Fitting Time Series Research Articles

Impact of Exchange Rate Devaluation in Ethiopia and Forecasting Foreign Exchange Rate Using ARIMA Model

The exchange rate is an important indicator of economic activity that policymakers use to formulate policies. This paper is based on fitting historical nominal exchange rate time series expressed in terms of past values of itself plus current and lagged values of error term using the Autoregressive Integrated Moving Average (ARIMA) model over the period 1971-2020, resulting in the model (2,1,1) to forecast the next 15 years. The projection's performance is assessed using data from the preceding fifty years sourced from World Bank, and the forecast indicates that domestic currency depreciation will become more prevalent in order to stimulate exports. Moreover, the ARDL model is used to examine the impact of exchange rate, import, export, and inflation rate on RGDP from 1977 to 2018. The unit root test (Augmented Dickey- Fuller test) was used to verify the integration order of the variables. The five variables are used in the cointegration analysis. The bounds test of cointegration was used in this work. The results showed that the F-statistics value is greater than the upper boundaries at all levels of significance, indicating that individual variables have a long-term relationship with RGDP. This led to the estimation of the Error Correction Model (ECM), in which 25.1 percent of the disequilibrium is adjusted annually to bring the system back into equilibrium. Furthermore, nominal exchange rate and import has positive contribution to RGDP while inflation has adverse effect on RGDP in the long-run. Besides, inflation has a negative impact to RGDP in the short run due to its lag period effects. Keywords : forecasting, ARIMA model, ARDL model DOI: 10.7176/EJBM/13-17-02 Publication date: September 30 th 2021

Current and Future Trends in Hospital Utilization of Patients With Schizophrenia in Korea: A Time Series Analysis Using National Health Insurance Data.

Objective This study aimed to investigate trends in hospital utilization of patients with schizophrenia during the last 10 years in Korea and to predict future trends using time series analysis. Methods We determined the numbers of patients receiving outpatient or inpatient treatment for schizophrenia per month between 2010 and 2019, using National Health Insurance claims data. Facebook’s Prophet was used to fit time series models based on observations for the previous 120 months, and to predict trends over the next 36 months. Results The number of hospitalized patients per month has declined rapidly since 2015, but the monthly number of outpatient visits has steadily increased. Monthly hospital utilization has increased in patients aged ≤29 and ≥50 years, but has declined rapidly since 2014–2015 in patients in their 30s and 40s. The upward trend in overall hospital utilization has slowed considerably in recent years. These trends are expected to continue over the next few years. Conclusion This study revealed some notable changes in the hospital utilization patterns of patients with schizophrenia in recent years. There is a need to closely monitor and anticipate potential problems caused by these changing trends.

Unexpected Features of Financial Time Series: Higher-Order Anomalies and Predictability

Examining the daily Dow Jones Industrial Average (DJI) we find evidence both of higher-order anomalies and predictability. While most researchers are only aware of the relatively harmless anomalies that occur just in the mean, the first part of this article provides empirical evidence of more dangerous kinds of anomalies occurring in higher-order moments. This evidence casts some doubt on the common practice of fitting standard time series models (e.g., ARMA models, GARCH models, or stochastic volatility models) to financial time series and carrying out tests based upon autocorre lation coefficients without making proper provision for these anomalies. The second part of this article provides evidence in favor of the predictability of the returns on the DJI and, more interestingly, against the efficient market hypothesis. The special value of this evidence is due to the simplicity of the involved methods.

Temperature-related effects on respiratory medical prescriptions in Spain

BackgroundThe increased risk of mortality during periods of high and low temperatures has been well established. However, most of the studies used daily counts of deaths or hospitalisations as health outcomes, although they are the ones at the top of the health impact pyramid reflecting only a limited proportion of patients with the most severe cases. ObjectivesThis study evaluates the relationship between short-term exposure to the daily mean temperature and medication prescribed for the respiratory system in five Spanish cities. MethodsWe fitted time series regression models to cause-specific medical prescriptions, including different respiratory subgroups and age groups. We included a distributed lag non-linear model with lags up to 14 days for daily mean temperature. City-specific associations were summarised as overall-cumulative exposure-response curves. ResultsWe found a positive association between cause-specific medical prescriptions and daily mean temperature with a non-linear inverted J- or V-shaped relationship in most cities. Between 0.3% and 0.6% of all respiratory prescriptions were attributed to cold for Madrid, Zaragoza and Pamplona, while in cities with only cold effects the attributable fractions were estimated as 19.2% for Murcia and 13.5% for Santander. Heat effects in Madrid, Zaragoza and Pamplona showed higher fractions between 8.7% and 17.2%. The estimated costs are in general higher for heat effects, showing annual values ranging between €191,905 and €311,076 for heat per 100,000 persons. ConclusionsThis study provides novel evidence of the effects of the thermal environment on the prescription of medication for respiratory disorders in Spain, showing that low and high temperatures lead to an increase in the number of such prescriptions. The consumption of medication can reflect exposure to the environment with a lesser degree of severity in terms of morbidity.

Decreased Global Interest in Oral Cancer During the COVID-19 Pandemic.

Objective:Oral cancer is one of the most common malignancies in developing countries, but studies using global data are scarce. The aim of this study is to analyze the search interests for oral cancer using mouth cancer, tongue cancer, gum cancer, and lip cancer as common keywords. Methods:Internet searches relating to oral cancer from 2010 to 2020, from 250 countries and dependent areas, were retrieved from Google Trends. Color densities in a heat map were used to show geographic differences. Kruskal-Wallis test with post hoc Dunn’s analysis was used to perform yearly comparisons of searches for mouth cancer, tongue cancer, gum cancer, and lip cancer. Search results within 2020 were also compared to determine differences. Forecasting searches from 2021 to 2022 were done by fitting time series models. Results:From 29 of 250 (11.6%) countries, the highest search values were observed for mouth cancer in Sri Lanka, Qatar, Bangladesh, Finland, Netherlands, Spain, and France. Compared to 2020, greater searches were seen in 2018 (Mdn = 91%, P = 0.023) and 2019 (Mdn = 94%, P = 0.012) for mouth cancer, and 2019 (Mdn = 17%, P = 0.035) for lip cancer. The relative search volumes for gum cancer and lip cancer were substantially lower than mouth cancer during the COVID-19 pandemic. Conclusion:Higher-income countries tend to be more interested in seeking information about oral cancer. Noteworthy decline in the interest in seeking information online for oral cancer may have crucial implications during the COVID-19 pandemic. Google Trends offer an invaluable and inexpensive means for oral cancer surveillance and health-seeking behavior.

The effects of multi-echo fMRI combination and rapid T2*-mapping on offline and real-time BOLD sensitivity

A variety of strategies are used to combine multi-echo functional magnetic resonance imaging (fMRI) data, yet recent literature lacks a systematic comparison of the available options. Here we compare six different approaches derived from multi-echo data and evaluate their influences on BOLD sensitivity for offline and in particular real-time use cases: a single-echo time series (based on Echo 2), the real-time T2*-mapped time series (T2*FIT) and four combined time series (T2*-weighted, tSNR-weighted, TE-weighted, and a new combination scheme termed T2*FIT-weighted). We compare the influences of these six multi-echo derived time series on BOLD sensitivity using a healthy participant dataset (N = 28) with four task-based fMRI runs and two resting state runs. We show that the T2*FIT-weighted combination yields the largest increase in temporal signal-to-noise ratio across task and resting state runs. We demonstrate additionally for all tasks that the T2*FIT time series consistently yields the largest offline effect size measures and real-time region-of-interest based functional contrasts and temporal contrast-to-noise ratios. These improvements show the promising utility of multi-echo fMRI for studies employing real-time paradigms, while further work is advised to mitigate the decreased tSNR of the T2*FIT time series. We recommend the use and continued exploration of T2*FIT for offline task-based and real-time region-based fMRI analysis. Supporting information includes: a data repository (https://dataverse.nl/dataverse/rt-me-fmri), an interactive web-based application to explore the data (https://rt-me-fmri.herokuapp.com/), and further materials and code for reproducibility (https://github.com/jsheunis/rt-me-fMRI).

Standardized flux seasonality metrics: a companion dataset for FLUXNET annual product

Abstract. Phenological events are integrative and sensitive indicators of ecosystem processes that respond to climate, water and nutrient availability, disturbance, and environmental change. The seasonality of ecosystem processes, including biogeochemical fluxes, can similarly be decomposed to identify key transition points and phase durations, which can be determined with high accuracy, and are specific to the processes of interest. As the seasonality of different processes differ, it can be argued that the interannual trends and responses to environmental forcings can be better described through the fluxes' own temporal characteristics than through correlation to traditional phenological events like bud break or leaf coloration. Here we present a global dataset of seasonality or phenological metrics calculated for gross primary productivity (GPP), ecosystem respiration (RE), latent heat (LE), and sensible heat (H) calculated for the FLUXNET2015 Dataset of about 200 sites and 1500 site years of data. The database includes metrics (i) on an absolute flux scale for comparisons with flux magnitudes and (ii) on a normalized scale for comparisons of change rates across different fluxes. Flux seasonality was characterized by fitting a single-pass double-logistic model to daily flux integrals, and the derivatives of the fitted time series were used to extract the phenological metrics marking key turning points, season lengths, and rates of change. Seasonal transition points could be determined with a 90 % confidence interval of 6–11 d for GPP, 8–14 d for RE, 10–15 d for LE, and 15–23 d for H. The phenology metrics derived from different partitioning methods diverged, at times significantly. This Flux Seasonality Metrics Database (FSMD) can be accessed at the US Department of Energy's (DOE) Environmental Systems Science Data Infrastructure for a Virtual Ecosystem (ESS-DIVE, https://doi.org/10.15485/1602532; Yang and Noormets, 2020). We hope that it will facilitate new lines of research, including (1) validating and benchmarking ecosystem process models, (2) parameterizing satellite remote sensing phenology and PhenoCam products, (3) optimizing phenological models, and (4) generally expanding the toolset for interpreting ecosystems responses to changing climate.

Effects of Hot Nights on Mortality in Southern Europe.

There is strong evidence concerning the impact of heat stress on mortality, particularly from high temperatures. However, few studies to our knowledge emphasize the importance of hot nights, which may prevent necessary nocturnal rest. In this study, we use hot-night duration and excess to predict daily cause-specific mortality in summer, using multiple cities across Southern Europe. We fitted time series regression models to summer cause-specific mortality, including natural, respiratory, and cardiovascular causes, in 11 cities across four countries. We included a distributed lag nonlinear model with lags up to 7 days for hot night duration and excess adjusted by daily mean temperature. We summarized city-specific associations as overall-cumulative exposure-response curves at the country level using meta-analysis. We found positive but generally nonlinear associations between relative risk (RR) of cause-specific mortality and duration and excess of hot nights. RR of duration associated with nonaccidental mortality in Portugal was 1.29 (95% confidence interval [CI] = 1.07, 1.54); other associations were imprecise, but we also found positive city-specific estimates for Rome and Madrid. Risk of hot-night excess ranged from 1.12 (95% CI = 1.05, 1.20) for France to 1.37 (95% CI = 1.26, 1.48) for Portugal. Risk estimates for excess were consistently higher than for duration. This study provides new evidence that, over a wider range of locations, hot night indices are strongly associated with cause-specific deaths. Modeling the impact of thermal characteristics during summer nights on mortality could improve decisionmaking for preventive public health strategies.

Fitting Time Series with Heavy Tails and Strong Time Dependence

Earlier, a model of a time series with heavy tails constructed from a Gaussian time series was developed. In the present paper, the reverse problem is considered: an estimator of the copula function is built; the copula function is a nonlinear function that maps Gaussian variables to the variables from the Frechet maximum domain of attraction. The statistical properties of this estimator are considered for a stationary time series with a low rate of covariance decay.

Combination of the Levenberg–Marquardt and differential evolution algorithms for the fitting of postseismic GPS time series

Postseismic global positioning system (GPS) time series are of fundamental importance for investigating the physical mechanisms of postseismic deformations, as well as the construction and maintenance of terrestrial reference frames. Particularly, methods for constructing accurate fitting models for such time series are critical. Based on the physical features of postseismic deformation models, we propose a new algorithm that combines the strengths of the Levenberg–Marquardt (LM) and differential evolution (DE) algorithms, that is, the LM + DE algorithm. In this algorithm, the parameters are initialised by the constrained DE algorithm; the final parameters of the postseismic model are then solved by the LM algorithm. To validate the proposed method, DE, LM, and LM + DE were compared using synthetic and observational data from the 2011 Tohoku Earthquake. For all tests based on synthetic data, the LM + DE algorithm consistently converged to the global solution and the residual is small, regardless of how the independent parameter was varied. In the 2011 Tohoku earthquake, the parameters calculated by the LM + DE algorithm matched consistently for the global solution with a 100% passing rate after constraints were provided for the ratios of the initial relaxation time parameters. In contrast, the LM and DE algorithms individually achieved passing rates of only 22% and 1%, respectively. These results demonstrate that the proposed LM + DE algorithm effectively solves the initial estimate problem in the fitting of nonlinear postseismic models, and also ensures that the fits are mathematically optimal and consistent with physical reality.

Recovering Within-Person Dynamics from Psychological Time Series

Idiographic modeling is rapidly gaining popularity, promising to tap into the within-person dynamics underlying psychological phenomena. To gain theoretical understanding of these dynamics, we need to make inferences from time series models about the underlying system. Such inferences are subject to two challenges: first, time series models will arguably always be misspecified, meaning it is unclear how to make inferences to the underlying system; and second, the sampling frequency must be sufficient to capture the dynamics of interest. We discuss both problems with the following approach: we specify a toy model for emotion dynamics as the true system, generate time series data from it, and then try to recover that system with the most popular time series analysis tools. We show that making straightforward inferences from time series models about an underlying system is difficult. We also show that if the sampling frequency is insufficient, the dynamics of interest cannot be recovered. However, we also show that global characteristics of the system can be recovered reliably. We conclude by discussing the consequences of our findings for idiographic modeling and suggest a modeling methodology that goes beyond fitting time series models alone and puts formal theories at the center of theory development.

Early prognostic factors of patients with acquired pneumonia under the analysis of autoregressive integrated moving average model-based pathogenic infectious influenza virus

In view of the high mortality rate and complications of acquired pneumonia (AP), the improved autoregressive integrated moving average (ARIMA) model was applied to predict the early prognostic factors of patients with AP. First, a multi-factor mixed forecast ARIMA-classification and regression trees (CART) classification tree model was established in this study, and the ARIMA-CART model was used for time series fitting analysis to observe the incidence trend of AP. Finally, a predictive model for the risk and prognosis of elderly patients with AP was constructed. The experimental results proved that the serum creatine kinase index and lactate dehydrogenase index of patients with AP had a resistance effect on their prognosis. Therefore, the serum creatine kinase index and lactate dehydrogenase index of patients with AP should be dealt with in actual medical scenarios. The indexes can be reasonably detected and can effectively improve the prognosis of patients. This had a certain reference for the promotion of ARIMA model in the research of early prognostic factors in patients with AP.

Forecasting hand-foot-and-mouth disease cases using wavelet-based SARIMA-NNAR hybrid model.

BackgroundHand-foot-and-mouth disease_(HFMD) is one of the most typical diseases in children that is associated with high morbidity. Reliable forecasting is crucial for prevention and control. Recently, hybrid models have become popular, and wavelet analysis has been widely performed. Better prediction accuracy may be achieved using wavelet-based hybrid models. Thus, our aim is to forecast number of HFMD cases with wavelet-based hybrid models.Materials and methodsWe fitted a wavelet-based seasonal autoregressive integrated moving average (SARIMA)–neural network nonlinear autoregressive (NNAR) hybrid model with HFMD weekly cases from 2009 to 2016 in Zhengzhou, China. Additionally, a single SARIMA model, simplex NNAR model, and pure SARIMA–NNAR hybrid model were established for comparison and estimation.ResultsThe wavelet-based SARIMA–NNAR hybrid model demonstrates excellent performance whether in fitting or forecasting compared with other models. Its fitted and forecasting time series are similar to the actual observed time series.ConclusionsThe wavelet-based SARIMA–NNAR hybrid model fitted in this study is suitable for forecasting the number of HFMD cases. Hence, it will facilitate the prevention and control of HFMD.

Fitting time series models for longitudinal surveys with nonignorable missing data

In this paper, we develop a method for handling nonignorable missing data in fitting time series models for longitudinal surveys. We assume that the response probability not only depends on auxiliary variables but also the current and past outcomes which are subject to missingness. Under a nonignorable missing mechanism, an observed likelihood estimation approach is proposed based on the distribution of the observed sample and the response probability. Also, we derive a series expansion approximation for an integral in the observed likelihood function. Results from simulation studies are presented to show the usefulness of the proposed methodology. An empirical example based on data from the AIDS Clinical Trial Group 193A Study is provided to illustrate the proposed method.

Model-based forecasting for Canadian COVID-19 data.

BackgroundSince March 11, 2020 when the World Health Organization (WHO) declared the COVID-19 pandemic, the number of infected cases, the number of deaths, and the number of affected countries have climbed rapidly. To understand the impact of COVID-19 on public health, many studies have been conducted for various countries. To complement the available work, in this article we examine Canadian COVID-19 data for the period of March 18, 2020 to August 16, 2020 with the aim to forecast the dynamic trend in a short term.MethodWe focus our attention on Canadian data and analyze the four provinces, Ontario, Alberta, British Columbia, and Quebec, which have the most severe situations in Canada. To build predictive models and conduct prediction, we employ three models, smooth transition autoregressive (STAR) models, neural network (NN) models, and susceptible-infected-removed (SIR) models, to fit time series data of confirmed cases in the four provinces separately. In comparison, we also analyze the data of daily infections in two states of USA, Texas and New York state, for the period of March 18, 2020 to August 16, 2020. We emphasize that different models make different assumptions which are basically difficult to validate. Yet invoking different models allows us to examine the data from different angles, thus, helping reveal the underlying trajectory of the development of COVID-19 in Canada.FindingThe examinations of the data dated from March 18, 2020 to August 11, 2020 show that the STAR, NN, and SIR models may output different results, though the differences are small in some cases. Prediction over a short term period incurs smaller prediction variability than over a long term period, as expected. The NN method tends to outperform other two methods. All the methods forecast an upward trend in all the four Canadian provinces for the period of August 12, 2020 to August 23, 2020, though the degree varies from method to method. This research offers model-based insights into the pandemic evolvement in Canada.

Characterizing urban land changes of 30 global megacities using nighttime light time series stacks

Worldwide urbanization has brought about diverse types of urban land use and land cover (LULC) changes. The diversity of urban land changes, however, have been greatly under studied, since the major focus of past research has been on urban growth. In this study, we proposed a framework to characterize diverse urban land changes of 30 global megacities using monthly nighttime light time series from VIIRS data. First, we developed a Logistic-Harmonic model to fit VIIRS time series. Second, by leveraging the uniqueness of urban land change and nighttime light data, we incorporated temporal information of VIIRS time series and proposed a new classification scheme to produce monthly maps of built-up areas and to disentangle urban land changes into five categories. Third, we provided an in-depth analysis and comparison of urban land change patterns of the selected megacities. Results demonstrated that the Logistic-Harmonic model yielded a robust performance in fitting VIIRS time series. Temporal features based classification can not only significantly improve the mapping accuracy of built-up areas, especially for regions with heterogeneous built-up and non-built-up landscapes, but also promoted temporal consistency and classification efficiency. Urban land changes occurred in 51% of the built-up pixels of the megacities. Compared with urban growth, other types of urban land change, particularly land use intensification, contributed to an unexpectedly large proportion of the changes (83%). The findings of this study offer an insightful understanding on global urbanization processes in megacities, and evoke further investigation on the environmental and ecological implications of urban land changes.

Forecasting COVID-19 pandemic in Alberta, Canada using modified ARIMA models

Background and objectivesAuto regressive integrated moving average (ARIMA) model is a popular model to forecast future values of a time series using the past values of the same series. However, if the variance of the time series varies with time, the 95% confidence interval estimated by the ARIMA will not be accurate. This study proposes a method to revise the ARIMA model to suit time series with heteroscedasticity. MethodsMultiple historical ARIMA models were constructed with publicly available COVID-19 data in Alberta, Canada. The time series between different time periods were applied for these models. The means and their 95% confidence intervals of the differences between the forecasted values and the corresponding actual values were computed. The forecasted values of the general ARIMA models were modified by adding these differences. ResultsThe average incident cases forecasted with the proposed method are lower than those with a general ARIMA model during the forecasted period. The 95% confidence intervals of the forecasted incidence with the proposed method are narrower. During the forecasted period (13 weeks) the average incidence was predicted to increase first and then decrease exponentially. ConclusionThe proposed method can be used to automatically specify the best ARIMA model, to fit time series with heteroscedasticity and to forecast longer period of the trends in the future. In the next 13 weeks, the Covid-19 incidence may decrease but not eliminate. To stop the transmission of infections eventually, persistent effects complying with accurate forecasts are necessary.

Estimating the Proportion of Antibiotics Attributable to Common Paediatric Respiratory Viruses: An Example Leveraging Unique Population-Based Prescribing and Laboratory Data

IntroductionInappropriate antibiotic prescribing, such as that for viral illness, is common in primary care. This is of growing interest given concerns around antimicrobial resistance and harms associated with unnecessary treatment; however, current data limitations have hindered population-based estimates of the proportion of community-prescribed antibiotics attributable to common respiratory viruses.
 Objectives and ApproachTo estimate the proportion of antibiotics prescribed in primary care to young children attributable to common respiratory viruses, including respiratory syncytial virus (RSV), influenza, human metapneumovirus (HuMPV) and parainfluenza. We leveraged two unique sources of comprehensive, linked population-based administrative data on dispensed antibiotic prescriptions and laboratory tests for respiratory viruses for all Scottish children (<5 years). We fit time series negative binomial models to predict weekly antibiotic prescribing rates from positive viral tests rates for the period April 1, 2009 through Dec 27, 2017. Using linked demographic and hospitalization data, we stratified our analysis by age, presence of high-risk chronic medical conditions, and antibiotic class.
 ResultsWe included data on over 6 million antibiotic prescriptions among nearly 800,000 children. An estimated 6.9% (95% CI: 5.6,8.3), 2.4% (1.7,3.1), and 2.3% (0.8,3.9) of prescribed antibiotics were attributable to RSV, influenza and HuMPV, respectively. RSV was consistently associated with the highest proportion of antibiotics prescribed across all analyses but particularly among children without chronic conditions [4.30% (3.19, 5.41)] and for amoxicillin [8.10% (6.43, 9.76)] and macrolide prescriptions [7.65% (6.14, 9.16)].
 Conclusion / ImplicationsNearly 14% of antibiotics prescribed to Scottish children in this study were attributable to common viral pathogens such as RSV for which antibiotics are not recommended. This highlights clear targets for antibiotic stewardship programs and suggests antibiotic prescribing could be reduced once an RSV vaccine is introduced.

PyAEM: A Python toolkit for aquatic ecosystem modelling

Aquatic ecosystem modelling has been a challenging task for scientists partly due to limited tools/software to support. This study attempted to develop a Python toolkit (PyAEM) that was able to support multiple procedures in aquatic ecosystem modelling. PyAEM included improved algorithms for sensitivity analysis, parameter optimization, data assimilation and model visualization. In PyAEM, one-at-a-time and variance-based methods were implemented to identify sensitive parameters in target models. Genetic algorithm was improved for global optimization of model parameters. Ensemble Kalman Filter was implemented for assimilating multi-source measured data to improve model performance. An aquatic ecosystem model viewer was specifically developed for model visualization with the advantages of multi-scenario comparison, model fit evaluation, multi-mesh support and time series data extraction. An application overview of PyAEM in watershed and lake modelling is given, and revealed that PyAEM can be easily adapted to support the implementation of a case for aquatic ecosystem modelling.

Time Series Predictive Models for Social Networking Media Usage Data: The Pragmatics and Projections

Aims: We have set forth three main objectives in the work presented in this paper, they are namely, to study how social networking media usage is surging over the time for three social media networks viz., Facebook, Twitter and LinkedIn, ii.to develop best fitting time series predictive models for predicting future usage of three network media and, iii. to make a comparative analysis to herald the ups and downs noticed in the usage across three network media considered.
 Study Design: Application of time series techniques for the analysis of social network user’s data. The main research question addressed by this work is to see how time series models augurs for time dependent data such as the one chosen in this research.
 Place and Duration of Study: Research Center, Department of Master of Computer Applications, Siddaganga Institute of Technology, Tumakuru, Karnataka, India, between January 2020- April 2020.
 Methodology: The work delved on collection three social network users (Facebook, LinkedIn, and Twitter) data for a span of nine years i.e., for the tenure 2011-2019. One dimensional, two dimensional and three dimensional visual analytics is made prior to time series analysis. Time series predictive analytics involved development of best fits for prediction. To select the best fits among linear, polynomial, exponential, power function and logarithmic models, mean absolute error and root mean square error metrics were used.
 Results: Linear, polynomial function trend lines proved to be the best for Facebook, LinkedIn and Twitter respectively with low values of MAE and RMSE and high values of regression coefficients as compared with other kinds of models. Apart from the error metrics, the Theil’s U-statistic values of 0.928, 1.008 and 1.21 for Facebook, Twitter and LinkedIn also heralded the fact that these functions are superior models when compared with other naïve models. It is also projected that by 2025, Facebook will see 10,000 billion, followed by LinkedIn at 1500 billion while Twitter would see 750 billion people if same kind of surge trend prevails in user numbers across three networks considered in this research.
 Conclusion: This paper presented a unique work which is supposedly deemed to be the first of its kind to the best of the knowledge of authors. The models come with a limitation that, they can provide accurate projection if the same trend prevails in the pattern of upheavals in usage.