Open Access Open Access  Restricted Access Subscription or Fee Access

Exploring Decline Curve Residual Modeling using Kalman Filter

N. Fitriyati, S. Darwis, A.Y. Gunawan, A.K. Permadi


In this paper we propose a new method to capture the fluctuations in decreasing of oil production that was not considered in the Arps model. The proposed method is called as the Decline Curve Residual (DCR) method. The DCR is defined as the difference between production data and the discretized Arps estimate for each corresponding time. The difference will then be modeled by time series model. The Kalman filter will be used to forecast the DCR using a state-space representation that is formed by an appropriate time series model. We also propose a scatter plot of Akaike’s Information Criterion (AIC) vs. Sum Square of Errors (SSE) value as a new tool to select the best model. Based on this scatter plot, the best model is selected from the point which gives the shortest distance from AIC and SSE value point to the origin. Based on our data, numerical study shows that the DCR is not stationary in variance. Therefore, we explore this DCR modeling using the autoregressive and moving average (ARMA) and generalized autoregressive conditional heteroscedasticity (GARCH) process. From the scatter plot of AIC vs. SSE value, the result shows that the best model is ARMA(2, 4)-GARCH(2, 1).


Arps model, ARMA-GARCH, decline curve residual, Kalman filter.

Full Text:


Disclaimer/Regarding indexing issue:

We have provided the online access of all issues and papers to the indexing agencies (as given on journal web site). It’s depend on indexing agencies when, how and what manner they can index or not. Hence, we like to inform that on the basis of earlier indexing, we can’t predict the today or future indexing policy of third party (i.e. indexing agencies) as they have right to discontinue any journal at any time without prior information to the journal. So, please neither sends any question nor expects any answer from us on the behalf of third party i.e. indexing agencies.Hence, we will not issue any certificate or letter for indexing issue. Our role is just to provide the online access to them. So we do properly this and one can visit indexing agencies website to get the authentic information. Also: DOI is paid service which provided by a third party. We never mentioned that we go for this for our any journal. However, journal have no objection if author go directly for this paid DOI service.