State space versus SARIMA modeling of the Nigeria’s crude oil export

Omorogbe Joseph Asemota

doi:10.4038/sljastats.v17i2.7872

Abstract

This paper analyzes the Nigeria’s crude oil export series using monthly data from January 1999 to December 2014. We employed the state space local level model with stochastic and deterministic seasonal to model the dynamic features in the Nigeria crude oil export. Our results clearly indicate that the local level model with deterministic seasonal is the most parsimonious model between the two state space models considered in this study. Also, a parsimonious SARIMA model is also fitted to the data. We compare the forecasting performance of the two parsimonious models and evaluate their forecasts using ex-post indicators such as mean absolute percentage error (MAPE), root mean square percentage error (RMSPE) and the Theil’s U statistic. The forecast analysis and evaluation results indicate that the state space local level model with deterministic seasonal outperforms the Box-Jenkins model in shorter and medium – range forecasting horizons. Howbeit, the forecast of the SARIMA model improves in the longer horizon. The Theil’s U statistic also indicates that the state space local level model with deterministic seasonal and SARIMA model outperform the naive model at most of the forecasting horizons. In conclusion, we recommend that the state space model with deterministic seasonal component should be used in shorter and medium range forecasting horizons of the Nigeria’s monthly crude oil export. Howbeit, for longer forecasting horizon, ten months and above, the seasonal ARIMA model should be considered.

Highlights

The statistical modeling of time series started a long time ago with the introduction of the Autoregressive (AR(p)) and Moving Average (MA(q)) models by Yule (1927) and Slutsky (1927) respectively. Wold (1938) in his IASSL ISSN-2424-6271celebrated theorem “Wold’s decomposition theorem” proved that any time series can be decomposed into two different parts
The forecast of the seasonal autoregressive moving average (SARIMA) model improves in the longer horizon
Prior to the forecasting competition, we employed two state space models, the local level model with stochastic and deterministic seasonal to model the dynamic features in the Nigeria crude oil export

Summary

Introduction

The statistical modeling of time series started a long time ago with the introduction of the Autoregressive (AR(p)) and Moving Average (MA(q)) models by Yule (1927) and Slutsky (1927) respectively. Wold (1938) in his IASSL. Since the variance of the seasonal disturbances in local level model with stochastic seasonal is found to be very small and not statistically significant (see Table 1), we presents the results of analysis of the Nigeria crude oil export time series with a local level model and a deterministic seasonal. Since the log-likelihood values of the two models are almost identical, 207.60 and 207.50 for the local level model with stochastic seasonal and the local level model with deterministic seasonal respectively, the improved fit of the second model can be completely attributed to its greater parsimony.Commandeur and Koopman (2007) pointed out that, in state space modelling, a small and insignificant state disturbance variance indicates that the corresponding state component may as well be treated as a deterministic effect, resulting in a more parsimonious model

SARIMA Model Estimation Results

Forecasting performance

Conclusions