasting when the predictive density functions are symmetric. However, in practice, using the median AR model alone may involve the loss of information about the data captured by other QAR models. We recommend that combined forecasts should be used whenever possible.

Keywords: combining forecasts, MCMC, predictive density functions, quantile forecasting, quantile modelling

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Authors: Nuwan Kuruwitaarachchi, M. K. M. Peiris, C. N. Madawala, K. M. A. R. Perera, V. U. N Perera

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Dealing with businesses with the foreign market always took a special place in a country’s economy. Political and social factors came into play making currency rate changes fluctuate rapidly. Currency rate prediction has become an important factor for larger international businesses since large amounts of money exchanged between countries. This research focuses on comparing the accuracy of mainly three models; Autoregressive Integrated Moving Average (ARIMA), Artificial Neural Networks(ANN) and Support Vector Machines(SVM). series of data import, export, USD currency exchange rate respect to LKR has been selected for training using above mentioned algorithms. After training the data set and comparing each algorithm, it was able to see that prediction in SVM performed better than other models. It was improved more by combining SVM and SVR models together.

Keywords: ARIMA, ANN, FFNN, RMSE, SVM, SVR

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Authors: Sumit Sen, Sohan Khedekar, Umang Shinde, Shivam Bhargava

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This study has been undertaken to investigate whether the deep learning models are able to predict the future stock prices by training the model with the historical stock price data. Since this work required time series analysis, various models are present today to perform time series analysis such as Recurrent Neural Network LSTM, ARIMA and Facebook Prophet. Applying these models the movement of stock price of stocks are predicted and also tried to provide the future prediction of the stock price of a stock. Final product will be a stock price prediction web application that is developed for providing the user the ease of analysis of the stocks and will also provide the predicted stock price for the next seven days.

Keywords: Autoregressive Integrated Moving Average, Deep Learning, Long Short Term Memory, Time-series

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Authors: Zahid Ahmad, Nosheen Imran, Nauman Ali, Farah Amir

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The objective of the study is to forecast the US Dollar and Pak Rupee exchange rate by using time series models. For this purpose, daily exchange rates of US and Pakistan for the period of January 01, 2007 - June 2, 2017, are employed. The data set is divided into in sample and out of sample data set where in-sample data are used to estimate as well as forecast the models, whereas out-of-sample data set is exercised to forecast the exchange rate. The ADF test and PP test are used to make the time series stationary. To forecast the exchange rate ARIMA model and GARCH model are applied. Among the different Autoregressive Integrated Moving Average (ARIMA) models best model is selected on the basis of selection criteria. Due to the volatility clustering and ARCH effect the GARCH (1, 1) is also applied. Results of analysis showed that ARIMA (0, 1, 1 ) and GARCH (1, 1) are the most suitable models to forecast the future exchange rate. Further the GARCH (1,1) model provided the volatility with non-constant conditional variance in the exchange rate with good forecasting performance. This study is very useful for researchers, policymakers, and businesses for making decisions through accurate and timely forecasting of the exchange rate and helps them in devising their policies.

Keywords: exchange rate, ARIMA, GARCH, PAK/USD

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Authors: C. Senabre, S. Valero, M. Lopez, E. Velasco, M. Sanchez

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This paper focuses on an application of linear mixed models to short-term load forecasting. The challenge of this research is to improve a currently working model at the Spanish Transport System Operator, programmed by us, and based on linear autoregressive techniques and neural networks. The forecasting system currently forecasts each of the regions within the Spanish grid separately, even though the behavior of the load in each region is affected by the same factors in a similar way. A load forecasting system has been verified in this work by using the real data from a utility. In this research it has been used an integration of several regions into a linear mixed model as starting point to obtain the information from other regions. Firstly, the systems to learn general behaviors present in all regions, and secondly, it is identified individual deviation in each regions. The technique can be especially useful when modeling the effect of special days with scarce information from the past. The three most relevant regions of the system have been used to test the model, focusing on special day and improving the performance of both currently working models used as benchmark. A range of comparisons with different forecasting models has been conducted. The forecasting results demonstrate the superiority of the proposed methodology.

Keywords: short-term load forecasting, mixed effects models, neural networks, mixed effects models

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Authors: Kassahun Birhanu Tadesse, Megersa Olumana Dinka

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Reliable future river flow information is basic for planning and management of any river systems. For data scarce river system having only a river flow records like the Waterval River, a univariate time series models are appropriate for river flow forecasting. In this study, a univariate Seasonal Autoregressive Integrated Moving Average (SARIMA) model was applied for forecasting Waterval River flow using GRETL statistical software. Mean monthly river flows from 1960 to 2016 were used for modeling. Different unit root tests and Mann-Kendall trend analysis were performed to test the stationarity of the observed flow time series. The time series was differenced to remove the seasonality. Using the correlogram of seasonally differenced time series, different SARIMA models were identified, their parameters were estimated, and diagnostic check-up of model forecasts was performed using white noise and heteroscedasticity tests. Finally, based on minimum Akaike Information (AIc) and Hannan-Quinn (HQc) criteria, SARIMA (3, 0, 2) x (3, 1, 3)12 was selected as the best model for Waterval River flow forecasting. Therefore, this model can be used to generate future river information for water resources development and management in Waterval River system. SARIMA model can also be used for forecasting other similar univariate time series with seasonality characteristics.

Keywords: heteroscedasticity, stationarity test, trend analysis, validation, white noise

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Authors: Beulah Rani Inbanathan

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In the present era, it is vivid from the numerous outcomes that data privacy is being compromised in various ways. Machine learning is one technology that uses the centralized server, and then data is given as input which is being analyzed by the algorithms present on this mentioned server, and hence outputs are predicted. However, each time the data must be sent by the user as the algorithm will analyze the input data in order to predict the output, which is prone to threats. The solution to overcome this issue is federated learning, where the models alone get updated while the data resides on the local machine and does not get exchanged with the other local models. Nevertheless, even on these local models, there are chances of data poisoning, and it is crystal clear from various experiments done by many people. This paper delves into many ways where data poisoning occurs and the many methods through which it is prevalent that data poisoning still exists. It includes the poisoning attacks on IoT devices, Edge devices, Autoregressive model, and also, on Industrial IoT systems and also, few points on how these could be evadible in order to protect our data which is personal, or sensitive, or harmful when exposed.

Keywords: data poisoning, federated learning, Internet of Things, edge computing

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Authors: Kalai Lamia, Jilani Faouzi

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Measuring and controlling risk is one of the most attractive issues in finance. With the persistence of uncontrolled and erratic stocks movements, volatility is perceived as a barometer of daily fluctuations. An objective measure of this variable seems then needed to control risks and cover those that are considered the most important. Non-linear autoregressive modeling is our first evaluation approach. In particular, we test the presence of “persistence” of conditional variance and the presence of a degree of a leverage effect. In order to resolve for the problem of “asymmetry” in volatility, the retained specifications point to the importance of stocks reactions in response to news. Effects of shocks on volatility highlight also the need to study the “long term” behaviour of conditional variance of stocks returns and articulate the presence of long memory and dependence of time series in the long run. We note that the integrated fractional autoregressive model allows for representing time series that show long-term conditional variance thanks to fractional integration parameters. In order to stop at the dynamics that manage time series, a comparative study of the results of the different models will allow for better understanding volatility structure over the Tunisia stock market, with the aim of accurately predicting fluctuation risks.

Keywords: asymmetry volatility, clustering, stylised facts, leverage effect

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Authors: Andres F. Ramirez, Carlos F. Valencia

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The increasing interest in renewable energies strategies application and the path for diminishing the use of carbon related energy sources have encouraged the development of novel strategies for integration of solar energy into the electricity network. A correct inclusion of the fluctuating energy output of a photovoltaic (PV) energy system into an electric grid requires improvements in the forecasting and simulation methodologies for solar energy potential, and the understanding not only of the mean value of the series but the associated underlying stochastic process. We present a methodology for synthetic generation of solar irradiance (shortwave flux) and air temperature bivariate time series based on copula functions to represent the cross-dependence and temporal structure of the data. We explore the advantages of using this nonlinear time series method over traditional approaches that use a transformation of the data to normal distributions as an intermediate step. The use of copulas gives flexibility to represent the serial variability of the real data on the simulation and allows having more control on the desired properties of the data. We use discrete zero mass density distributions to assess the nature of solar irradiance, alongside vector generalized linear models for the bivariate time series time dependent distributions. We found that the copula autoregressive methodology used, including the zero mass characteristics of the solar irradiance time series, generates a significant improvement over state of the art strategies. These results will help to better understand the fluctuating nature of solar energy forecasting, the underlying stochastic process, and quantify the potential of a photovoltaic (PV) energy generating system integration into a country electricity network. Experimental analysis and real data application substantiate the usage and convenience of the proposed methodology to forecast solar irradiance time series and solar energy across northern hemisphere, southern hemisphere, and equatorial zones.

Keywords: copula autoregressive, solar irradiance forecasting, solar energy forecasting, time series generation

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Authors: Nor Zila Abd Hamid, Mohd Salmi M. Noorani

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This study is focused on the development of prediction models of the Ozone concentration time series. Prediction model is built based on chaotic approach. Firstly, the chaotic nature of the time series is detected by means of phase space plot and the Cao method. Then, the prediction model is built and the local linear approximation method is used for the forecasting purposes. Traditional prediction of autoregressive linear model is also built. Moreover, an improvement in local linear approximation method is also performed. Prediction models are applied to the hourly ozone time series observed at the benchmark station in Malaysia. Comparison of all models through the calculation of mean absolute error, root mean squared error and correlation coefficient shows that the one with improved prediction method is the best. Thus, chaotic approach is a good approach to be used to develop a prediction model for the Ozone concentration time series.

Keywords: chaotic approach, phase space, Cao method, local linear approximation method

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Authors: Masahiro Ohmura, Koh Kakusho, Takeshi Okadome

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This paper presents a regression model with autocorrelated errors in which the inputs are social moods obtained by analyzing the adjectives in Twitter posts using a document topic model. The regression model predicts Dow Jones Industrial Average (DJIA) more precisely than autoregressive moving-average models.

Keywords: stock market prediction, social moods, regression model, DJIA

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Authors: A. Boateng, La Gil-Alana, M. Lesaoana; Hj. Siweya, A. Belete

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This study examines long memory or long-range dependence in the CPI inflation rates of Ghana and South Africa using Whittle methods and autoregressive fractionally integrated moving average (ARFIMA) models. Standard I(0)/I(1) methods such as Augmented Dickey-Fuller (ADF), Philips-Perron (PP) and Kwiatkowski–Phillips–Schmidt–Shin (KPSS) tests were also employed. Our findings indicate that long memory exists in the CPI inflation rates of both countries. After processing fractional differencing and determining the short memory components, the models were specified as ARFIMA (4,0.35,2) and ARFIMA (3,0.49,3) respectively for Ghana and South Africa. Consequently, the CPI inflation rates of both countries are fractionally integrated and mean reverting. The implication of this result will assist in policy formulation and identification of inflationary pressures in an economy.

Keywords: Consumer Price Index (CPI) inflation rates, Whittle method, long memory, ARFIMA model

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Authors: Chokri Slim

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The relative failure of simultaneous equation models in the seventies has led researchers to turn to other approaches that take into account the dynamics of economic and financial systems. In this paper, we use an approach based on vector autoregressive model that is widely used in recent years. Their popularity is due to their flexible nature and ease of use to produce models with useful descriptive characteristics. It is also easy to use them to test economic hypotheses. The standard econometric techniques assume that the series studied are stable over time (stationary hypothesis). Most economic series do not verify this hypothesis, which assumes, when one wishes to study the relationships that bind them to implement specific techniques. This is cointegration which characterizes non-stationary series (integrated) with a linear combination is stationary, will also be presented in this paper. Since the work of Johansen, this approach is generally presented as part of a multivariate analysis and to specify long-term stable relationships while at the same time analyzing the short-term dynamics of the variables considered. In the empirical part, we have applied these concepts to study the dynamics of of the exchange rate in Tunisia, which is one of the most important economic policy of a country open to the outside. According to the results of the empirical study by the cointegration method, there is a cointegration relationship between the exchange rate and its determinants. This relationship shows that the variables have a significant influence in determining the exchange rate in Tunisia.

Keywords: stationarity, cointegration, dynamic models, causality, VECM models

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