Inflation is the persistent increase in the level of consumer prices or a persistent decline in the purchasing power of money. Inflation is of global concerns because it can distort economic patterns and can result in the redistribution of wealth when not anticipated, thus there is a need to know the pattern of inflation in the country. In this study, we employed an empirical modeling and model selection for monthly inflation in Ghana from January 2009 to December 2013 using the Box-Jenkins approach. The results showed that ARIMA (1, 2, 1) model was appropriate for modelling the inflation rates with a maximum log likelihood value of -64.21, and least AIC value of 134,43, AICc value of 134.87 and BIC value of 140. 61. An ARCH-LM test and Ljung-Box test on the residuals of the models revealed that the residuals are free from heteroscedasticity and serial correlation respectively. Ghana is likely to experience a persistence increase in inflation rate with double digit hence the government should reconsider his monetary policies. Keywords: Inflation, Box-Jenkins, Empirical, Ghana

Mensah, Charles

Okyere, Francis

English

International Institute for Science, Technology and Education (IISTE): E-Journals

Mathematical Theory and Modeling                                                                                          www.iiste.org ISSN 2224-5804 (Paper)    ISSN 2225-0522 (Online) Vol.4, No.3, 2014  99 Empirical Modelling and Model Selection for Forecasting Monthly Inflation of Ghana   Francis Okyere1* Charles Mensah2 1. School of Graduate Studies, University of Ghana, P. O. Box LG 571, Legon, Accra, Ghana 2.  Graduate School of Social Sciences, Anadolu Üniversitesi, Yunusemre Kampusü, 26470, Eskişehir, Turkey. * E-mail of the corresponding author: francokyere@yahoo.com  Abstract Inflation is the persistent increase in the level of consumer prices or a persistent decline in the purchasing power of money. Inflation is of global concerns because it can distort economic patterns and can result in the redistribution of wealth when not anticipated, thus there is a need to know the pattern of inflation in the country. In this study, we employed an empirical modeling and model selection for monthly inflation in Ghana from January 2009 to December 2013 using the Box-Jenkins approach. The results showed that ARIMA (1, 2, 1) model was appropriate for modelling the inflation rates with a maximum log likelihood value of -64.21, and least AIC value of 134,43, AICc value of 134.87 and BIC value of 140. 61. An ARCH-LM test and Ljung-Box test on the residuals of the models revealed that the residuals are free from heteroscedasticity and serial correlation respectively. Ghana is likely to experience a persistence increase in inflation rate with double digit hence the government should reconsider his monetary policies. Keywords: Inflation, Box-Jenkins, Empirical, Ghana.  1. Introduction Price stability is a healthy monetary policy that can enhance economic growth and prosperity. It is now universally accepted that price stability is a cornerstone of modern well-functioning economies. High inflation distorts wealth redistribution in an economy, because it arbitrarily redistributes wealth among different groups of people in a society. Not only does inflation direct the link between effort and reward, it typically hits hardest those who least can afford it, Owusu (2010). Inflation is widely discussed because it changes the purchasing power of money and real values of variables such as interest rates, wages and many others. This explains why it is a very important issue of concern to policy makers especially when it assumes a relatively high level. Inflation can also be expressed as a situation where the demand for goods and services exceeds their supply in the economy (Hall, 1982).  The most common measure of inflation is the consumer price index, which measures the inflation of a country over a time period (e.g. monthly, quarterly or annually). According to Ghana Statistical Service (2013), The Consumer Price Index (CPI) measures the change over time in the general price level of goods and services that households acquire for the purpose of consumption, with reference to the preceding year’s price level (for example, 2012as reference for 2013). Modeling inflation using the Box-Jenkins ARIMA approach is plausible to stakeholders because it generates reliable inflation forecast which follows closely with the actual data. Empirical researches have been carried out in the area of forecasting using Autoregressive Integrated Moving Average (ARIMA) models popularised by Box and Jenkins (1976). Meyer et al, (1998) considered the autoregressive integrated moving average (ARIMA) for forecasting Irish inflation and justified that ARIMA models are surprisingly robust with respect to alternative Mathematical Theory and Modeling                                                                                          www.iiste.org ISSN 2224-5804 (Paper)    ISSN 2225-0522 (Online) Vol.4, No.3, 2014  100 (multivariate) model. Candelaria et al., (2007), analyzed a set of countries which adopted inflation targeting as a policy tool and modelled the pre-IT period with ARMA and GARCH methods. They conducted the one-step ahead forecasting for the remainder of the times series data by comparing the actual and forecasted inflation levels for each country. Appiah and Adetunde (2011) used the Box and Jenkins (1976) approach to model and forecast the exchange rate between the Ghana cedi and the US dollar. In their study, they found that ARIMA (1, 1, 1) model was appropriate for forecasting, the exchange rate. Nasiru and Sarpong (2012) employed an empirical approach in modelling monthly data in Ghana using the Box-Jenkins approach. The result showed that ARIMA (3, 1, 3) (2, 1, 1)[12] model was appropriate for modelling the inflation rates.  In this study, our main objective was to model and forecast twelve (12) months inflation rate of Ghana outside the sample period. The post-sample forecasting is very important for economic policy makers to foresee ahead of time the possible future requirements to design economic strategies and effective monetary policies to combat any expected high inflation rates in Ghana. Forecasts will also play a crucial role in business, industry, government, and institutional planning because many important decisions depend on the anticipated future values of inflation rate. 2. Materials and Methods  This study was carried out in Ghana in January, 2014, using data on inflation rates from January, 2009 to December, 2013. The data was obtained from the website of the Bank of Ghana. The data was modeled using Autoregressive Integrated Moving Average (ARIMA) stochastic model. An autoregressive integrated moving average (ARIMA) model is a generalization of an autoregressive moving average (ARMA) model. These models are fitted to time series data either to better understand the data or to predict future points in the series.  Trends in time series can be removed by differencing the time series. This differencing is integrated into the ARMA models creating the ARIMA models. ARIMA (p, d, q) define models with an AutoRegressive part of order p, a Moving average part of order q and having applied d order differencing. An ARIMA (p, d, q) model is a combination of Autoregressive (AR) which shows that there is a relationship between present and past values, a random value and a Moving Average (MA) model which shows that the present value has something to do with the past residuals.  The general form of the ARIMA (p, d, q) is represented by the backward shift operator as (1− Ө1B – Ө2B2  … – ӨPBP)(1 – B)dyt = (1− ∝1B– ∝2B2  …– ∝PBP) 𝜀t                AR(p)             I(d)               MA(q) Where, p is the Autoregressive order of the polynomial operator q is the Moving Average order of the polynomial operator Ө is the parameter estimate of the Autoregressive order 𝛼 is the parameter estimate of the Moving Average order 𝜀t is purely a random process with mean zero and variance 𝜎2  The modelling of an ARIMA (p, d, q) model as delineated by Box–Jenkins consist of Model identification, Parameter Estimation and Diagnostic of selected model. 2.1 Model Identification Identification step involves the use of the techniques to determine the values of p, q and d. The values are Mathematical Theory and Modeling                                                                                          www.iiste.org ISSN 2224-5804 (Paper)    ISSN 2225-0522 (Online) Vol.4, No.3, 2014  101 determined by using Autocorrelation Function (ACF) and Partial Autocorrelation Function (PACF). For any ARIMA (p, d, q) process, the theoretical PACF has non-zero partial autocorrelations at lags 1, 2, ..., p and has zero partial autocorrelations at all lags, while the theoretical ACF has non zero autocorrelation at lags 1, 2, …, q and zero autocorrelations at all lags. The non-zero lags of the sample PACF and ACF are tentatively accepted as the p and q parameters.  2.1.1 Unit root test:  This test was performed to check whether the data was stationary. In view of this, the Augmented Dickey-Fuller (ADF) test. The test is based on the assumption that a time series data yt follows a random walk: Yt = 𝜌yt-1 + et And Hypothesis H0: 𝜌 = 1 (non-stationary) H0: 𝜌  1 (stationary) Where 𝜌 is the characteristic root of an AR polynomial and et is purely a random process with mean zero and variance 𝜎2 2.2 Estimation Parameters The second step is the estimation of the model parameters for the tentative models that have been selected. Here, the model with the maximum log-likelihood and minimum values of Akaike Information Criterion (AIC), modified Akaike Information Criterion (AICc), and Normalized Bayesian Information Criterion (BIC) was considered as the best model. 2.3 Model Diagnostics The estimated model must be check to verify if it adequately represents the series. Diagnostic checks are performed on the residuals to see if they are randomly and normally distributed. Here, the plot of the ACF of the residuals was examined to see if the residuals are white noise. An overall check of the model adequacy was made using the Ljung-Box Q statistics.  An overall check of the model adequacy was made using the modified Box-Pierce Q statistics. The test statistics is given by: 𝑄𝑚 = 𝑛(𝑛 + 2) ∑(𝑛 − 𝑘)−1𝑟𝑘2𝑛𝑘=1≈ 𝜒𝑚−𝑟2  where: 𝑟𝑘2 = the residuals autocorrelation at lag 𝑘 𝑛 =  the number of residual 𝑚 = the number of time lags included in the test. When the p-value associated with the Q is large the model is considered adequate, else the whole estimation process has to start again in order to get the most adequate model. Here all the tests were performed at the 95% confidence interval. Furthermore, a plot of the ACF squared residual and PACF squared residuals was performed on the residuals of the fitted model to check for heteroscedasticity and again an ARCH LM-test for conformity of the presence of, or otherwise ARCH effect was performed. 3. Results and Discussion Figure 1 shows the monthly inflation rate of Ghana. It is revealed from that Figure  that inflation rate for the Mathematical Theory and Modeling                                                                                          www.iiste.org ISSN 2224-5804 (Paper)    ISSN 2225-0522 (Online) Vol.4, No.3, 2014  102 period of 2009 to 2013 is non-stationary due to an unstable mean which increase and decrease at certain points. The mean and variance ought to be adjusted to form stationary series, so that the values vary more or less uniformly about a fixed level over time. This is also seen from the ACF plot of the series in Figure 2, which shows a slow decline also from Figure 3 of the PACF plot which has a very significant spike at lag 1. The Augmented Dickey-fuller test further confirms this affirmation. The series was therefore first differenced and tested for stationary with the Augmented Dickey-fuller test: The first difference was not sufficient to make the series stationary as shown by the test but rather the second difference achieved stationarity as shown in Table 1. Table 2 shows the different models fitted to the series, ARIMA (1, 2, 1) appears to be the best model as it has the least AIC, AICc, BIC values. The estimates of the parameters of the model, shown in table 4.3, indicates that MA(1) model was significant at 0.05 significant level. Our diagnostic checking of the ARIMA (1, 2, 1), model revealed that the model was adequate for the series. The ACF plot of Squared of Residuals, PACF plot of Squared of Residuals and an ARCH-LM test showed that there were no ARCH effects; hence the residuals have a constant variance. The Ljung-Box p–values (> 0.05) showed that there is no serial correlation in the residuals of the model. The ACF plot of the residuals also shows that the residuals are white noise series. 4. Conclusion This study used time series to model monthly inflation rate in Ghana using data from the Bank of Ghana (BoG) from the year 2009 to 2013. The modeling of the inflation rate was done mainly by ARIMA model. The Study revealed that, inflation rate is best modeled with ARIMA (1, 2, 1). The diagnostics of this model showed that the model adequately fits the series hence is adequate for the forecasting of inflation rate in Ghana. A twelve (12) month’s forecast with our model for the year 2014 showed continues increase in the inflation pattern. From the out-sample forecast, we surmise that the country is likely to experience double digit inflation for the year 2014. Hence, policy makers should re-evaluate their policies in other to determine other factors that contribute to the high inflation rates in Ghana. References Appiah, S.T. & Adetunde, I.A. (2011). Forecasting exchange rate between the Ghana cedi and the US dollar using time series analysis. Current Research Journal of Economic Theory, 3(2): 76-83. Asel, I. (2007). Modeling and Forecasting Inflation in Developing Countries. The Case of Economies in Central Asia. CERGE-EI Discussion Papers 2007-174, Center for Economic Research and Graduate Education, Academy of Science of the Czech Republic Economic Institute. Box, G.E.P. & Jenkins, G.M. (1976). Time Series Analysis, Forecasting and Control. San Francisco, Holden-Day, California, USA. Candelaria O., Ismail, H., & Minsoolee Z.L., (2007). Time series analysis of inflation targeting in selected countries. Journal of Economics Policy Reform Vol.10 issue 1, Uni. Of Idaho. U.S.A pp 15-27. David, F.H. (2001). Modelling UK Inflation, 1875-1991. Journal of Applied Econometrics, 16(3): 255-275. Ghana Statistical Service (2013). Newsletter Consumer Price Index December 2013 New series. [Online] Available: www.statsghana.gov.gh. (January 18, 2014). Hall, R. (1982). Inflation, Causes and Effects. University of Chicago Press, Chicago  Lucas, R. (1973). Some International Evidence on Output-Inflation Tradeoffs. American Economic Review, 63, 326-334. Meyler, A.G.K. & Quin, T., (1998). Forecasting Irish inflation in using ARIMA models. Central Bank of Ireland, Technical Paper 3/RT/ 98. (December) PP. 85-102. Nasiru S., & Sarpong S., (2012). Empirical Approach to Modelling and Forecasting Inflation in Ghana. Current Mathematical Theory and Modeling                                                                                          www.iiste.org ISSN 2224-5804 (Paper)    ISSN 2225-0522 (Online) Vol.4, No.3, 2014  103 Research Journal of Economic Theory 4(3): 83-87. Owusu, F. K. (2010). Time series Arima modelling of inflation in Ghana: (1990 – 2009). [Online] Available:http://dspace.knust.edu.gh:8080/xmlui/bitstream/handle/123456789/866/FRANK%20KOFI%20OWUSU.pdf. (December 10, 2013). Webster, D. (2000). Webster's New Universal Unabridged Dictionary. Barnes & Noble Books, New York. Appendix Tables and figures of inflation rate of Ghana  Figure 1: General trend of Ghana’s monthly inflation rate LagAutocorrelation1514131211109876543211.00.80.60.40.20.0-0.2-0.4-0.6-0.8-1.0Figure 2 :Autocorrelation Function for Infaltion Rate(with 5% significance limits for the autocorrelations)LagPartial Autocorrelation1514131211109876543211.00.80.60.40.20.0-0.2-0.4-0.6-0.8-1.0Figure 3: Partial Autocorrelation Function for Inflation Rate(with 5% significance limits for the partial autocorrelations)  Table 1 Augmented Dickey Fuller Test for Inflation Rate Oder of Differencing ADF Test Statistic P-Value 0 -1.0035 0.93 1 -3.3808 0.07 2 -6.2167 0.01  TimeInflation_Rate2009 2010 2011 2012 2013 201468101214161820Mathematical Theory and Modeling                                                                                          www.iiste.org ISSN 2224-5804 (Paper)    ISSN 2225-0522 (Online) Vol.4, No.3, 2014  104 LagAutocorrelation1514131211109876543211.00.80.60.40.20.0-0.2-0.4-0.6-0.8-1.0Figure 4: ACF of Second Difference of Inflation Rate(with 5% significance limits for the autocorrelations)LagPartial Autocorrelation1514131211109876543211.00.80.60.40.20.0-0.2-0.4-0.6-0.8-1.0Figure 5: PACF of Second Difference of Inflation Rate(with 5% significance limits for the partial autocorrelations)  Table 2: Different ARIMA (p, 2, q) Models fitted     Model AIC AICC BIC Log-Likelihood ARIMA(1,2,1) 134.43* 134.87* 140.61* -64.21 ARIMA(1,2,3) 136.89 138.04 147.19 -63.45 ARIMA(2,2,1) 135.85 136.61 144.09 -63.93 ARIMA(2,2,3) 135.14 136.79 147.51 -61.57 ARIMA(2,2,7) 142.35 147.03 162.95 -61.17* ARIMA(3,2,1) 137.80 138.95 148.10 -63.90 ARMA(3,2,3) 141.66 143.90 156.08 -63.83 ARIMA(3,2,7) 145.75 151.49 168.42 -61.88 *Best model based on the selection criterion   Table 3: Estimate of ARIMA (1,2,1) model   Type Coefficient SE T statistic P-Value Constant 0.012 0.021 0.590 0.560 AR(1) -0.279 0.147 -1.900 0.063 MA(1) 0.789 0.094 8.390 0.000  Mathematical Theory and Modeling                                                                                          www.iiste.org ISSN 2224-5804 (Paper)    ISSN 2225-0522 (Online) Vol.4, No.3, 2014  105  Figure 4.6 Diagnostic Plot of Residuals of ARIMA (1, 2, 1)  Figure 7 Plot of ACF Squared Residuals   Figure 8 Plot of PACF Squared Residuals Table 4 ARCH LM Test for ARIMA (1,2,1) Residuals  Lag Chi-squared P-Value 12 18.829 0.093 24 19.722 0.712 36 24.000 0.937 48 12.000 1.000   Standardized ResidualsTime0 10 20 30 40 50 60-40240 5 10 15-0.20.41.0LagACFACF of Residuals2 4 6 8 100.00.40.8p values for Ljung-Box statisticlagp value0 5 10 15-0.20.00.20.40.60.81.0LagACFACF Squared Residuals5 10 15-0.20.00.20.4LagPartial ACFPACF Squared ResidualsMathematical Theory and Modeling                                                                                          www.iiste.org ISSN 2224-5804 (Paper)    ISSN 2225-0522 (Online) Vol.4, No.3, 2014  106 Table 5: 12 Months Out Sample Forecast For the Year 2014 Month Forecast LCL UCL January 13.885 12.465 15.304 February 14.244 12.271 16.217 March 14.611 11.969 17.253 April 14.976 11.653 18.299 May 15.341 11.293 19.389 June 15.706 10.897 20.516 July 16.072 10.897 21.68 August 16.437 10.463 22.88 September 16.802 9.994 24.115 October 17.167 9.489 25.385 November 17.533 8.95 26.687 December 17.898 8.378 28.021    13.885 14.244 14.611 14.976 15.341 15.706 16.072 16.437 16.802 17.167 17.533 17.898 02468101214161820Inflation Rate Forecast for 2014

Empirical Modelling and Model Selection for Forecasting Monthly Inflation of Ghana

https://www.iiste.org/Journals/index.php/MTM/article/download/11323/11630

Empirical Modelling and Model Selection for Forecasting Monthly Inflation of Ghana

Abstract

Similar works

Full text

Available Versions

International Institute for Science, Technology and Education (IISTE): E-Journals