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- CBN Journal of Applied Statistics (JAS) (20)
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Articles 1 - 30 of 32
Full-Text Articles in Multivariate Analysis
Syntax-Enhanced Boundary-Aware Named Entity Recognition Model, Chuanming Yu, Bin Deng, Zhengang Zhang
Syntax-Enhanced Boundary-Aware Named Entity Recognition Model, Chuanming Yu, Bin Deng, Zhengang Zhang
Journal of Scientific Information Research
[Purpose/significance] This study addresses the issue of inadequate perception of entity boundaries in traditional character-level modeling-based named entity recognition models by integrating syntax information containing entity boundary features into the task using a multi-head graph attention network with dense connections. This integration enhances the effectiveness of named entity recognition.
[Method/process] This study proposes a Syntax-enhanced Boundary-aware Named Entity Recognition Model (SynBNER), which utilizes BERT for text semantic representation and integrates syntax information using a dense-connected graph attention network. This integration incorporates implicit entity boundary information from syntax information into word representations, thereby enhancing the model's entity boundary perception capability.
[Result/conclusion] …
A Machine-Learning Tool-Supported Methodology For Nonprofit Donor Analysis, Corbin Weiss
A Machine-Learning Tool-Supported Methodology For Nonprofit Donor Analysis, Corbin Weiss
Campus Research Month
We developed a machine-learning tool-supported methodology for modeling the nonprofit donor relationship. This approach was demonstrated in the case of a US-based nonprofit. Conclusions were drawn from this example and tool-support provided for use by other nonprofits.
Stock Market Volatility In The United Kingdom: Simulating Post-Covid-19 Recovery, Bala A. Dahiru, Mohammed Shuaibu, Najibullah Hassanov
Stock Market Volatility In The United Kingdom: Simulating Post-Covid-19 Recovery, Bala A. Dahiru, Mohammed Shuaibu, Najibullah Hassanov
CBN Journal of Applied Statistics (JAS)
This paper investigates the time it would take for the FTSE-100 index to reach its post-COVID-19 peak. The paper utilises an exponential generalised autoregressive conditional heteroscedasticity (EGARCH) model that accounts for leverage effect and asymmetries. The preferred models amongst competing variants was the Autoregressive Moving Average (ARMA)-EGARCH(2,1) specification and was used to predict daily FTSE-100 data from 5th January 2000 to 21st June 2024. The empirical exercise showed that the COVID-19-induced financial crisis negatively affected the United Kingdom’s stock market performance. The results show that the FTSE100 index could reach its post-pandemic peak around 27th August, 2024 (two months after …
Understanding Social Dynamics In Toxic Conversations And Public Health Intervention Acceptance On Social Media, Ana Aleksandric
Understanding Social Dynamics In Toxic Conversations And Public Health Intervention Acceptance On Social Media, Ana Aleksandric
Computer Science and Engineering Dissertations - Archive
Social media is now central to daily life, offering users a space to share content and opinions. However, these platforms also facilitate the spread of hate speech and misinformation, which can negatively impact public health. This dissertation develops methodologies to analyze social media data for insights that could inform health interventions. The research first examines user responses to toxic content, focusing on behavioral and emotional reactions, as well as group dynamics and bystander effects in toxic interactions. Another key focus is public opinion toward health interventions, particularly COVID-19 vaccination, using geolocated posts and analyzing factors such as race, ethnicity, and …
Reducing Food Scarcity: The Benefits Of Urban Farming, S.A. Claudell, Emilio Mejia
Reducing Food Scarcity: The Benefits Of Urban Farming, S.A. Claudell, Emilio Mejia
Journal of Nonprofit Innovation
Urban farming can enhance the lives of communities and help reduce food scarcity. This paper presents a conceptual prototype of an efficient urban farming community that can be scaled for a single apartment building or an entire community across all global geoeconomics regions, including densely populated cities and rural, developing towns and communities. When deployed in coordination with smart crop choices, local farm support, and efficient transportation then the result isn’t just sustainability, but also increasing fresh produce accessibility, optimizing nutritional value, eliminating the use of ‘forever chemicals’, reducing transportation costs, and fostering global environmental benefits.
Imagine Doris, who is …
Improving The Efficiency Of Exponential Ratio-Type Estimator For Population Median: A Calibration Weight Adjustment Approach, Mathew J. Iseh, Kufre J. Bassey
Improving The Efficiency Of Exponential Ratio-Type Estimator For Population Median: A Calibration Weight Adjustment Approach, Mathew J. Iseh, Kufre J. Bassey
CBN Journal of Applied Statistics (JAS)
This paper modifies the Bahl and Tuteja exponential ratio-type estimator for population median under simple random and stratified sampling schemes using calibration weight adjustment technique with supplementary information to vary the stratum weights. The bias and mean square error of the modified estimator were obtained up to the second-order approximation, which satisfies the necessary conditions for efficiency. The findings show that the new estimator surpasses existing estimators in efficiency gain. This suggests the appropriateness of calibration weight modification in boosting the efficiency of a population parameter estimator under stratified random sampling especially where the population parameter of the auxiliary variable …
Fraud Pattern Detection For Nft Markets, Andrew Leppla, Jorge Olmos, Jaideep Lamba
Fraud Pattern Detection For Nft Markets, Andrew Leppla, Jorge Olmos, Jaideep Lamba
SMU Data Science Review
Non-Fungible Tokens (NFTs) enable ownership and transfer of digital assets using blockchain technology. As a relatively new financial asset class, NFTs lack robust oversight and regulations. These conditions create an environment that is susceptible to fraudulent activity and market manipulation schemes. This study examines the buyer-seller network transactional data from some of the most popular NFT marketplaces (e.g., AtomicHub, OpenSea) to identify and predict fraudulent activity. To accomplish this goal multiple features such as price, volume, and network metrics were extracted from NFT transactional data. These were fed into a Multiple-Scale Convolutional Neural Network that predicts suspected fraudulent activity based …
Effect Of Monetary Policy Rate On Market Interest Rates In Nigeria: A Threshold And Nardl Approach, Oluwafemi E. Awopegba, Joseph O. Afolabi, Lydia T. Adeoye, Godwin O. Akpokodje
Effect Of Monetary Policy Rate On Market Interest Rates In Nigeria: A Threshold And Nardl Approach, Oluwafemi E. Awopegba, Joseph O. Afolabi, Lydia T. Adeoye, Godwin O. Akpokodje
CBN Journal of Applied Statistics (JAS)
This study examines the effect of monetary policy rate (MPR) on market interest rates in Nigeria. For parsimony, we develop two indexes called the short-term interest rate (SINT) and Lending interest rate (LINT) to represent deposit and lending rates respectively. The nonlinear autoregressive distributed lag (NARDL) and threshold regression models are adopted. The study uses monthly data from 2002:M1 to 2019:M12. The results of the threshold regression model indicate that the degree of the effect of MPR on SINT and LINT above the estimated threshold of 11 and 13 percent respectively is greater and significant than if MPR were to …
Social Dimension Of Inclusive Growth In Ecowas: Implication For Poverty Reduction, Toriola K. Anu, Goerge O. Emmanuel, Ajayi O. Felix
Social Dimension Of Inclusive Growth In Ecowas: Implication For Poverty Reduction, Toriola K. Anu, Goerge O. Emmanuel, Ajayi O. Felix
CBN Journal of Applied Statistics (JAS)
This study investigates the implication of the social dimension of inclusive growth on poverty reduction in Economic Community of West African States (ECOWAS) countries. It specifically examines how social indices of inclusive growth comprising of income inequality, education, and health outcomes affect poverty reduction. The study uses a panel dataset of the six (6) lower-middle income countries in ECOWAS which was analysed via panel Difference Generalised Method of Moment (D-GMM). The results show that GDP per capita exerts significant negative effect on poverty while inequality, education and health outcomes do not show significant effect on poverty. Although, the estimates of …
Effect Of Fdi Inflows On Employment Generation In Selected Ecowas Countries: Heterogeneous Panel Analysis, Timothy A. Aderemi, Olawunmi Omitogun, Bukonla G. Osisanwo
Effect Of Fdi Inflows On Employment Generation In Selected Ecowas Countries: Heterogeneous Panel Analysis, Timothy A. Aderemi, Olawunmi Omitogun, Bukonla G. Osisanwo
CBN Journal of Applied Statistics (JAS)
The aim of this study is to examine the effect of FDI on employment in ECOWAS sub region between 1990 and 2019. The study utilizes a panel autoregressive distributed lag model to analyse the short run and long run relationship between FDI and employment across ECOWAS sub region. In the short run, the impact of FDI on employment is negative and statistically not significant. Meanwhile, in the long run FDI has a positive and statistically significant impact on employment rate. This implies that FDI has the capacity to generate employment in countries in ECOWAS sub region. Therefore, this study recommends …
Impact Of Covid-19 Pandemic On The Nigeria Stock Market: A Sectoral Stock Prices Analysis, Peter A. Adekunle, Yakubu A. Bello, Udochukwu G. Nwachukwu
Impact Of Covid-19 Pandemic On The Nigeria Stock Market: A Sectoral Stock Prices Analysis, Peter A. Adekunle, Yakubu A. Bello, Udochukwu G. Nwachukwu
CBN Journal of Applied Statistics (JAS)
This study examines the impact of the COVID-19 pandemic on sectoral stock prices in Nigeria stock market using daily data covering from February 28, 2020 to June 26, 2020. Applying the autoregressive distributed lag (ARDL) bounds test, the study finds that COVID-19 pandemic had adverse impact on the stock market indices in the short run. Furthermore, the study documents negative response of sectoral stock prices to the pandemic while the stock prices of the banking sub-sector are the worst hit. Compared to the consumer goods, and industrial subsector indices, the speed of adjustment to long run equilibrium is faster for …
Intra-Hour Solar Forecasting Using Cloud Dynamics Features Extracted From Ground-Based Infrared Sky Images, Guillermo Terrén-Serrano
Intra-Hour Solar Forecasting Using Cloud Dynamics Features Extracted From Ground-Based Infrared Sky Images, Guillermo Terrén-Serrano
Electrical and Computer Engineering ETDs
Due to the increasing use of photovoltaic systems, power grids are vulnerable to the projection of shadows from moving clouds. An intra-hour solar forecast provides power grids with the capability of automatically controlling the dispatch of energy, reducing the additional cost for a guaranteed, reliable supply of energy (i.e., energy storage). This dissertation introduces a novel sky imager consisting of a long-wave radiometric infrared camera and a visible light camera with a fisheye lens. The imager is mounted on a solar tracker to maintain the Sun in the center of the images throughout the day, reducing the scattering effect produced …
On The Use Of Minimum Penalties In Statistical Learning, Ben Sherwood, Bradley S. Price
On The Use Of Minimum Penalties In Statistical Learning, Ben Sherwood, Bradley S. Price
Faculty & Staff Scholarship
Modern multivariate machine learning and statistical methodologies estimate parameters of interest while leveraging prior knowledge of the association between outcome variables. The methods that do allow for estimation of relationships do so typically through an error covariance matrix in multivariate regression which does not scale to other types of models. In this article we proposed the MinPEN framework to simultaneously estimate regression coefficients associated with the multivariate regression model and the relationships between outcome variables using mild assumptions. The MinPen framework utilizes a novel penalty based on the minimum function to exploit detected relationships between responses. An iterative algorithm that …
Stock Markets Performance During A Pandemic: How Contagious Is Covid-19?, Yara Abushahba
Stock Markets Performance During A Pandemic: How Contagious Is Covid-19?, Yara Abushahba
Theses and Dissertations
Background and Motivation: The coronavirus (“COVID-19”) pandemic, the subsequent policies and lockdowns have unarguably led to an unprecedented fluid circumstance worldwide. The panic and fluctuations in the stock markets were unparalleled. It is inarguable that real-time availability of news and social media platforms like Twitter played a vital role in driving the investors’ sentiment during such global shock.
Purpose:The purpose of this thesis is to study how the investor sentiment in relation to COVID-19 pandemic influenced stock markets globally and how stock markets globally are integrated and contagious. We analyze COVID-19 sentiment through the Twitter posts and investigate its …
Data Patterns Discovery Using Unsupervised Learning, Rachel A. Lewis
Data Patterns Discovery Using Unsupervised Learning, Rachel A. Lewis
College of Graduate Studies: Theses & Dissertations
Self-care activities classification poses significant challenges in identifying children’s unique functional abilities and needs within the exceptional children healthcare system. The accuracy of diagnosing a child's self-care problem, such as toileting or dressing, is highly influenced by an occupational therapists’ experience and time constraints. Thus, there is a need for objective means to detect and predict in advance the self-care problems of children with physical and motor disabilities. We use clustering to discover interesting information from self-care problems, perform automatic classification of binary data, and discover outliers. The advantages are twofold: the advancement of knowledge on identifying self-care problems in …
Using The Qbest Equation To Evaluate Ellagic Acid Safety Data: Generating A Qnoael With Confidence Levels From Disparate Literature, Cynthia Rose Dickerson
Using The Qbest Equation To Evaluate Ellagic Acid Safety Data: Generating A Qnoael With Confidence Levels From Disparate Literature, Cynthia Rose Dickerson
Theses and Dissertations--Pharmacy
QBEST, a novel statistical method, can be applied to the problem of estimating the No Observed Adverse Effect Level (NOAEL or QNOAEL) of a New Molecular Entity (NME) in order to anticipate a safe starting dose for beginning clinical trials. The NOAEL from QBEST (called the QNOAEL) can be calculated using multiple disparate studies in the literature and/or from the lab. The QNOAEL is similar in some ways to the Benchmark Dose Method (BMD) used widely in toxicological research, but is superior to the BMD in some ways. The QNOAEL simulation generates an intuitive curve that is comparable to the …
Offline And Online Density Estimation For Large High-Dimensional Data, Aref Majdara
Offline And Online Density Estimation For Large High-Dimensional Data, Aref Majdara
Dissertations, Master's Theses and Master's Reports
Density estimation has wide applications in machine learning and data analysis techniques including clustering, classification, multimodality analysis, bump hunting and anomaly detection. In high-dimensional space, sparsity of data in local neighborhood makes many of parametric and nonparametric density estimation methods mostly inefficient.
This work presents development of computationally efficient algorithms for high-dimensional density estimation, based on Bayesian sequential partitioning (BSP). Copula transform is used to separate the estimation of marginal and joint densities, with the purpose of reducing the computational complexity and estimation error. Using this separation, a parallel implementation of the density estimation algorithm on a 4-core CPU is …
Hpcnmf: A High-Performance Toolbox For Non-Negative Matrix Factorization, Karthik Devarajan, Guoli Wang
Hpcnmf: A High-Performance Toolbox For Non-Negative Matrix Factorization, Karthik Devarajan, Guoli Wang
COBRA Preprint Series
Non-negative matrix factorization (NMF) is a widely used machine learning algorithm for dimension reduction of large-scale data. It has found successful applications in a variety of fields such as computational biology, neuroscience, natural language processing, information retrieval, image processing and speech recognition. In bioinformatics, for example, it has been used to extract patterns and profiles from genomic and text-mining data as well as in protein sequence and structure analysis. While the scientific performance of NMF is very promising in dealing with high dimensional data sets and complex data structures, its computational cost is high and sometimes could be critical for …
Short-Term Inflation Forecasting Models For Nigeria, Sani I. Doguwa, Sarah O. Alade
Short-Term Inflation Forecasting Models For Nigeria, Sani I. Doguwa, Sarah O. Alade
CBN Journal of Applied Statistics (JAS)
Short-term inflation forecasting is an essential component of the monetary policy projections at the Central Bank of Nigeria. This paper proposes four short-term headline inflation forecasting models using the SARIMA and SARIMAX processes and compares their performance using the pseudo-out-of-sample forecasting procedure over July 2011 to September 2013. According to the results the best forecasting performance is demonstrated by the model based on the all items CPI estimated using the SARIMAX model. This model is, therefore, recommended for use in short-term forecasting of headline inflation in Nigeria. The forecasting performance up to eight months ahead, of the models based on …
An Efficient Two Sample Capture-Recapture Model With High Recaptures, Danjuma Jibasen, Yusuf J. Adams
An Efficient Two Sample Capture-Recapture Model With High Recaptures, Danjuma Jibasen, Yusuf J. Adams
CBN Journal of Applied Statistics (JAS)
This paper proposed an efficient two sample capture-recapture model (Ma) with high recaptures and compared it with the existing models like the model of no factor effect (Mo), behavioral response model (Mb) and the Petersen model (Ms), using simulated data. We found that the Petersen model provides a better estimate of the population size when the observations follow a hypergeometric distribution and the population is overestimated when recapture is high. It was also found that the proposed model provides a better estimator of the population size than the existing ones when the recapture is high. This model is particularly useful …
Causal Relationship Between Stock Market Index And Exchange Rate: Evidence From Nigeria, Abdulrasheed Zubair
Causal Relationship Between Stock Market Index And Exchange Rate: Evidence From Nigeria, Abdulrasheed Zubair
CBN Journal of Applied Statistics (JAS)
This paper uses Johansen’s cointegration to test for the possibility of cointegration and Granger-causality to estimate the causal relationship between stock market index and monetary indicators (exchange rate and M2) before and during the global financial crisis for Nigeria, using monthly data for the period 2001–2011. Results suggest absence of long-run relationship before and during the crisis. The Granger-causality tests show a uni-directional causality running from M2 to ASI before the crisis while during the period of the crisis there is absence of causality between the variables. This suggests that ASI show responsiveness to M2. Thus, absence of the direct …
Investigating Chaos In The Nigerian Asset And Resource Management (Arm) Discovery Fund, Ibiyinka A. Fuwape, Samuel T. Ogunjo
Investigating Chaos In The Nigerian Asset And Resource Management (Arm) Discovery Fund, Ibiyinka A. Fuwape, Samuel T. Ogunjo
CBN Journal of Applied Statistics (JAS)
This paper investigates chaos in a Nigerian mutual fund, Asset and Resource Management Company Limited (ARM) for a period of eleven years. The existence of chaotic signals in the data was identified by the reconstruction of the phase space of the daily closing price of the fund and the delay time was quantified using mutual information function and the embedding dimension by the false nearest neighbours, where the values were identified to be 15 and 20 respectively. The presence of chaotic signals in the ARM data was further confirmed by the correlation dimension method which yielded a dimension of 2.2 …
Modeling The Nigerian Inflation Rates Using Periodogram And Fourier Series Analysis, Chukwuemeka O. Omekara,, Emmanuel J. Ekpenyong, Micheal P. Ekerete
Modeling The Nigerian Inflation Rates Using Periodogram And Fourier Series Analysis, Chukwuemeka O. Omekara,, Emmanuel J. Ekpenyong, Micheal P. Ekerete
CBN Journal of Applied Statistics (JAS)
This work considers the application of Periodogram and Fourier Series Analysis to model all-items monthly inflation rates in Nigeria from 2003 to 2011. The main objectives are to identify inflation cycles, fit a suitable model to the data and make forecasts of future values. To achieve these objectives, monthly all-items inflation rates for the period were obtained from the Central Bank of Nigeria (CBN) website. Periodogram and Fourier series methods of analysis are used to analyze the data. Based on the analysis, it was found that inflation cycle within the period was fifty one (51) months, which coincides with the …
Nigerian Stock Index: A Search For Optimal Garch Model Using High Frequency Data, Olaoluwa Simon Yaya
Nigerian Stock Index: A Search For Optimal Garch Model Using High Frequency Data, Olaoluwa Simon Yaya
CBN Journal of Applied Statistics (JAS)
This paper attempts to fit the best Generalized Autoregressive Conditional Heteroscedastic (GARCH) model for All Share Index (ASI) of Nigerian Stock Exchange (NSE) returns. A search is made on various GARCH variants specified on the assumptions of stationarity and asymmetry. Fractionally integrated types are also considered to capture the possibility of return series having property of long range dependency. The parameter estimations are carried out on the assumptions of normality and non-normality of GARCH innovations, with models and forecasts evaluated using information criteria and loss functions respectively. Under normality assumption, Hyperbolic GARCH (HYGARCH(1,d,1)) model is selected and Integrated GARCH (IGARCH(1,1)) …
Time Series Modeling Of Nigeria External Reserves, Iheanyichukwu S. Iwueze, Eleazar C. Nwogu, Valentine U. Nlebedim
Time Series Modeling Of Nigeria External Reserves, Iheanyichukwu S. Iwueze, Eleazar C. Nwogu, Valentine U. Nlebedim
CBN Journal of Applied Statistics (JAS)
This paper discusses the levels and trend of external reserves in Nigeria. The relevance of this lies in the fact that it could help to monitor the reserves and throw early warning signal about any economic crisis. Monthly data on Nigeria external reserves for the period January 1999 to December, 2008 derived from the 2008 CBN Statistical Bulletin was analyzed using ARIMA model. Results of the analyses show that (i) the data requires logarithmic transformation to stabilize the variance and make the distribution normal (ii) the appropriate model that best describes the pattern in the transformed data is the Autoregressive- …
A Markov Decision Process Approach To Optimal Control Of A Multi-Level Hierarchical Manpower System, Akaninyene U. Udom
A Markov Decision Process Approach To Optimal Control Of A Multi-Level Hierarchical Manpower System, Akaninyene U. Udom
CBN Journal of Applied Statistics (JAS)
A recurrent problem in manpower control is how to attain the desired structural configuration in an optimal way, since it is possible to reach a desired structural configuration using different control inputs. The major aim of this paper is to develop a Markov Decision Process for optimal control of a Multi-level Hierarchical Manpower System (MHMS) by promotion and interdepartmental transfers. This is examined under control by intervention and contraction cost Markov Decision Process.
Contributions Of Financial Sector Reforms And Credit Supply To Nigerian Agricultural Sector (1978-2009), Anthony O. Onoja, M. E. Onu, S. Ajodo-Ohiemi
Contributions Of Financial Sector Reforms And Credit Supply To Nigerian Agricultural Sector (1978-2009), Anthony O. Onoja, M. E. Onu, S. Ajodo-Ohiemi
CBN Journal of Applied Statistics (JAS)
This study analyzed the trends and pattern of institutional credit supply to agriculture during pre- and post-financial reforms along with their determinants. It then compared the effects of reform policies on access to institutional credits in Nigerian agricultural sector before and after the reforms (1978 - 1985; and 1986 -2009). Relying mainly on time series data from CBN and NBS, it used ordinary least squares method (linear, semi-log and double log) to model the determinants of banking sector lending to the agricultural sector during the review period. The models were subjected to several econometric tests before accepting one. Chow test …
Determinants Of Foreign Reserves In Nigeria: An Autoregressive Distributed Lag Approach, David Irefin, Baba N. Yaaba
Determinants Of Foreign Reserves In Nigeria: An Autoregressive Distributed Lag Approach, David Irefin, Baba N. Yaaba
CBN Journal of Applied Statistics (JAS)
On global scale, central banks’ holdings of foreign reserves have escalated sharply in recent years. World international reserves holdings have risen significantly from US$1.2 trillion in 1995 to nearly US$10.0 trillion in June 2011. Dominant among these reserves are concentrated in the hands of few countries. Ten major holders of foreign reserves are mostly from Asia. Oil exporting countries in Africa and the Middle East are not left out in this trend. Nigeria’s foreign reserves rose from US$5.5 billion in 1999 to US$62.40 billion in July 2008, making Nigeria the twenty-fourth largest reserves holder in the world. This pace of …
Effects Of Exchange Rate Movements On Economic Growth In Nigeria, Eme O. Akpan, Johnson A. Atan
Effects Of Exchange Rate Movements On Economic Growth In Nigeria, Eme O. Akpan, Johnson A. Atan
CBN Journal of Applied Statistics (JAS)
This study investigates the effect of exchange rate movements on real output growth in Nigeria. Based on quarterly series for the period 1986 to 2010, the paper examines the possible direct and indirect relationship between exchange rates and GDP growth. The relationship is derived in two ways using a simultaneous equations model within a fully specified (but small) macroeconomic model. A Generalised Method of Moments (GMM) technique was explored. The estimation results suggest that there is no evidence of a strong direct relationship between changes in exchange rate and output growth. Rather, Nigeria’s economic growth has been directly affected by …
Exchange Rate Volatility In Nigeria: Consistency, Persistency & Severity Analyses, Babatunde Adeoye, Akinwande A. Atanda
Exchange Rate Volatility In Nigeria: Consistency, Persistency & Severity Analyses, Babatunde Adeoye, Akinwande A. Atanda
CBN Journal of Applied Statistics (JAS)
The adoption of the International Monetary Fund (IMF) Structural Adjustment Programme (SAP) in 1986 resulted in the transition from fixed exchange rate regime to floating exchange rate regime in Nigeria. Ever since, the exchange rate of naira vis-à-vis the U.S dollar has attained varying rates all through different time horizons. On this basis, this study examines the consistency, persistency, and severity (degree) of volatility in exchange rate of Nigerian currency (naira) vis-a-vis the United State dollar using monthly time series data from 1986 to 2008. The standard Purchasing Power Parity (PPP) model was used to analyze the long-run consistency of …