Modeling and Forecasting the Macroeconomic Driver of Time-Varying Coffee Price Volatility in Ethiopia

Recently, modeling and forecasting of high frequency data (such as daily price) volatility using GARCH-MIDAS attracts the attention of many researchers. Thus, the objective of this study is to model and forecast the average daily coffee price volatility using GARCH-MIDAS model over the sample period from January 01, 2010 to June 30, 2019. The GARCH-MIDAS component model decomposes the conditional variance into short run component which follows a mean-reverting unit GARCH process and long run component which consider different frequency macroeconomic indicators (in this study GDP, interest rate, trade openness and money supply) via mixed interval data sampling (MIDAS) specification. Unit root test results show the return series are stationary at level, while macroeconomic variables are stationary at first difference except interest rate, which is stationary at level. From the result of estimated GARCH-MIDAS component model, all selected indicators are crucial in explaining the long-term component price volatility.The Conrad &Schienleregression based result shows the absence of model specification. Moreover, the estimated GARCH-MIDAS component model with money supply as a main driver is used for out-sample forecast. Finally, the DM test statistic used for comparing the forecasting performance of GARCH-MIDAS component model against the standard GARCH model.The result shows that multiplicative GARCH-MIDAS component model provide an explanation for stylized facts that cannot be captured by standard GARCH model.


Introduction
Modeling and forecasting volatility of financial returns have become a research area of interest in recent time since volatility modeling is an important tool for policymaking, investment analysis, asset pricing and risk management (Andersen, 2005). Specifically, forecasting volatility is a crucial part of decision-making for financial market traders as well aspolicy-makers.
In this regard, Robert Engle in 1982 introduced the first volatility model called Autoregressive conditional heteroscedasticity(ARCH) model. Consequently, different ARCH family modelslike GARCH model (Bollerslev, 1986), EGARCH (Nelson, 1991), and Threshold GARCH (Zakoian, 1994) have been introduced. However, most of the ARCH family models have been developed to capture low frequency data and considered as inappropriate for high frequency data because such data possess a particular characteristic of persistency in unconditional variance (Andersen, 2005).
According to Bollerslev (1998), the standard GARCH family models are accurate for shortterm volatility forecasts. However, long-horizon forecasts for volatility can be important for instance for portfolio allocation and risk management since forecastaccuracy generally varies over time (Engle et al., 2013).
Thus, recently, a number of models for high frequency data were developed by augmenting the traditional ARCH family models to component GARCH models. Engle and Lee (1999) introduced the first additiveGARCHcomponent model, which decomposes volatility into shortterm and long-term volatility component. Subsequently, Engle and Rangel (2008) introduced a multiplicative GARCH component model where the conditional variance is decomposed into transitory and permanent volatility components. The transitory volatility component captures a mean reverting unit GARCH process, while the permanent component captures by the Spline-GARCH process that handles theslowly varying deterministic (long-term) componentsince predictability varies over macroeconomic states or conditions. According to Park et al. (2007)  (MIDAS) approach, which was introduced by Ghyselset al. (2007) and allows to directly linking lower frequency macroeconomic variables to high frequency long-term volatility component.
In order to simplify the estimation process in GARCH-MIDAS component model, Engleet al. (2013) applied a beta-weighting scheme to link high frequency financial return series to low frequency macroeconomic variables. Even though asymptotic results for the general GARCH-MIDAS model are not yet available, Wang and Ghysels (2014) establish the asymptotic normality of the quasi-maximum likelihood estimator for a GARCH-MIDAS model. Moreover, according to Wang & Ghysels, volatility component models found considerable attention not only because of their ability to capture complex dynamics via a parsimonious parameter structure, but also because they can handle well structural breaks or non-stationarity in financial return volatility.
In this regard, daily coffee price series of Ethiopia have the characteristics of high price volatility and their associated price variation worsen when the macroeconomic conditions of the county become unstable. However, the price series of coffee is available at daily level, while macroeconomic variables cannot be available at higher frequency (like daily) rather they can be measured at lower frequency (annually, quarterly and monthly) since its economy mainly depend on agriculture which is inelastic in supply.
Therefore, this paper explores the time-varying predictive ability provided by macroeconomicvariables, through comparing the out-of-sampleforecasting performance of GARCH-MIDAS models to a standard GARCH model on average daily coffee price of Ethiopia.Specifically, the study aims at (1) to fit an appropriate volatility component model for average daily coffee price volatility, (2) to identify the best determinants of coffee price volatility and (3) to conduct an out-sample forecast on average coffee price volatility using GARCH-MIDAS component model. The remaining part of the paper is organized as follows. Section 2 presents the general methodology of the paper. Section 3 presents the data. Section 4 presents results and discussion.
Section 5 presents conclusions and recommendations.

Literature Review
Volatility is defined as the spread of all likely outcomes of uncertainty or risk of financial assets.
Volatility measurement is necessary for the implementation of most economic or financial theories that guide investment and market decision. Volatility is also important for assessing the quality of financial markets performance.
Traditionally, the concept of volatility may be confused with rising prices. However, volatility measures how much a price change either with regard to its constant long-term level, or to its trend. In this respect, it is important to note that volatility does not measure the direction of price changes; rather it quantifies the variation of prices around the mean. Data with higher frequencies often result in higher volatility, whereas volatility diminishes when frequencies decrease. Annual data are less volatile than quarterly data and quarterly data are less volatile than monthly data (European Commission, 2009).
According to Poon (2005), the traditional way of volatility measurement is a simple standard deviation or variance. However, such volatility measurement is unconditional and does not capture some characteristics of volatility such as volatility clustering (i.e., large shocks tend to be followed by large shocks and small shocks tend to be followed by small shocks), leverage effect (i.e. volatility reacts differently to a big price increase or a big price drop) and volatility evolves over time in a continuous manner.Therefore, in order to resolve these weaknesses of the traditional measure of volatility, a number of volatility models (ARCH family models) were developed subsequently.
However, models in the standard GARCH type assume constant level of unconditional variance even if they let the conditional variances to fluctuate around a changing level. For the GARCH type model, the unconditional variance of the return is constant over time provided that the weak stationarity condition is satisfied. However, this assumption is not consistent with the volatility behavior of the high frequency data (e.g. daily commodity price) if the dynamic behavior of volatility changes in the long run. In other words, these standard GARCH type models are nonstationary since the unconditional variance is time varying which makes the level of the unconditional variance to be affected by macroeconomic variables independent of the short run GARCH dynamics.
The basic idea of decomposing volatility into short-term and long-term components can be traced back to Ding and Granger (1996). Engle and Rangel (2008) considered the long-term component as the setting of the time-varying variance, and proposed the Spline-GARCH model, but both the long-term component and short-term component keep the same frequency in the model setting. Engle et al.(2013) combined the mixed data sampling (MIDAS) technique and the volatility model (Ghysels, Santa-Clara and Valkanov, 2006;Ghysels, Sinko and Valkanov, 2007) into the GARCH-MIDAS model to separate the long-term low-frequency components and shortterm high-frequency components, and the new model allowed the use of low-frequency macroeconomic factors to characterize long-term components. Therefore, literature review shows that commodity price volatility is determined by the macroeconomic fundamentals as defined by GARCH-MIDAS component model. Hence, the research a problem of this study is derived from literature review. Therefore, the finding of the study contributes to the existing literature by testing the relation betweenthe fundamental macroeconomic variables and price volatility in commodity market. Even though, the study is conducted in Ethiopia coffee market, the result provides information for market participants, and the policymakers to make decision according to the macroeconomic conditions.

Characteristics of Financial Time Series
According to Brooks (2008), financial time series have the property of leptokurtic, volatility clustering and leverage effects. Leptokurtic refers to the tendency for financial asset returns to have distributions that exhibit fat tails and peaked at the mean. Volatility clustering indicates that large returns (of either sign) are expected to follow large returns, and small returns (of either sign) to follow small returns that arise as a results of non-normality (non-constant variance of the error terms) in the return series.Leverage effects is a tendency for volatility to rise more following a large price fall than following a price rise of the same magnitude.
Moreover, Harris &Sollis (2003) stated that financial time series are often available at a higher frequency and such a high-frequency data have the property of long-memory, which is defined as the present information has a persistent impact on future values. Therefore, the theoretical characteristics of financial time series tell us the need of an advanced model for handling high frequency data (e.g. daily coffee price series of Ethiopia) and its driving forces (macroeconomic variables).
In financial studies, log return series can be analyzed, rather than the actual prices value since the log returns series are more manageable, have better statistical properties and economic interpretation. In this study, the log return series can be written as: where , is averagecoffee price on day i of period t, , is log return series on day i of period t.

Unit root test
Empirical work based on time series data assumes that the underlying time series is stationary since non-stationarity leads to spurious (non-sense) results.Nevertheless, most trending variables, like macroeconomic variables are non-stationary by nature. When we have a stationary system, effect of a shock will die out gradually. However, when we have a non-stationary system, effect of a shock is permanent. In order to test this effect, the Augmented Dickey Fuller (ADF) and Phillips-Perron (PP) test were used. If the variables have unit root then the series needs to be differenced to achieve stationarity.

The Augmented Dickey Fuller (ADF) Test
The ADF approach controls higher-order correlation by adding lagged difference terms of the dependent variable to the right-hand side of the regression, which are required to account for possible occurrence of autocorrelation. Consider the AR (p) model given by: If the null H 0 : = 0 is not rejected, apply differencing to make the series stationary. Phillips and Perron (1987) have developed a more comprehensive theory of unit root test. The Phillips-Perron (PP) unit root tests differ from the ADF tests inthe way to deal serial correlation and heteroscedasticity in the errors.

The Phillips and Perron (PP) Test
Consider the differencedPPtest equation as an AR (1) processes given by: DF: .~ iid, while PP: , is serially correlated. The null is given by H 0 : = 0.
Thus Phillips and Perron's test statistic can be viewed as Dickey-Fuller statistic that have been made robust to serial correlation by using the Newey-West (1987) heteroscedasticity and autocorrelation-consistent covariance matrix estimator of the error term, , by modifying the test statistics =0 and ̂, given that =0 =(̂) and ̂=(̂).
wherê and ̂ are OLS estimate of and , and (̂) and (̂) are standard errors of and , respectively.
The modified statistic is given by: where ̂2 is consistently estimate from sample varince of , and ̂2 is estimated consistently from the Newey-West long run variance estimate of , . ̂2 = lim ) 2 . Reject the null hypothesis indicates the series is stationary. where , is the return on day i (i=1,… , ) in period ( =1,…, T). The period may be monthly, quarterly or annually depend on the frequency of macroeconomic variables. The expected return is assumed to be constant i.e. ( , | −1, ) = for all i and t, where −1, contains the information set up to ( − 1) ℎ day of period .

The GARCH-MIDAS Component Models Specification
The innovation sequence, , in the given mean equation is , | −1, ~ (0, , 2 ). Furthermore, each innovation sequence, , in high frequency data is decomposed as , = , , , where , > 0, , and , are independent by assumptions. , is a shock with a standardized normal distribution as defined , | −1,~. . . (0,1). Within the GARCH-MIDAS framework, the conditional variance, σ i,t 2 , is given by the product of two components. One varying by each day i, namelyℎ , as a transitory (short-run) component and the other by each period t, namely , as permanent (long-run) component as given by

Ttransitory volatility component specification
According to Engle et al. (2013), the volatility dynamics of the short-term(transitory)component, ℎ , follows a mean reversion GARCH (1, 1) process: where represents ARCH term, is the GARCH term, Equation (6) is assumed to satisfy conditions for non-negativity of the variance, i.e. ≥ 0, ≥ 0 and weak stationary of the conditional variance i.e. + < 1should be satisfied.

Permanent Component (MIDAS) specification
Thepermanent ( This can be derived as follows: Building an optimal model representation with macroeconomic variables requires the selection of the time span t and the MIDAS lag (k) which is used in the MIDAS polynomial specification of the long-term component. Therefore, the effect of macroeconomic variables on the long-term variance component as defined by Engle et al.(2013) is specified as: where (

Estimation of the GARCH-MIDAS component model
To estimate volatility model, maximum likelihood can be employed. Moreover, volatility model specification also requires an assumption about the conditional distribution of the error term such as normal distribution, t-distribution, and Generalized Error Distribution (GED).
However, in most financial data, normality assumption is questionable, so the usual standard error estimates will be inappropriate, and a different variance-covariance matrix estimator that is robust to non-normality due to Bollerslev and Wooldridge (1992) should be used. This maximum likelihood with Bollerslev-Wooldridge standard errors is known as quasi-maximum likelihood (QML). Consistency and asymptotic normality of the QML estimator for GARCH-MIDASmodel with realized volatility was established in Wang and Ghysels (2014.

Model Selection Test
In the estimation process of GARCH-MIDAS model, identification of the number of time lag and determination of the most drivers of price return volatility, the Akaike information criterion (AIC) can be used as defined by: where is the log likelihood function, is the number of estimated parameters. The model that has a minim value of information criterion will be chosen

Model Misspecification Test
In  Engle et al. (2013) use a variance ratio to determine the effect of explanatory value on the longterm volatility. Thus, the variance ratio (VR) test is defined as:

Goodness of fit
where variance ratio ( ) is the measure describes the proportion of variance of the logarithmic long-term volatility and the variance of the logarithmic conditional volatility. The variance ratio can be interpreted as a measure of fit in the sense that the higher the variance ratio is, the larger is the share of the total expected volatility that can be explained by the variation in the long-term component.

Forecasting using GARCH-MIDAS component model
After the model was estimated and a misspecification tests were conducted, the next step is to forecast the price return volatility using the identified GARCH-MIDAS model with macroeconomic variables. The out-of-sample forecasting period was from January 2019 to June 2019. For the GARCH model the forecastfor day i is formed as: (ℎ , | −1 ) = 1 + ( + ) −1 (ℎ 1 , − 1) where is the number of trading days in period t, and −1 denotes the information set in period − ,t is time of the forecast origin and is the lead time forecast.
As we remember, we estimate the parameters from the in-sample period up to T. Therefore, thestep-head forecast of ̂, + 2 is given by:

Evaluation of Forecasting Accuracy
In order to check whether the forecasted value is valid or not, we need to apply a test that evaluate the forecasted value in reference to the actual vale. For evaluating the forecasted value, the Modified Diebold and Mariano Test wasemployed. Diebold and Mariano (1995)  From the two forecast error we can calculate the loss difference ( = ℎ − ) with mean,

Modified Diebold and Mariano Tests
Then the null hypothesis is given by 0 : ̅ = 0: where is the ℎ autocovariance of given by The DM test statistic is given by: Reject the null for all | | > 1.96

Data Sources
Daily data on average price of coffeecover from the period January 1, 2010 to June 30, 2019 were obtained from Ethiopian commodity exchange (ECX) market, while data on macroeconomic variables, such as GDP,interest rate, trade openness and money supplywere obtained from NBE andMoFED. The variables of interest in this study are average daily coffee price, which is to be used as dependent variable, whileGDP, trade openness, money supply (M2) and interest rate are exogenous variables.

Summary Statistics Results
The following graph displays daily average coffee price and return series in the full sample period over January 01, 2010 to June 30, 2019. The plot on Figure 2 shows an average daily price return series. The series seems to satisfy the stylized fact of financial time series that is the existence ofvolatility clustering (highvolatility events tend to clusterin time) in the series.

Unit Root Test Results
Before estimating the models, the first step is to check the stationarity of the series. In this study, the ADF and PP unit root test were used. Table 3 shows that the ADF and PP test of daily log return series for coffee is stationary at 1% level of significance indicating the return series are stationary at level than the price series. variables at level become stationary after first differences as indicated by the p-value. Therefore, we should to use the first difference of those explanatory variables in the estimation process.

Money Supply (M2)
From the Table 5, 12 lags in the MIDAS filter of money supply specification was identified based on AIC. It is clear that the mean of the returns, is insignificant (not significantly differ from zero), meaning that the average mean doesn't explain the returns volatile, while is statistically significant at 1% level of significance. The weight scheme 2 is statistically significant at 1% level of significance, which indicates it gives highest weight for most recent observation or lags. Moreover, and are strongly significant at 1% level of significance

Interest rate (Real Interest Rate)
The real interest rate effect on long-term price volatility under MIDAS specification is negative and statistically significant at 5% level of significance for coffee price return volatility.
Economically lower interest rate results higher price volatility while higher interest rates results lower price volatility. This might be due to that low interest rate promote price volatility via low interest rates tend to reduce the opportunity cost of carrying inventories and increasing the demand for coffee which results an increase in price volatility. The magnitude effect of real interest rate on the long-term volatility component is -0.3371% =-3.37%. Thus, a 1% increase in real interest rate results 3.37%declines in price volatility in the long-run. This supports the hypothesis that a decline in interest rate reduces the opportunity cost to hold inventories, hence making the market thinner and reducing the ability to cope with shocks.
From Table 5, the long-term component of the GARCH-MIDAS explained by the fluctuation of the variation in the explanatory variable in a range between 56% and 83% as indicated by variance ratio (VR) test. In order to decide which model is the best and which independent variables best fits the sample data we take into consideration the Akaike InformationCriterion (AIC). Thus, the GARCH-MIDAS model, which incorporates the monthly money supply (M2) yields the best goodness-of-fit of the model (based on minimum AIC). Hence, money supply is considered as the main deriver of average daily coffee price return volatility in the long run. The Figure 3 shows the daily long-term (blue line) and short-term (red line) volatility components as estimated by the GARCH-MIDAS models with money supply as explanatory variables.

Out sample Forecasting using GARCH-MIDAS Component model
In this study, the GARCH-MIDAS specifications with macroeconomic variables are used for forecasting commodity price volatility, which is helpful for managers, traders, consumers and other stakeholders. Thus, after fitted the in sample data, the selected model will be used for outsample forecasting. In this case, the out sample data was used from January 1, 2019 to June 3, 2019. Moreover, to forecast the future value of the series, money supply is used as the main deriver (based on minimum AIC; see Table 5) of average daily coffee price volatility in GARCH-MIDAS model. From the result in Figure 4, the forecast seems stable except on April (the fourth month) in which there is a rise in the price of the series might be due to domestic market supply conditions.

Modified Diebold and Mariano Tests Results
Table7shows the results of the estimated DM-test for the out-of-sample performance of the

Conclusions
The main motives of this article is to forecast the future value of average coffee price series

Recommendations
Based on the finding of the study researcher forwarded the following recommendations for the concerned stakeholders: • The government should take policy measure (like expansionary fiscal policy) to improve the overall production in the country since the value of gross domestic product has statistically significant and decreasing effect on price volatility.
• Interest rate has decreasing effect, while money supply has increasing effect on coffee price volatility. Thus, the monetary authority particularly the central bank should take appropriate monetary policy measure to stabilize the coffee market.
• Trade openness also has increasing effect on coffee price volatility. Hence, the concerned stakeholder should work to liberalize the foreign trade sector through signing interregional and international trade agreement,work on improvement the quality and diversification of its export sector.
Generally, the significance of this finding is important and is mostly attributable to the ability of the new models to incorporate different frequency macroeconomic variables directly into the specification ofhigh frequency volatility dynamicsand open a path for future researchers.However, a single model cannot be the best-suited specification for all commodity futures we consider. Hence, in the light of this empirical finding, the concerned stakeholders would have to pay a close watch on the trends of identified macroeconomic variables before making any measures related to commodity futures.

MIDAS) component model which was introduced by Engel et al. (2013). The model is important to
analysis high frequency data (such as daily average coffee price) volatility through decomposing conditional variance into short-term and long-term volatility component model and helps to relate different frequency macroeconomic variables (which is considered as the main source of such price volatility) to long-term volatility component. Therefore, Mr. Teshome conducted proposal development, data collection, analysis, and preparation of the manuscript well and approved it for publication.

Conflict of Interest
I confirm that there are no conflicts of interest to disclose since I am the only author of this paper with personal expenditure.

Data Availability Statement
All data generated or analyzed during this study are included in this published article (and its supplementary information files).

Funding
The author received no financial support for the research, authorship and/or publication of this article.

ECX:
Ethiopian Commodity Exchange

GDP:
Gross Domestic Product

MoFED:
Ministry of Finance and Economic Development

NBE:
National Bank of Ethiopia