Fractional dynamic behavior in Forcados Oil Price Series: An application of detrended fluctuation analysis

Abstract

Nigeria experienced a long history of macroeconomic instability since political independence. For many years, Nigerian policymakers had been unsuccessful in their attempts to manage the national economy to deal with macroeconomic instability. They have been accused of mismanagement and incompetence when it comes to preparation and execution of national budgets. In an effort to arrest this problem, the federal government recently introduced structure into public budgeting. A Fiscal Responsibility Act was passed to improve the budgetary process. Consistent with the law, policymakers are required to devise a process for forecasting revenue. Thus, with the help of experts from the International Monetary Fund, an ARMA(p,q) (autoregressive moving average) process was recommended. An ARMA model combines an autoregressive component which captures past values of a time series with a moving average component which captures past forecast errors associated with the time series. As a mono-cultural economy with crude oil as the main source of government revenue, an ARMA(p,q) process assumes that the oil price series is stationary with a short memory. In this paper, we set out to test for the presence of long memory or persistence in oil price series using weekly data from 1978 to 2007. The results of the detrended fluctuation analysis (DFA) suggest Nigeria's oil price series is anti-persistent. A Hurst exponent of 0.48 is indicative of a time series which is covariance stationary but mean-reverting. In other words, we can fit a stationary ARMA(p,q) model driven by fractional noise to the series. This implies that a low price level has a tendency to be followed by a high price level and vice versa. Thus, past price trends are more likely to change in the future. Moreover, the effect of shocks to the price system dies away in the long run. Therefore, the current revenue forecasting tool would need to be overhauled in the presence of price reversals. This is more critical in the face of constant disruptions to oil production in the Niger Delta where the Forcados variety is produced.