FORECASTING THE CONSUMER PRICE INDEX OF GHANA USING EXPONENTIAL SMOOTHING METHODS

Consumer price index is a social and economic indicator that measures changes over time in the general level of prices of consumer goods and services that households acquire, use or pay for consumption. Rising CPI also often leads to the central bank to raise interest rates, tightening money supply, reduce the money supply and other measures to tighten monetary policy, which flow into reduction of capital stock funds for greater returns, often accompanied by high inflation. The study seeks to determine a time series exponential smoothing method which fit the CPI and use it forecast the future values of CPI. Minitab software is used to analyze the CPI from March 2013 to November 2018. Out three exponential smoothing methods, it is realized that the method which best fit the series is the Winters’ additive method with exponential smoothing constants for the level, trend and seasonal variation as α = 0.7, γ = 0.2 and δ = 0.2 respectively. This method is chosen on the basis that it has the lowest MAPE, MAD and MSD. The validity of the model is further checked by comparing the fitted values with the actual values. The errors in prediction were very minimal. The model is therefore recommended for forecasting CPI of Ghana in the next twelve months.


Introduction
The consumer price index (CPI) in Ghana measures changes in the prices paid by consumer for a basket of goods and services. In another words, CPI is a social and economic indicator that measures changes over time in the general level of prices of consumer goods and services that households acquire, use or pay for consumption. If the CPI rises faster than wages, the purchasing power which is the amount we can buy with our cedi decreases and therefore affects our cost of living.
The CPI is a key economic indicator since a rising CPI is an early warning signal of imminent economic challenges since it triggers a rise in inflation. A rising inflation affects the policy rate of the central bank (Bank of Ghana) and results increase in interest rates of loans. The CPI actually controls the policy direction of the central bank. Apart from its role as a guide for future central bank policies, the CPI release can be useful in predicting the course of national politics, due to the tendency of voters to punish governments which cannot help them at times of rising food prices or prices of petroleum products (Forexfraud.com, 2019).
The CPI has more macroeconomic consequences also which include pension benefits and large-scale spending plans. Since pension obligations and other large-scale spending plans are often pegged to the CPI, even very minor changes in the CPI can alter the prices of financial portfolios by millions of pounds (Powell et. al., 2016).
In trying to build a formidable and resilient economy, it is imperative to know the long run behavior of the CPI and it is in the light of this that the study is being conducted to find the appropriate time series model for forecasting the CPI of Ghana using data from March 2013 to December 2018. A lot of Mathematical Theory and Modeling www.iiste.org ISSN 2224-5804 (Paper) ISSN 2225-0522 (Online) DOI: 10.7176/MTM Vol.9, No.3, 2019 2 methods have been used to analysis and forecast time series data, such as autoregressive model autoregressive moving average (ARIMA) model and exponential smoothing models (Jie et al., 2015) but this study seeks to find the suitable exponential smoothing model for CPI and use it to forecasts for the next ten (10) months.

1.1
Literature Review A lot of intensive works have been done using times series modeling. One of the most popular and frequently used stochastic time series models is the autoregressive integrated moving average (ARIMA) and the popularity of the ARIMA model is mainly due to its flexibility to represent several varieties of time series with simplicity as well as the associated Box-Jenkins methodology (Zhang, 2003, Hipel andMcLeod, 2003).
Adams et al., modeled Nigeria's consumer price index using ARIMA model. The Box-Jenkins Autoregressive Integrated Moving Average (ARIMA) models were estimated and the best fitting ARIMA model was used to obtain the post-sample forecasts. It was discovered that the best fitted model was ARIMA (1, 2, 1). The model was validated by Ljung-Box test (Q = 19.105 and p>.01) with no significant autocorrelation between residuals at different lag times. Finally, the five years forecast was made, which showed an average increment of about 2.4% between 2011 and 2015 with the highest CPI being estimated as 279.90 in the 4th quarter of the year 2015. Papalaskaris et al., 2016, employed seasonal autoregressive integrated moving average (SARIMA) (0, 0, 0)(0, 1, 1) 12 model to perform short term of monthly rainfall in parts Greece and North-Eastern Mediterranean basin. In fitting of a SARIMA model to monthly Naira-Euro exchange rates, Etuk (2013), proposed and fitted SARIMA (0, 1, 1)(1, 1, 1)12 . This model was shown to adequately explain the variation in the monthly Naira-Euro exchange rates.
Exponential smoothing method has established itself as one of the leading forecasting strategies (Nur et al., 2013). Siregar et al., 2016, conducted to determine the performance of the system in forecasting realization palm oil production using exponential smoothing method. The study compared several methods based on exponential smoothing (ES) technique such as single ES, double exponential smoothing holt, triple exponential smoothing, triple exponential smoothing additive and multiplicative to predict the palm oil production. The result showed that triple ES additives had lowest error rate compared to the other models with RMSE of 0.10 with a combination of parameters α = 0.6, β =0.02, and γ = 0.02. According to Tirkeş et al., 2017, several statistical models have been used in demand forecasting in food and beverage (F&B) industry and the choice of the most suitable forecasting model remains a central concern. Their main goal was to propose an optimization model based on demand forecasting approach depending on a comparative study using trend analysis, Holt-Winters' exponential smoothing and decomposition method of time series forecasting for estimating a realistic future demand. Karmaker et al., 2017, in their study of time series model for predicting jute yarn demand, performed by statistical analysis using Minitab 17 software to determine the appropriate exponential forecasting techniques. Performance of all methods was evaluated on the basis of forecasting accuracy and the analysis showed that Winter's additive model gave the best performance in terms of lowest error determinants.

2.0
Methodology The purpose of the study is to identify the appropriate exponential smoothing method which fits the data based on the forecasting errors and use it to forecast the next nine months CPI of Ghana. Three exponential smoothing methods will be looked at especially, the simple exponential smoothing method, double exponential smoothing or Holt's method and the Winters' method using Minitab 16. 3 Exponential smoothing models (Gardner, 1985) are classified as either seasonal or nonseasonal. Holt exponential smoothing method is the most popular double exponential smoothing method proposed by Holt (1957) as an extension of the simple exponential smoothing method to allow forecasting of data with a trend (Jie et al., 2015).

2.1
Simple Exponential Smoothing The simple exponential smoothing (SES) model is best suited for a short-term forecasting, and usually this model is used for the prediction a future when the series has no trend and no seasonal variation. The forecasting equation is

2.2
Holt's Method Double exponential smoothing or Holt's method by Holt (1957), an extension of the simple exponential method, is used to forecast data having linear trend. It consists of a forecasting equation, level and trend equations.

Forecast equation:
Winters ' Method Holt (1957) and Winters (1960) extended Holt's method to capture seasonality and the method is called Hot-Winters' method or simply Winters' method. The method comprises the forecast equation and three smoothing equations namely, the level equation, the trend equation and the seasonal equation. There are two types of Winters' method. These are two types of the additive and multiplicative methods. When the magnitude of seasonal pattern appears constant the additive model is used and when it varies with the size of the sample, the multiplicative method is used.

Forecasting equation for additive model
Forecasting equation: Forecasting equation for multiplicative model   Clearly from the plot in figure 1 above, the CPI has an increasing trend suggesting that the simple exponential method must be ruled out as a possible method of forecasting the CPI of Ghana. It is now left with two possible methods (Holt's and Winters' methods). From table 2 above, it is realized that as the smoothing constant increases, the mean absolute percentage error (MAPE) decreases but as the smoothing constant is inversely proportional to the mean absolute deviation (MAD) and the mean squared deviation (MSD). The least of three measures of accuracy values are 1.29, 2.03 and 5.80 for the MAPE, MAD and MSD respectively. Among the three, the MAPE value of 1.29 with a smoothing constant of 0.9 is the minimum.  From table 4 above, the smoothing constant, alpha is varied between 0.4 and 0.9 while the gamma was between 0.2 and 0.3. The other constant, delta, was also varied between 0.1 and 0.3. of the nine trials, the minimum measures of accuracy was 0.3281 with smoothing constants = 0.7, = 0.2 and = 0.2. In table 5 above, there were 13 trials in all and values varied between 0.1 and 0.2. The gamma, , varied between 0.1 and 0.2 and delta, , varied between 0.1 and 0.9. The optimal smoothing constants are = 0.2, = 0.1 and = 0.9 and the least value of the MAPE is 0.0148.
The simple exponential smoothing method has been ruled out earlier as the plot of the CPI is characterized by upward movement. Clearly, there is a trend in the series and as indicated earlier, the exponential smoothing method is used when the series has no trend and seasonal variation.

3.2
In-sample and Post-sample Forecast To judge the forecasting ability of the selected exponential smoothing method, the sample period forecasts are computed. The sample period forecasts are obtained by simply plugging the actual values of the explanatory variable in the Minitab using the Winters' additive method. For the in-sample forecast, the forecast values are compared with the actual values of the CPI to validate the exponential Mathematical Theory and Modeling www.iiste.org ISSN 2224-5804 (Paper) ISSN 2225-0522 (Online) DOI: 10.7176/MTM Vol.9, No.3, 2019 7 smoothing method or procedure chosen. The post-sample forecast is done to obtain the future values of the CPI. The results of the in-sample and post-sample forecasts are shown in table 6.  Table 6 indicates that the differences between the actual and the predicted values (errors) are not great and this also confirms the validity of the Winters' additive method and is used to forecast the next nine months CPI of Ghana provided there is no intervention.

Conclusion
The objective of the study is to determine the appropriate time series exponential smoothing method for forecasting the CPI of Ghana for the next nine months. The results show that the Winters' additive method with smoothing constants = 0.7, = 0.2 and = 0.2 is most appropriate for the series based on the least measures of accuracy. The minimum values of its MAPE, MAD and MSD are 0.3281, 0.5159 and 0.4662 respectively. It is therefore recommended for forecasting the next 12-month CPI of Ghana provided no interventions will be put in place during the period.