International Journal of Mathematics and Physical Sciences Research ISSN 2348-5736 (Online) Vol. 6, Issue 1, pp: (106-112), Month: April - September 2018, Available at: www.researchpublish.com Page | 106 Research Publish Journals A STUDY OF THE SUITABLE TIME SERIES MODEL FOR MONTHLY CRUDE OIL PRODUCTION IN NIGERIA Sadeeq S. A. and Ahmadu A. O. Email Address: sadeeqsa@feca.edu.ng Abstract: Petroleum production and export play a dominant role in Nigeria's economy and account for about 90% of her gross earnings. This dominant role has pushed agriculture, the traditional mainstay of the economy, from the early fifties and sixties, to the background. In this research work we fitted a univariate Seasonal Autoregressive Integrated Moving Average model (SARIMA) to the monthly crude oil production in Nigeria between 2002 and 2016. Different Box-Jenskin Autoregressive Integrated Moving Average (ARIMA) models are fitted and diagnosed. However, ARIMA (2,1,0)(2,1,1) 12 was the best model for the data. The model was further validated and it was discovered that autocorrelation between residuals at different lag times was not significant. Finally, the time plot of the in-sample forecast errors shows that the variance of the forecast errors seems to be roughly constant over time and the histogram of the time series shows that the forecast errors are roughly normally distributed and the mean seems to be close to zero, it seems plausible that the forecast errors are normally distributed with mean zero and constant variance. Keywords: SARIMA, petroleum, Box-jenskin, model, residuals, autocorrelatiom. 1. INTRODUCTION Modern time series forecasting methods are essentially rooted in the idea that the past tells us something about the future. The question of how exactly we are to go about interpreting the information encoded in past events, and furthermore, how we are to extrapolate future events based on this information, constitute the main subject matter of time series analysis. Typically, the approach to forecasting time series is to first specify a model, although this need not be so. This model is a statistical formulation of the dynamic relationships between that which we observe (i.e. the so called information set), and those variables we believe are related to that which we observe. It should thus be stated immediately that this discussion will be restricted in scope to those models which can formulated parametrically. The “classical” approach to time series forecasting derives from regression analysis. The standard regression model involves specifying a linear parametric relationship between a set of explanatory variables and the dependent variable. The parameters of the model can be estimated in a variety of ways, going back as far as Gauss in 1794 with the “Least Squares” method, but the approach always culminates in striving for some form of statistical orthogonality between the explanatory variables and the residuals (or innovations) of the regression. That is, we wish to express the linear relationship in a dichotomous form in which the innovations represent that part of our information which is completely unpredictable. It should probably also be emphasized that in the engineering context this is analogous to reducing a signal to “white noise.” However, this review is to be concerned with more “modern” approaches and in many ways, it was the practical necessities of engineering that provided an initial impetus. Both Wiener (1949) and Kolmogorov (1941) were pioneers in the field of linear prediction, and while their approaches differed (Wiener worked in the frequency domain popular amongst engineers, while Kolmogorov worked in the time domain), it is clear that their solutions to the same basic geometrical problem were equivalent (see Priestley (1981) ch.10). Wiener’s work, in particular, was especially relevant to modern time series forecasting in that he was among the first to rigorously formulate the problem of “signal extraction.” That is, given observations on a time series corrupted by additive noise, what is the optimal estimator (in the Mean-Squared Error (MSE) sense) of the latent or underlying signal (or state variable). Given the historical context of massive systems of