Tag Archives: Vector Auto Regression


The objective of the paper is to empirically examine the static and dynamic short-run and long-run interaction between the prices (and their volatility)  of natural gas, crude oil, propane and heating oil   in the  US economy, using the Toda and Yamamoto (1995) procedure of Granger’s Causality. Long-run equilibrium relationship is examined using Johansen’s maximum likelihood procedure. The price volatility spill over is also examined between the energy markets using ARCH model. The relationship between prices of energy products may have several implications for the pricing of their derivative products and risk management. This study also examines the efficiency of these markets using the Lo-Mackinlay and Chow-Denning’s (1993) multiple variance ratio tests.   The study uses daily timeseries data from 7th January 1997 to 4th April 2012. To avoid non-stationarity in the variables, all prices are converted into returns form. Based on this data, we found that the return on Henry Hub Natural gas is , well explained by the explanatory variables such as the return of WTI crude oil, Heating oil, propane and the  past values (two days lags) of its own  return. The study found that there is bidirectional causality between Henry Hub Natural Gas return and Heating Oil return. Unidirectional causality is found between three pairs of energy products and the causality runs from Propane return to Crude Oil return, Crude Oil return to Heating Oil return and Heating Oil return to Propane return. Surprisingly, we did not find any causal relationship between Henry Hub Natural Gas return and WTI crude oil return. .There exists a long run equilibrium relationship between the each pair of commodities except between Henry Hub Natural gas and WTI crude oil price. Bidirectional volatility spillover is found between Henry Hub natural gas return and heating oil return, Henry Hub natural gas return and Propane return, WTI crude oil return and Heating Oil return, WTI crude oil return and Propane return. The result from efficient market hypothesis reveals that the energy market in the U.S. does not seem to follow the weak form of efficiency during the study period

Keywords: EGARCH, GARCH, Heating oil, Natural Gas, Toda and Yamamoto causality, Vector Auto Regression, crude oil, volatility clustering, volatility spike

Real Interest Rate and Savings Mobilization in Nigeria (Published)

This study empirically assessed the impact of real interest rate on savings mobilization in Nigeria. The Vector- Auto Regression (VAR) was employed, using the time series data from 1980 to 2008. The study revealed that real interest rate has negatively impacted on the level of savings mobilization in Nigeria. The need for government in Nigeria to bridge the existing gap between the lending and savings rates and increase per capita income level of the populace, to stimulate savings for investment and economic growth were revealed by the study. Therefore, efforts should be geared towards reducing domestic inflation rate to arrest its negative impact on real rates in Nigeria.

Keywords: Inflation Rate, Lending Rate, Real Interest Rate, Savings Mobilization And Nigeria, Vector Auto Regression