ARIMA INTERVENTION ANALYSIS OF NIGERIAN MONTHLY CRUDE OIL PRICES

Transcription

1 ARIMA INTERVENTION ANALYSIS OF NIGERIAN MONTHLY CRUDE OIL PRICES EBERECHI HUMPHREY AMADI AND ETTE HARRISON ETUK ABSTRACT It has been observed that between January 2011 to June 2014 the price of crude oil had a more or less horizontal trend coming mostly within the $100 to $110 per barrel bracket and fell sharply thereafter and reaches the $30 to $50 per barrel bracket in This fall is seen as responsible for the current economic depression bedeviling the Nigerian country and this calls for an intervention. The point of intervention is herein chosen as June 2014, after which the prices started reducing consistently to an all-time low value. The realization of this series from January 2011 to May 2016 is studied in this investigation. The pre-intervention data have been adjudged stationary. Following its autocorrelation structure, an adequate ARMA(1, 3) model is fitted to it; its residuals are uncorrelated and follow a normal distribution. On the basis of this model, post-intervention forecasts are obtained. The difference between these forecasts and their corresponding actual observations are modelled for the intervention transfer function. The estimated transfer function is statistically significant, which is an indication of its adequacy. The resultant intervention model may be used to carry out an intervention to salvage this unfortunate situation. KEY WORDS: Intervention, Crude oil, Prices, Nigeria, ARIMA modelling INTRODUCTION: The mainstay of the Nigerian economy is still crude oil. Of late production and sales of the commodity has been on the decline so much as to call for an intervention. For instance, a look at the oil prices from January 2011 to early 2016 shows that from prices within the range US$ between 2011 to early 2014 they have fallen to below $50 per barrel. This calls for intervention. The subject of crude oil prices in Nigeria has been of interest to many researchers of late. For instance, Osigwe (2015) observed that a 1% increase in the price of crude oil would positively influence the economic performance of Nigeria by 4%. Asaolu and Ilo (2012) posited that Nigerian stock market return and oil price are tied together in the long run. The dwindling oil prices have been attributed to the sluggish world economy among other reasons by Isihak and Rousselet (2017). Imobighe (2015) recommends as a panacea that more petrochemical plants should be set and gas flaring prohibited to improve upon oil revenue. Etuk (2013) has fitted a SARIMA(0,1,1)x(1,1,1) model to the prices. 12 The purpose of this study is to propose an intervention model for the oil price. The approach to adopt is the Box-Tiao (1975) approach based on Box-Jenkins (1976) or ARIMA modelling. Since its inception this approach has been widely applied by scholars. For example, Hull et al. (1993) used intervention analysis to document the effectiveness of fluoxetine therapy. Afifi et al. 107

2 Nigerian Journal Of Oil And Gas Technology - Vol 3 No. 1 (2010) noticed a positive change in mental health after teaching a group of students individual skills and problem-solving. A rainfall intervention model for prediction of temporal changes in daily water consumption given rainfall forecasts has been proposed by Sastri and Valdes (1989). Stiller-Ostrowski et al. (2009) have shown that some psychosocial and referral intervention caused a rise in the extent of acquisition of knowledge and skill usage. Etuk and Victor-Edema (2017) have proposed an intervention model for monthly Euro-Naira exchange rates. This is to mention just a few. MATERIALS AND METHODS Data The data for this work are monthly crude oil prices in US dollars per barrel from January 2011 to May 2016 from the website of the Central Bank of Nigeria under the Data & Statistics heading and the Crude Oil Price subheading. Intervention Analysis Let {Xt}be a time series. Suppose there is an event occurring which changes the trend in the series. This event is referred to as an intervention. Suppose it occurs at time t = T. Box and Tiao (1975) propose that the pre-intervention observations of {Xt}be modelled as a Box-Jenkins (1976) or autoregressive integrated moving average (ARIMA) model. That is, for t < T, 108

3 Arima Intervention Analysis Of Nigerian Monthly Crude Oil Prices Estimation of (1) is done by first of all determining the orders p, d and q. The differencing order d is obtained by trying d=0. If the series is stationary, then d=0, else d=1; if the series is stationary, then d=1; else d=2. The augmented Dickey Fuller (ADF) test shall be used for this test for stationarity. The autoregressive (AR) order p is obtained as the cut-off point of the partial autocorrelation function (PACF). The moving average (MA) order q is obtained as the cut-off point of the autocorrelation function (ACF). The á's and â's are estimated using the least squares criterion. Equation (2) is estimated also by the least squares criterion. Computer Software: All computational work in the sequel shall be done using Eviews 7. It uses the least error sum of squares criterion for estimation. RESULTS AND DISCUSSION The time plot of the 65-point monthly series in Figure 1 shows a fairly horizontal trend until June 2014 after which there is sharp fall in the prices till May The intervention point T was therefore taken to be t = T = 42. Pre-intervention time plot in Figure 2 shows a fairly horizontal trend and with a test statistic value of and the 10%, 5% and 1% critical values of -2.61, 2.94, and respectively and p = , the pre-intervention data are adjudged stationary by the ADF Test. Therefore d=0. On the basis of their correlogram of Figure 3 the ARMA(1,3) Xt = Xt åt åt-3 (±0.0012) (4) (±0.0886) (±0.0875) is fitted as summarized in Table 1. Adequacy of model (4) is not in doubt since virtually all its residual correlations are non-significant (See Figure 4) and normally distributed (See Figure 5). Based on model (4) post-intervention forecasts Ft are obtained. The difference Zt = Xt - Ft modeled as summarized in Table 2 is given by Zt = *( ^(t-41))/( ), t > 42 (5) It is noteworthy that model (5) is statistically significant which is an indication of its adequacy. Therefore the overall intervention model is given by 109

4 Nigerian Journal Of Oil And Gas Technology - Vol 3 No. 1 where I t = 0, t > 42, I t = 1, otherwise. CONCLUSION: Model (6) is an intervention model for the monthly crude oil prices. Further evidence of its adequacy is on the basis of Figure 6 in which there is close agreement between the postintervention forecasts and the observations and Figure 7 in which goodness-of-fit of the model across the entire series could be observed. Intervention can therefore be based on it by policy makers, planners and managers. REFERENCES Afifi, R., Nakkash, R., Hajj, T. E., Mahfoud, Z., Hammad, S., Makhoul, J., Abdulrahim, S. Kanj, M. and Haddad, P. (2010). Qaderoon youth health promotion programme in the Burj El Barajneh Palestinian refugee camp, Beirut, Lebanon: a community-intervention analysis pdf Asaolu, T. O. and Ilo, B. M. (2012). The Nigerian Stock Market and Oil Price: A Cointegration Analysis. Kuwait Chapter of Arabian Journal of Business and Management Review, 1(5): Box, G. E. P. and Jenkins, G. M. (1976). Time series analysis, forecasting and control, Revised Edition, Holden-day, San Francisco. Box, G. E. P. and Tiao, G. C. (1975). Intervention Analysis with applications to economic and environmental problems. Journal of American Statistical Association, 70: Etuk, E. H. (2013). Seasonal ARIMA Modelling of Nigerian Monthly Crude Oil Prices. Asian Economic and Financial Review, Volume 3, No. 3, pp Etuk, E. H. and Victor-Edema, U. A. (2017). Box-Tiao Intervention Modelling of Monthly EUR- NGN Exchange Rates due to Nigerian Economic Recession. Journal of Scientific and Engineering Research, 4(3): Hull, J. W., Clarkin, J. F. and Alexopoulos, G. S. (1993). Time Series Analysis of Intervention Effects Fluoxetine Therapy as a Case Illustration. Journal of Nervous & Mental Disease, 181(1): Imobighe, M. D. (2015). The Impact of Oil Price Instability on the Growth Process of the Nigerian Economy. Journal of Resource Development and Management, 14:

5 Arima Intervention Analysis Of Nigerian Monthly Crude Oil Prices Isihak, S. R. and Rousselet, S. (2017). Dwindling Crude Oil Price: Implications for the Nigerian Economy. Osigwe, A. C. (2015). Exchange Rate Fluctuations, Oil Prices and Economic Performance. Empirical Evidence from Nigeria. International Journal of Energy Economics and Policy, 5(2): Sastri, T. and Valdes, J. B. (1989). Rainfall Intervention Analysis for On-Line Applications. Journal of Water Resources Planning and Management, 115(4). DOI: Stiller-Ostrowski, J. L., Gould, D. R. and Covassin, T. (2009). An Evaluation of an Educational Intervention in Psychology of Injury for Athletic Training Students. Journal of Athletic Training, 44(5): The Pennsylvania State University (2016). Welcome to STAT 510! Applied Time Series Analysis. Department of Statistics Online Program

6 Nigerian Journal Of Oil And Gas Technology - Vol 3 No. 1 FIGURE 3: CORRELOGRAM OF THE PRE-INTERVENTION DATA TABLE 1: ESTIMATION OF THE PRE-INTERVENTION ARMA(1,3) MODEL 112

7 Arima Intervention Analysis Of Nigerian Monthly Crude Oil Prices FIGURE 4: CORRELOGRAM OF THE PRE-INTERVENTION ARMA(1,3) RESIDUALS 113

8 Nigerian Journal Of Oil And Gas Technology - Vol 3 No. 1 FIGURE 5: HISTOGRAM OF THE PRE-INTERVENTION ARMA(1,3) RESIDUALS TABLE 2: ESTIMATION OF THE INTERVENTION TRANSFER FUNCTION 114

9 Arima Intervention Analysis Of Nigerian Monthly Crude Oil Prices 115