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Abstractrespectively. These models are found useful in modelling most of the economic and financial data.

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The interest to carry out volatility analysis of crude oil production in Nigeria in this paper is motivated by the shortfalls in quantities of crude oil produced in recent past, given the country's high dependence on oil and its contribution to the nation's economic development. In 2016 precisely, the country experienced drastic instability in prices of crude oil at international markets and dwindling production quantities due to vandalism on oil facilities and other corrupt practices in the sector. This paper aims at using volatility measures to investigate variability of crude oil production as an assumed contributor to the economic downturn observed in the recent past in Nigeria. The data used are crude oil production data in millions of barrels collected from NNPC Statistical Bulletin. Variance of the crude oil series has been fitted with ARCH (2) model. ARCH (3) and GARCH (3,3) models are also fitted to the variance of the error obtained from ARIMA(0,1,1). ARCH and GARCH models have shown evidence of volatility in the series. The parameter estimate of the non-linear component of the bilinear model fitted to the crude oil data could not capture volatility clustering. This explains the superiority of ARCH and GARCH model over bilinear model when fitting volatile series. Synonymous with oil price volatility, evidence has it that crude oil production data are volatile. Although, Nigerian government's intervention and negotiations with Niger Delta Militants to end operational attacks on oil facilities yielded positive results, fact has been established that the two economic variables (production and price) are volatile, as contributors to the recent past economic recession in Nigeria. It is important for the stakeholders in the sector and Nigerian government to always exhibit proactive measures against illicit activities that negatively affect oil production at all times and ensure maximum control of crude oil production process and militating factors during price shocks to avoid uncontrollable economic instability.

Bilinear Autoregressive Moving Average Vector (BARMAV) Models are models aggregated with the linear and non-linear vector components of autoregressive and moving average processes. The linear part is the sum of the two vector processes, while the non-linear part is the product of the processes. From the general BARMAV models, Bilinear Autoregressive Vector (BARV) Models and Bilinear Moving Average Vector (BMAV) Models have been isolated. Under certain conditions, the models are proved to exist. Empirically, Nigerian consumer price index and inflation rate are used to test the fitness of the bilinear models. Data for the analysis are from Central Bank of Nigeria Statistical Bulletin, collected from January 2009 to December 2016 with November 2009 as the base year for each of the series. The bilinear autoregressive moving average vector models are fitted to the data. Parameters are tested and found to be significant. The adequacy of each estimated model is confirmed with ACF, PACF and descriptive statistics adopted in the paper. The plots of the actual and fitted CPI and IR have shown that models are adequate as estimates compete favourably with the actual values. The models are useful in modelling some economic and financial data that exhibit some characteristics of non-linearity.