Inflation Forecasting Models For Saudi Arabia - October 2015

Transcription

1. WP /15/7 SAMA Working Paper INFLATION FORECASTING MODELS FOR SAUDI ARABIA October 2015 Dr. Hussain Abusaaq Economic Research Department Saudi Arabian Monetary Agency The views expressed are those of the author(s) and do not necessarily reflect the position of the Saudi Arabian Monetary Agency (SAMA) and its policies. This Working Paper should not be reported as representing the views of SAMA.
2. INFLATION FORECASTING MODELS FOR SAUDI ARABIA  Abstract This study consists of one essay related to modeling and out-of sample forecasting monthly headline and core inflation for the economy of Saudi Arabia. The primary contribution is to provide a short term inflation forecast (STIF) model based on disaggregated consumer price index data of Saudi Arabia. The study predicts headline and core inflation rates and CPI for the period from February 2015 until June 2015. For headline inflation, the expected rates are 2.33, 2.29, 2.26, 2.33, 2.33 for the period from February 2015 to June 2015 respectively. Moreover, the forecasted core inflation rates for the same period are 2.21,2.16,2.16, 2.34,2.37 respectively. Thus, headline and core inflation rates will be increasing in February, decreasing in March and April and eventually increasing again in May and June. Also, core inflation will be higher than headline inflation in May and June. We can conclude that the study's estimation and forecasting are consistent and provide stable and accurate results. Keywords: Headline Inflation, Core Inflation, consumer Price Index,  Author contacts: Hussain Abusaaq, Economic Research Department, Saudi Arabian Monetary Agency ,P. O. Box 2992 Riyadh 11169, Email: habusaaq@sama.gov.sa. 2
3. 1 . Introduction Monetary policymakers focus on economic predictions of only a few crucial macroeconomics variables such as GDP, inflation and unemployment rate. However, many other variables should be looked into when creating these forecasts. In principle, information extracted from other economic variables should be useful and add some prediction power when forecasting macroeconomic variables. Recent studies such as [Stock and Watson, 2005] have shown that inflation has become hard to forecast. Also, if we follow the literature over the last 20 years on inflation modeling and forecasting, the reader will notice that these forecasting models range from simple to very complicated ones. The goal of these models is to come up with a precise and accurate model to predict inflation in short and medium terms. In 2001, [Atkeson and Ohanian, 2001] concluded their study onforecasting inflation, showing that for the period between 1985 and 1999, simple random walk forecasting would outperform more sophisticated and complicated models. Moreover, Brave and Fisher (2004) expanded on the work of [Atkeson and Ohanian, 2001], finding that it might work well for time periods other than 1985 to 1999. However, they also suggested that it would be hard to come up with a unique model that performs better than the random walk in different sample periods. In this paper, I will concentrate on short term inflation forecast (STIF) based on disaggregated consumer price index data of Saudi Arabia. It is worth mentioning that there is a lack of literature related to forecasting short term inflation in Saudi Arabia. Thus most references go back to original 3
4. economists work on the economy of United States or Euro area such as [Blake and Rummel, 2013]. 2. Background There are many ways to forecast future inflation, ranging from the most sophisticated statistical models, involving a lot of variables, to simple models based on past experience. This paper provides an example of a shortterm inflation forecast (STIF) in Saudi Arabia. The aim is to construct a STIF on a disaggregated consumer price index CPI data for Saudi Arabia. In particular, it generates a STIF for the total CPI index or the headline and core inflation. The forecasting model can predict in-sample headline and core inflation up to six months ahead, which can then be compared to the actual inflation numbers. Moreover, it is predicted out-of sample headline and core inflation up to five months ahead The methodology of the STIF is straightforward: a time-series model is constructed for each CPI component at a chosen level of disaggregation. Each of these models is then used to produce a short-term forecast for the respective CPI component. The individual forecasts are then (re)aggregated into the CPI index, using the weights of each component in the all-items CPI index. The forecast for the CPI index in levels can then be used to calculate (short-term) inflation forecasts. This analysis uses an example of a STIF first applied by the Bank of England when forecasting inflation in South Africa. 4
5. 3 . Data The data consist of a monthly dataset of 12 disaggregated Saudi Arabia CPI components, spanning the period from January 2011 through November 2014. Depending on the respective sample periods, we have approximately 47 observations. The data are taken from Saudi Arabian Monetary Agency. The 12 disaggregate components of Saudi Arabia CPI basket are: food and beverages, tobacco, clothing and footwear, housing; water; electricity and other fuels, furnishing, household equipment and maintenance, health, transport, communications, recreation and culture, education, restaurants and hotels, and finally miscellaneous goods and services. The weights of the 12 components are shown in Table (1). Table 1:The weights of the 12 components of CPI. Number 1 2 3 CPI component Food and Beverages Tobacco Clothing and Footwear weight number CPI component weight 21.7 7 Transport 10.4 0.5 8 8.1 8.4 9 Communications Recreation and Culture 3.5 4 Housing 20.5 10 Education 2.7 5 Furnishing 9.1 11 Restaurants and Hotels 5.7 6 Health 2.6 12 Miscellaneous 6.8 The three components with the largest weights are food (21.7 percent), housing, water, electricity and other fuels (20.5 percent) and transport (10.4 percent). Altogether, these three components account for more than 50 percent of the Saudi Arabia all-items CPI index. The time series of the price levels for the 12 components are given in Figures (1) and (2). 5
6. Sep-14 May-14 Jan-14 94 Sep-13 96 May-13 98 Jan-13 100 Sep-12 102 May-12 104 105 100 95 Jan-14 Sep-13 May-13 Jan-13 Sep-12 May-12 Jan-12 Sep-11 May-11 Sep-14 110 Sep-14 115 May-14 TRANSPORT May-14 Jan-14 Sep-13 May-13 Jan-13 Sep-12 May-12 Jan-12 Sep-11 FURNISHINGS Jan-12 106 Jan-11 Oct-14 May-14 Dec-13 Jul-13 Feb-13 Sep-12 Apr-12 Nov-11 Jun-11 Jan-11 FOOD Sep-11 108 May-11 CLOTHING May-11 135 130 125 120 115 110 105 Jan-11 Oct-14 May-14 Dec-13 Jul-13 Feb-13 Sep-12 Apr-12 Nov-11 Jun-11 Jan-11 150 145 140 135 130 125 120 115 110 Jan-11 Oct-14 May-14 Dec-13 Jul-13 Feb-13 Sep-12 Apr-12 Nov-11 Jun-11 Jan-11 Figure1 : Monthly Dataset of the First 6 Saudi Arabia CPI Components, Spanning from the Period January 2011 through November 2014. HOUSING 165 160 155 150 145 140 135 130 125 COMMUNICATION 95.5 95 94.5 94 93.5 93 92.5 92 91.5 91 90.5 90 6
7. 115 110 105 100 95 90 Jan-13 Sep-14 Sep-14 Sep-14 May-14 Sep-13 May-13 Jan-13 Sep-12 May-12 Jan-12 Sep-11 Jan-14 180 160 140 120 100 80 60 40 20 0 May-14 TOBACCO Jan-14 118 116 114 112 110 108 106 104 May-14 Sep-13 May-13 EDUCATION Jan-14 Sep-13 HEALTH Jan-13 95 May-13 100 Sep-12 105 Sep-12 110 Jan-12 115 May-12 120 Jan-12 RECREATION May-12 105 Sep-11 100 Sep-11 110 Jan-11 105 May-11 110 May-11 Sep-14 May-14 Jan-14 Sep-13 May-13 Jan-13 Sep-12 May-12 Jan-12 Sep-11 May-11 120 Jan-11 Sep-14 May-14 Jan-14 Sep-13 May-13 Jan-13 Sep-12 May-12 Jan-12 Sep-11 Jan-11 MISCELLANEOUS May-11 Jan-11 May-11 125 Jan-11 Sep-14 May-14 Jan-14 Sep-13 May-13 Jan-13 Sep-12 May-12 Jan-12 Sep-11 May-11 Jan-11 Figure2 : Monthly Dataset of the second 6 Saudi Arabia CPI Components, Spanning from the Period January 2011 through November 2014. RESTAURANTS 135 130 115 125 120 115 7
8. 4 . Analyzing the Data 4.1 Unit Root test Figures (1) and (2) above show that all 12 Saudi Arabia CPI components have unit roots and suffer from autocorrelations, since most of the components are likely to have a random walk pattern. Thus, they move up and down in the line graph above. Also, in the correlogram, it is clear that the 12 disaggregated Saudi Arabia CPI components suffer autocorrelations as shown in Figure (3).1 Mandatory initial step in modern time series analysis is testing for unit roots to check whether data are stationary. The food time series has to be tested for a unite root using Augmented Dickey-Fuller (D-F) test as follows: The hypothesis in the Augmented Dickey-Fuller (D-F) test are:  H0: There is a Unit Root  H1: There is no Unit Root  Decision rule: 1. If Augmented Dickey-Fuller-t.value > Augmented Dickey-Fuller critical value. Thus, do not reject null hypothesis, i.e., a unit root exists. 2. If Augmented Dickey-Fuller-t.value < Augmented Dickey-Fuller critical value. Thus, reject null hypothesis, i.e., a unit root does not exist. 1 To avoid redundancy, the paper concentrates on food time series only and the other 11 Saudi Arabia CPI components will be discussed in the appendix. 8
9. The autocorrelation function (ACF)2 in figure (3) confirms that food time series has a unit root since the values of ACF are very large and persist for many lags (The ACF of food is slowly declining which is an indicator of non-stationary time series). In addition, Augmented Dickey-Fuller test confirms that the food time series has a unit root as shown in figure (4). The computed Augmented Dickey -Fuller t-statistic for the food time series is -0.409974 which is greater than Augmented Dickey-Fuller critical value -2.602225, -2.928142 and -3.584743 at 10%, 5% and 1% significant level, respectively. Thus Ho cannot be rejected and the food time series has a unit root problem (not stationary). Figure3 : The autocorrelation function (ACF) for Food. Autocorrelation FOOD 1 150 145 0.8 140 0.6 AUTOCORRELATION 135 130 125 120 0.4 0.2 0 2 4 6 8 10 12 14 16 18 20 115 -0.2 Oct-14 May-14 Dec-13 Jul-13 Feb-13 Sep-12 Apr-12 Nov-11 Jun-11 Jan-11 110 -0.4 LAGS 2 The ACF is a plot of ρk for k lags that measures to what extent the value of yt in one period is correlated with values in previous periods yt‐k 9
10. Null Hypothesis : FOOD has a unit root Exogenous: Constant Lag Length: 1 (Automatic based on SIC, MAXLAG=9) Prob.* t-Statistic 0.8986 -0.409974 -3.584743 -2.928142 -2.602225 Augmented Dickey-Fuller test statistic 1% level Test critical values: 5% level 10% level *MacKinnon (1996) one-sided p-values. Augmented Dickey-Fuller Test Equation Dependent Variable: D(FOOD) Method: Least Squares Date: 12/16/14 Time: 09:45 Sample (adjusted): 2011M03 2014M11 Included observations: 45 after adjustments Prob. t-Statistic Std. Error Coefficient Variable 0.6839 0.0913 0.5156 -0.409974 1.727999 0.655661 0.011688 0.148765 1.588077 -0.004792 0.257065 1.041241 FOOD(-1) D(FOOD(-1)) C 0.522222 0.542255 1.654439 1.774883 1.699340 1.964808 Mean dependent var S.D. dependent var Akaike info criterion Schwarz criterion Hannan-Quinn criter. Durbin-Watson stat 0.067849 R-squared 0.023461 Adjusted R-squared 0.535856 S.E. of regression 12.05996 Sum squared resid -34.22488 Log likelihood 1.528535 F-statistic 0.228672 Prob(F-statistic) Figure: 4 Augmented Dickey-Fuller Test Equation for food time series. 4.2 Solving Unit Root Problem To solve the unit root problem, first it is better to check if the first difference can attain level-stationary time series. If the answer is yes, then the Auto-Regressive Integrated Moving Average (ARIMA) (p,d,q) can be used. More precisely, ARIMA (1, 1, 0) = differenced first-order autoregressive model is used, which makes the first component a stationary time series. Otherwise, it is advised to move to the second difference. Fortunately, all 12 disaggregated Saudi Arabia CPI components are stationary when the transform is made to the first difference form. 01
11. Taking the first difference of the food time series and calculating Augmented Dickey -Fuller proves that the first difference of food time series is stationary at the mean and variance since the computed Augmented Dickey -Fuller t-statistics -5 .095407 which is less than the Augmented Dickey-Fuller critical value -2.602225, -2.928142 and -3.584743 at 10%, 5% and 1% significant level, respectively as shown in figure (6). Thus Ho is rejected and the food time series does not have a unit root problem (stationary). The autocorrelation function (ACF) in figure (4) confirms that first difference of food time series does not have a unit root since the values of ACF are very small and decay rather quickly. Figure5 : The autocorrelation function (ACF) for Food first difference. Autocorrelation Food First Difference 0.3 2011M01 2011M05 2011M09 2012M01 2012M05 2012M09 2013M01 2013M05 2013M09 2014M01 2014M05 2014M09 AUTOCORRELATION 0.2 0.1 0 2 4 6 8 101214161820 -0.1 -0.2 -0.3 LAGS 00
12. The same conclusion can be derived for all other 11 disaggregated Saudi Arabia CPI components . Thus, all 12 disaggregated Saudi Arabia CPI components have a unit root problem, and this obstacle can be avoided by taking the first difference. Also, The recommended model is ARIMA (1, 1, 0). Null Hypothesis: D(FOOD) has a unit root Exogenous: Constant Lag Length: 0 (Automatic based on SIC, MAXLAG=9) Prob.* t-Statistic 0.0001 -5.095407 -3.584743 -2.928142 -2.602225 Augmented Dickey-Fuller test statistic 1% level Test critical values: 5% level 10% level *MacKinnon (1996) one-sided p-values. Augmented Dickey-Fuller Test Equation Dependent Variable: D(FOOD,2) Method: Least Squares Date: 12/16/14 Time: 11:31 Sample (adjusted): 2011M03 2014M11 Included observations: 45 after adjustments Prob. t-Statistic Std. Error Coefficient Variable 0.0000 0.0009 -5.095407 3.570981 0.146804 0.109706 -0.748027 0.391756 D(FOOD(-1)) C 0.004444 0.664337 1.613989 1.694285 1.643922 1.957467 Mean dependent var S.D. dependent var Akaike info criterion Schwarz criterion Hannan-Quinn criter. Durbin-Watson stat 0.376479 R-squared 0.361978 Adjusted R-squared 0.530647 S.E. of regression 12.10823 Sum squared resid -34.31474 Log likelihood 25.96318 F-statistic 0.000007 Prob(F-statistic) Figure6 : Augmented Dickey-Fuller Test Equation for the first difference of food time series. 02
13. 5 . Forecasting Evaluation and Forecasting Accuracy Criteria 5.1 Headline Inflation It is advisable to retain some observations at the end of the sample period, which are not included in the estimation model, to test the outof sample forecasting ability of the model. However, in this paper, insample forecasts and out-of sample forecasts were used. First, the entire period from January 2011 to January 2015 was used to model each of the 12 disaggregated Saudi Arabia CPI components, then, in-sample forecasts were computed for the period from August 2014 to January 2015 and out- of sample forecasts were computed for the period from February 2015 to June 2015. Figure (7) shows the forecasted food time series with minus and plus one standard deviation. Forecasted CPI for Food Time Series 155 150 145 140 135 130 125 120 115 2011M01 2011M03 2011M05 2011M07 2011M09 2011M11 2012M01 2012M03 2012M05 2012M07 2012M09 2012M11 2013M01 2013M03 2013M05 2013M07 2013M09 2013M11 2014M01 2014M03 2014M05 2014M07 2014M09 2014M11 2015M01 2015M03 2015M05 110 Axis Title Food+SD Food-SD FOODF Figure 7 Forecasted CPI for food time series 03
14. Forecasting all CPI components is now straightforward: we simply weigh together the 12 disaggregated Saudi Arabia CPI components using the CPI weights as a model of the all-items CPI inflation rate. The underlying weights are defined as the weights of the 12 disaggregate components are 21.7,0.5, 8.4, 20.5,9.1,2.6,10.4.8.1,3.5,2.7,5.7 and 6.8 for the following CPI components: food and beverages, tobacco, clothing and footwear, housing, water, electricity and other fuels, furnishing, household equipment and maintenance, health, transport, communications, recreation and culture, education, restaurants and hotels, and finally miscellaneous goods and services respectively. Forecasted CPI can be calculated as follows: