Can Cameroon become an emerging economy by the year 2035 ? Projections from univariate time series analysis

Cameroon is among the African countries aspiring to become an emerging economy by the year 2035. Therefore, projecting into the future by policy makers in order to know the right course of action is imperative. The objective of this study is to identify a good forecasting model that can predict Cameroon’s future economic growth rate and to ascertain whether policy makers could maintain a steady and sustainable growth rate that will fructify its vision of becoming an emerging economy by 2035. The study employed ARIMA and ARIMA/GARCH models on quarterly data from 1994q1 to 2014q4 on economic growth rate extracted from World Bank Development Indicators. Among the different models used, the mixed ARIMA(0,1,3)/E-GARCH(1,2) model was selected on the basis of the root mean squared error (RMSE), mean absolute percentage error (MAPE), mean absolute error (MAE) and the Theil's inequality coefficient (U-STATISTICS) criteria. The major finding of this study is that Cameroon’s future growth rate is slow and not sustainable with an average annual projected growth of approximately 6.099 %, unlike China that maintained a steady growth rate till it transcended into an emerging economy. The projected rate compared to China’s growth rates, shows that Cameroon needs to double her efforts in order to fructify its vision of becoming an emerging economy by the year 2035.

leading economies of the world by the year 2035.To fructify its vision, the government has prioritized five areas of development: (i) infrastructure development in energy; (ii) telecoms and transport; (iii) development of the rural and mining sectors; (iv) improvement in human resources through health, education, and training; (v) greater regional integration and export diversification; and financial sector deepening and strengthening (Cameroon, 2009).It is expected that all these will be achievable through a robust industrialization strategy, greater national integration and the advancement of democracy, private-sector promotion strategy, good governance and management strategy with blueprint for a resource allocation strategy, a strategy for sub-regional and international integration, a strategy for partnership and development assistance, and a development funding strategy (Cameroon, 2009).
However, the aspirations of becoming an emerging economy seem to be fading gradually, simply because the government does not want to relinquish its centrally planned economic structure to a decentralized system that fully integrates the private sector.The emergence of China began with a transition from a centrally planned economy to a socialist market economy initiated by the then Vice Premier of China Deng Xiaoping (Barth et al., 2009).Also, the country is saddled with a high rate of corruption, severe insurgency that is diverting attention and resources and a despondent democratic society.Freedom House Assessment (2014) shows that the regime is authoritarian and restrains the political rights and civil liberty of its citizens (Freedom House, 2014).Though Cameroon's growth indicator exhibited a positive upward trend within the last five years, that is, approximately 3. 27, 4.14, 4.49, 5.56 and 5.89% in 2010, 2011, 2012, 2013and 2014respectively (World Development Index, 2015), the process is still very slow and not promising.World Bank Development Index (2015) shows that China grew at an approximate rate of 7. 81, 8.17, 9.02, 10.75% and 15.21% in 1980, 1981, 1982, 1983 and 1984 respectively just immediately after the transition process was initiated in 1979.
However, since the government is determined and is effortlessly strategizing towards an emerging economy by the year 2035 despite its socio-politico economic upheavals, it needs to gauge the tempo of its future economic growth.Projecting into the future will give a clearer picture of how the state of the economy is likely to perform and also inform policy makers on whether they are progressing or not and how they need to fine-tune their efforts, the quantum of resources to be mobilized and allocated efficiently and whether they can sustain a steady and increasing economic growth that will guarantee the country's emergence by the year 2035.
Therefore, the rationale for this study is to identify a forecasting model that can project Cameroon's future growth rates that will eventually guide policy makers to carefully strategise ahead of time, thereby, fructifying its vision of an emerging Cameroon in 2035.

Theoretical literature
Historical patterns in time series data can be generated with the use of forecasting models predicated on mathematical formulae.Time series data by their nature, display a pattern such that their successive observations are dependent or correlated.The principal aim of modelling is to capture this underlying phenomenon using the observed time series in order to predict the likely realization of future values (Nkwatoh, 2012).
Early traditional forecasting models range from; the Naïve model to the Moving Averages and Exponential Smoothing models and to the Holt's and Winter's models.Nasir et al. (2008) note that though the applicability of the naïve method is simple and can be used for relatively short time series, yet the model is highly sensitive to changes in actual values such that a sudden drop or sharp increase in the series will affect the forecast.Furthermore, fitting this model type will result in the loss of the first two observations in the series, just like the moving averages method which gives equal weighting to each and every observation, with the average value being over dominated by extreme values (Yule, 1926;Pardhan, 2012).The major advantage of the exponential smoothing method among others is that, it embodies the advantages of weighted moving averages since current observations are assigned larger weights and also, it reacts more quickly to changes in data patterns than the moving averages (Pardhan, 2012).However, the main difficulty encountered when using this method resides in the determination of the size of a smoothing coefficient (α) (Nasir et al., 2008).The Holt's method is highly adaptable for data with small local trend with no seasonal patterns while the Winter's method suitably works for data that has both seasonal and a trend factor alongside a random pattern (see, Eviews-2).However, it poses the same problem of choosing α just like with exponential smoothing.
In recent years, forecasters have applied alternative approaches (Multiple Regression Models and the Box-Jenkins' Autoregressive Integrated Moving Average (ARIMA) Model) to forecast future values, owing to the fact that the traditional methods of forecasting are generally rigorous and time consuming, and also they require a laborious iterative approach.
The regression method has appeared in contemporary motivating literature: (Syariza and Noorhafiza, 2005;Taylor, 2008;Javadadi and Suhartono, 2010) etc.However, the major setback of the regression approach reposes on the severity of its underlying assumptions, thereby paving way for the Box-Jenkins methodology being extensively used in recent times (Floros, 2005;Kamil, and Noor, 2006;Purna, 2012) etc.Two important assumptions of regression analysis that pose a threat to model building and forecasting are: independence of residuals (No Autocorrelation) and constant variance of residuals (Homoscedasticity).Violation of these two assumptions may make the regression estimates meaningless (Nanda, 1988;Greene, 2003;Bourbonnais, 2004 andGujarati, 2004).Another key assumption of regression analysis is the independence of explanatory variables (Multicollinearity) and its violation which leads to a singular matrix (Determinant Equals to Zero) thus, making it impossible to obtain regression estimates.
For the sake of forecasting, the Box-Jenkins' method is considered to be superior as it directly takes into consideration the problem of autocorrelation (Nanda, 1988).Yule (1926) first introduced the autoregressive (AR) models, which was later complemented in 1937 by Slutsky with the introduction of Moving Averages (MA) models.Wold (1938) combined the two mathematical models commonly referred to as the ARMA model (Autoregressive Moving Average).
He showed that ARMA processes could be used to model any stationary time series as long as the appropriate number of AR terms (p), and the appropriate number of MA terms (q), was correctly specified.This implies that any series (y t ) can be modelled as a linear combination of its previous time value and a finite number of its past errors.That is: (1) However, ARMA models could not be applied to real series until the mid 1960s when computing technology became available and economical (Makridakis and Hison, 1979).The use of ARMA models was made popular by Georg Box and Gvily Jenkins (1970), with the provision of guidelines for making the series stationary in both its mean and variance1 .Makridakis and Hison (1979) also suggest the use of the coefficients of the sample autocorrelation functions (ACF) and partial autocorrelation functions (PACF) for determining appropriate order of p and q (Nanda, 1988;Greene, 2003;Bourbonnais, 2004;Gujarati, 2004).Their approach to modelling ARIMA models otherwise known as the Box-Jenkins methodology has become highly applicable in recent times.The applicability of this methodology has permeated other areas of science chiefly because of the development of new statistical procedures accompanied by more powerful computers that can manage larger data sets with ease.The integrated component (I), gives the model leverage over non-stationary time series.This methodology is found in the empirical works of (Cooper, 1972;Nelson,1972;Elliot, 1973), among others (Narasimham et al., 1974;McWhorter, 1975) etc and recently in the 2000s (Proiettti, 2001;Mandal, 2005;Ghosh, 2008;Pei, 2008;Wankhade et al., 2010;Ahmad and Latif, 2011;Lee et al, 2012) etc.
Just like other forecasting methods, the short comings of the Box-Jenkins' methodology are not farfetched.First, the interpretation of the autocorrelation functions (ACF and PACF)2 is sometimes difficult and requires a lot of expertise.Second, ARIMA models are susceptible to outliers leading to false results.However, Javendani and Suhartono (2010) showed that, the exponential smoothing method can suitably replace the ARIMA model in this case, because it gives more weight to the most recent observation.

Empirical Literature
Modelling macroeconomic variables and projecting into the future, with the use of historical data from time series (univariate or multivariate time series) is not only a fascinating and academic exercise but also, it gives a bearing to policy makers' decision making-process.Modelling economic growth like any other macroeconomic variable has either been analyzed using the traditional moving averages method or the use of econometric models, often related to stationary time series, ranging from the simple ordinary least square technique, to the Autoregressive Integrated Moving Average (ARIMA) models and to the Generalised Autoregressive Conditional Heteroscedastic (GARCH) models (Elham, 2010;Assis et al., 2010).
Recently, the Box and Jenkins methodology has been extensively used, to project future macroeconomic variables including economic growth.
However, other econometric techniques have been used other than the ARIMA models proposed by Box and Jenkins.For instance, Gan and Wang (1993) used the Base Bayesian Vector Autoregressive (BVAR) model to project the economic growth of Singapore.Abeysinghe (1998) employed an exponential nonlinear approach to predict Singapore's seasonal GDP.Hukkinen and Viren (1999) used a model based on the Keynesian theory to project 50 macroeconomic variables for Finland.Similarly, Jaafar (2006) and Nasir et al. (2008) have used methods other than ARIMA models.Other econometric models have proven their predictive power over ARIMA models.Baffigi, Golinelli and Parigi (2004), predicted the growth rate of GDP in Germany, France, Italy and Europe region using the Bridge Model (BM) and other basic models such as ARMA, VAR and a structural model.They concluded that the Bridge Model (BM) outperformed all 3) DIAGNOSTIC TEST other techniques used in their study.A more recent submission by Sarbijan (2014) shows that the Markov switching model could better forecast Iran's economic growth than ARIMA models.Gil-Alana ( 2001) showed that a Bloomfield exponential spectral model gave a feasible result, in lieu of ARMA models, for UK's unemployment rate while, Golan and Perloff (2002) concluded that nonparametric methods of forecasting unemployment rates in the U.S outperformed other models.

4) MAKE FORECAST
Many studies have focused entirely on the ARIMA models to predict macroeconomic variables.Maity and Chatterjee (2012) showed that a simple tentative ARIMA (1, 2, 2) model was well fitted for projecting Indian's GDP growth rates.Similarly, Reynolds et al. (1995) and Reilly (1980) have also projected economic growth rates using ARIMA models.
The choice of the ARIMA models for forecasting other macroeconomic variables other than GDP can also be found in studies: Purna (2012) forecasting cement production output in India; Mordi et al. (2006) analyzing inflation rates in Nigeria; Fatimah and Roslan (1998) forecasting cocoa prices in Malaysia, Nkwatoh (2012) forecasting unemployment rates for Nigeria etc. Notably, Assis et al. (2010) observed that the research costs of ARIMA models is relatively low compared to other econometric models, and relatively more efficient in short term forecasting.
Recently, studies have captured the heteroskedastic property of time series by incorporating the Autoregressive Conditional Heteroscedastic (ARCH) model introduced by Engle (1982).However, the Generalized Autoregressive Conditional Heteroscedastic (GARCH) models have provided more parsimonious results than ARCH models.This is similar to situations where ARMA models have perform better than simple AR models (Assis et al., 2010).Floros (2005) compared the out-of-sample forecast accuracy for the United Kingdom unemployment rate and established that, though an MA(4) model performed well, the MA(4)-ARCH (1) model provided superior forecasts.Zhou et al. (2006) showed that the ARIMA/GARCH model outperformed the Fractional Autoregressive Integrated Moving Average (FARIMA) 3 for predicting telecommunication network.Assis et al (2010) have also demonstrated the superiority of the mixed ARIMA/GARCH model over the exponential smoothing, ARIMA, and GARCH models in forecasting future prices of cocoa beans in Malaysia.Similarly, Kamil and Noor (2006) concluded that the mix ARIMA/GARCH model outperformed the Autoregressive Conditional Heteroskedasticity (ARCH) model when used to forecast the price of raw palm oil in Malaysia (Figure 1).

METHODOLOGY/FORECASTING MODELS
This work used GDP growth rates data from 1994 to 2015 obtained from World Bank Development Indicators Website 2015.The initial data was annual but later transformed into quarterly data using Eviews software.The rationale for splitting the data is because short term forecast is better than long term forecast.The starting date 1994 is considered because it is the period immediately after devaluation when Cameroon's growth rate assumed a continuous positive value.This study employed ARMA, and the mixed ARIMA/GARCH models with aim of identifying the best model suitable for predicting future growth rates for Cameroon.

ARIMA Models
The analysis of ARIMA models follows the Box-Jenkins methodology 3 For Fractional Autoregressive Integrated Moving Average model,(see, Green 2004, 647-648).
that combines both the moving average (MA) and the autoregressive (AR) models.Initially, these models were analyzed by Yule-Walker.However, a systematic approach that synchronizes both approaches for identifying, estimating and forecasting the models was advanced by Box and Jenkins (1970).The Box-Jenkins methodology begins with an ARMA (p,q) model which combines both the AR and MA models as follows: (2) (3) Where, xt represents the explanatory variables, et is the disturbance term.In equation ( 3), (yt-i) are AR terms of order p, are MA terms of order q and is a white-noise innovation term.In case of a non-stationary data, the series is differenced (integrated) such: , (d is the number of times a series is differenced to become stationary; I=d) then the ARMA (p,q) model becomes ARIMA(p,d,q) models (Auto-regressive Integrated Moving Average of order p,q).

Conceptual Framework for the Box-Jenkins Methodology
The process of Box-Jenkins ARIMA modeling requires four major steps: identification, estimation, diagnostic checking and forecasting.
1) The identification process starts by testing for the stationary properties of the series.This is done by analyzing the correlogram of the time series or carrying out a unit root test (Augmented Dickey Fuller Test and Phillips Perron test) 4 .After testing the stationary properties, it is essential to find the order of the ARIMA process.An autoregressive process AR (p) model has partial autocorrelations (PACF) that truncates at lag 'p' while its autocorrelation functions (ACF) dies off smoothly at a geometric rate.A moving average process MA (q) has an ACF that is truncated at lag 'q', while its partial autocorrelations (PACF) declines geometrically.
Alternative model selection criteria such as Akaike Information Criteria, Schwarz Bayesian Criteria 5 , Adjusted R 2 , and Final Prediction Error can be used to verify the order (p,q).2) After determining the order of p and q the specified regression model is estimated which entails a nonlinear iterative process of the parameters and .An optimization criterion like least error of sum of squares, maximum likelihood or maximum entropy is used.An initial estimate is usually used.Each iteration, is expected to be an improvement of the last one until the estimate converges to an optimal one (Etuk et al., 2012).

ADF test:
: ΔXtis the first difference of the series X, k is the lag order, t is the time.

PP test:
a, b, and c are the coefficients and T is the total number of observations.Therefore, the ADF and PP unit root tests posits a null hypothesis = 0 versus an alternative hypothesis < 0, where the ADF and PP statistics is compared with the observed Mackinnon critical values.3) The fitted model is tested for goodness-of-fit.It can be tested using the above mentioned model selection criteria.Alternatively, the ACF and PACF obtained from the residual of the specified ARIMA model as well as the χ2 and Ljung-Box Q statistics are diagnostic checking tools.If the residual is free from all classical assumption of the regression model and stationary then the model is correct (Purna, 2012).4) The estimated ARIMA model is used to recursively forecast periods ahead.Consider the general ARMA model: (4) Then the forecasted ARIMA model: (5) Where a, is the intercept term, are the parameters of the autoregressive process, are the parameters of moving average process.

ARCH/GARCH Model
The Autoregressive Conditional Heteroscedastic (ARCH) model was formulated by (Engle, 1982) and extended to the Generalised Autoregressive Conditional Heteroscedastic (GARCH) model by Bollerslev (1986).This approach requires a joint estimation of the mean and variance equations.The current conditional variance a time series depends on the past squared residuals of the process and on the past conditional variances.
A univariate regression with GARCH (p,q) effects in a polynomial form with a lag operator is represent as: Mean Equation: ) and Variance Equation: Where, p is the order of GARCH term and q is the order of ARCH term.
Whereas yt is the endogenous variable and xt exogenous,  is all collected messages up to t-1 period, and is conditional variance which depends linearly on past squared-error terms and past variances.

ARIMA/GARCH
A combination of the ARIMA (p,d,q) and the GARCH(p,q) are expressed as:

𝜎 𝑡
ARIMA/E-GARCH Nelson (1991) proposed the extended version of GARCH model known as the exponential GARCH (E-GARCH) that captures the volatility clustering and measures the asymmetric effect.The main advantage over the GARCH model, proposed by Bollerslev (1986), is that it gives a leverage effect which is exponential, rather than quadratic; and the forecasts of the conditional variance are expexted to be non-negative.

PRESENTATION AND ANALYSIS OF RESULTS
The initial step in employing the Box-Jenkins methodology is determine whether the series is either trend stationary or difference stationary.Three important approaches are considered: graphical method, correlogram (which analyzes the ACF and PACF) and the unit root test (Augmented Dickey-Fuller test (ADF) and Phillips-Perron test (PP)).The shaded areas in Figure 2 show that significant booms were recorded in 1997 and 2014 as well as significant recessions recorded in 2005 and 2009.The recession periods coincide with the global financial meltdown while the boom that assumed an upward trend form 1994 reaching its pick in 1997 depicts the recovery period immediately after the CFA franc was devalued.The boom and recession periods of the economy show that GDP growth is affected by seasonal variations.Hence the series is non-stationary.
Figure 3 shows the correlogram plot of GDP growth rate.The spikes of the autocorrelation function (ACF) extend outside the band confidence interval at some points while the spikes of partial autocorrelation function (PACF) start with a high value and decline slowly.Also the Q-statistic6 at lag 36 shows that the series is affected by seasonal variations.The series is deseasonalized after calculating the seasonal coefficients as shown in Table 1.The graph in Figure 2 shows that the series is multi-plicative and hence the quarterly seasonal coefficients sum up to 4. The seasonally adjusted GDP growth rate series becomes GDPSA.Table 2 shows the results of Augmented Dickey-Fuller (ADF) and Phillips-Perrons (PP) test.The t-statistic values for both ADF and PP tests are greater than their corresponding critical values; implying that the null hypothesis of the presence of unit root in the series is not rejected.This implies that the series follows a 'difference' stationary process and not 'trend' stationary process.
Table 3 shows the results of Augmented Dickey-Fuller (ADF) and Phillips-Perrons (PP) for DGDPSA after first differencing.The t-statistic values for both ADF and PP tests are less than their corresponding critical values; implying that the null hypothesis of the presence of unit root in the series is rejected.Hence the series is stationary.Figure 4 shows the correlogram plot of  DGDPSA series.Only the first three spikes of the simple autocorrelation function (SACF) are significantly different from zero because they extend outside the band confidence interval while the remaining spikes die down slowly with the band up to the last lag.The spikes of partial autocorrelation function (PACF) follow a sinusoidal pattern within the first nine lags and dies down slowly within the band confidence interval.It implies the anticipated model that can be used to project Cameroon's growth rate is a moving average model of order three  4 shows the estimated result of ARMA (0, 1, 3) inconformity with p q 5 criteria.The values of DW and R 2 are good and the values of the Akaike and Schwarz criteria are small.Also, all the coefficients of the model are statistical different from zero.Conclusively, the model is well fitted and can be used for projections.The correlogram in Figure 5 shows that none of the spikes extends out of the intervals and also, the Q-statistic has a critical probability value closer to 1 as we move downwards to the last lag.Thus, the residuals can be assimilated to a white noise.
However, the series exhibits a heteroskedastic property because the ARCH (1) test has a probably value of 0.000102 smaller than 0.05.Thus, to make the model void of heteroskedasticity, the series is modelled as ARIMA/ARCH or GARCH process.

Model selection criteria
The Root mean squared error (RMSE), mean absolute percentage error (MAPE), mean absolute error (MAE) and Theil's inequality coefficient (U-Statistics) 7 were used to determine the best forecasting model: The table below shows that, ARIMA(0,1,3)/E-GARCH (1,2) is the best      model for forecasting Cameroon's future economic growth rate.ARIMA (0,1,3) though is good, was rejected because it exhibited a heteroskedastic property (Table 7).
Projections based on ARIMA (0,1,3)/E-GARCH (1,2) The study used the method employed earlier by Dobre and Alexandru (2008) adopted from Bourbonnais (2005:256).The itinerary for the projection based on the estimated results in Table 8 is as follows: The residual values for the last three quarters are: = -0.0628;= -0.06830;= -0.05412.The above result suggests that Cameroon's economic growth rate will increase approximately from 6.06% to 6.07% and to 6.13% in 2015 quarters 1, 2 and 3 respectively and will drop thereafter by 0.012% in quarter 4.This implies that Cameroon cannot sustain a steady growth path.On an average, Cameroon's annual growth rate will be approximately 6.099% everything being equal.The results show that the growth pace is still very slow as compared to China that maintained a steady and sustainable annual growth rate of 9.02 and 10.75% in 1982 and 1983 and jumped significantly to 15.21% in 1984 just immediately after the transition program to emergence was initiated.Therefore, policy makers in Cameroon need to double their efforts if they really want to fructify the vision of an emerging economy by the year 2035.

Conclusion
Cameroon is among the African countries aspiring to become an emergent economy by the year 2035.The fundamental objective of this study was to project Cameroon's future economic growth rate and to ascertain whether policy makers could maintain a steady and sustainable growth rate like China that transcended from a developing economy into an emerging economy.The study employed the ARIMA/GARCH models and concluded that the ARIMA (0,1,3)/E-GARCH(1,2) is the best model for projecting Cameroon's future growth rates and relevant for policy implication.This model is very appealing because the forecasted results are in conformity with the current annual growth rate of Cameroon as established by the government in December.
An important finding from this study is that Cameroon's growth pattern is slow and not sustainable.Therefore, Cameroon's policy makers need to double their efforts in order to become like China by the year 2035.
maximum likelihood estimate of the residual variance when the model has k parameters.The optimum model corresponds to the minimum of the criteria within the explored range.

Figure 2 .
Figure 2. Time series plot of GDP growth rate series in Cameroon.
The actual value at time t; =The forecast value at time t; n = The number of observations; ESS = The error sum of square.
Source: Author's Calculations Based on Estimated Results.