Mathematical Theory and Modeling www.iiste.org ISSN 2224-5804 (Paper) ISSN 2225-0522 (Online) Vol.3, No.11, 2013 102 Modelling the Rate of Treasury Bills in Ghana Ida Anuwoje Logubayom * , Suleman Nasiru, Albert Luguterah Department of Statistics, University for Development Studies, P. O. Box 24 Navrongo, Ghana *: Corresponding Author’s Email: idalogubayom@yahoo.com Abstract Treasury bills rate is a preeminent default-risk free rate asset in Ghana’s money market whose existence can affect the purchasing power of other assets in the security market. Bank of Ghana sells its Bills to mop up excess liquidity and buys Bank of Ghana Bills to inject liquidity into the system. This paper empirically models the monthly Treasury bill rate of two short term Treasury bills (91 day and 182 day) from the year 1998 to 2012 from the BoG using ARIMA models. From the results, it was realized that ARIMA 3, 1, 1 model is appropriate for modelling the 91-day Treasury bill rate with a log likelihood value of -328.58, and least AIC value of 667.17, AICc value of 667.52 and BIC value of 683.05. Also, ARIMA 1, 1, 0 best models the 182-day Treasury bill rates with a log likelihood value of -356.50, and AIC value of 717.00, AICc value of 717.06 and least BIC value of 723.35. An ARCH-LM test and Ljung-Box test on the residuals of the models revealed that the residuals are free from heteroscedasticity and serial correlation respectively. Keywords: Treasury bills, Ghana, Asset, Empirical, Short term. 1. Introduction The acceptance of financial risk is inherent to the business of banking and insurance roles as financial intermediaries. To meet the demands of customers and communities and to execute business strategies, financial institutions make loans, purchase securities and deposit with different maturities and interest rates. A treasury bill which is one of the common securities being purchased in many societies is a default-risk free short-term bonds that matures within one year or less from their time of issuance. Treasury bills are sold with maturities of four weeks (1month), 13 weeks (3 months-91-day), 26 weeks (6 months-182-day), and 52 weeks (12 months- 360-days) weeks, which are more commonly referred to as the one-, three-, six-, and 12-month T-bills, respectively. Like a zero-coupon bond, Treasury bills are sold at a discount to par. “Par” is the value at which all T-bills mature. Treasury Bills are issued to finance government deficits and Bank of Ghana sells Bank of Ghana Bills to mop up excess liquidity and buys Bank of Ghana Bills to inject liquidity in the system (Brilliant, 2011). Treasury Bills have so gained a high appeal among the population as securities with high returns and virtually no default risk. Jacoby, et al., (2000) provided theoretical arguments to show how treasury bills impacts stock market prices. Jones (2001) showed that stock prices predicted expected returns in the time-series. As more data has become available, recent work has shifted focus on studying time-series properties of risk in equity markets as well as in Treasury bills. Huang, et al., (2001) related risk to return volatility, while Brandt (2002) studied the relationship between liquidity, order flow and the yield curve. Aboagye et al., (2008) in studying the performance of stocks in Ghana, using an investment of the same amount in treasury bills and shares over a period of 1991 and 2001, found out that investors in stock exchange traded shares earned on average 54% per annum, whereas treasury bill investors Earned 36.3%. The changing rate relationship across the spectrum of maturities is analyzed by some researchers by a yield curve risk: A yield curve is the graph of required interest rates for various maturity times. Ghanaians are so impressed with the observable high rate of returns on treasury bills that many believe treasury bills offer the chance to earn higher returns than can be earned on other financial securities. Due to the impressive nature of treasury bills in the financial market, many researchers on the Ghanaian economy focus much on comparative study on the performance of treasury bills and other stock investments but none in this country has concentrated on modeling Treasury bills. This study therefore is focused on modeling the 91-day and 182-day Treasury bills, to determine an appropriate times series model for predicting these Treasury bills and forecast future outcomes. The Modelling of Treasury bills in useful to investors in their choice of Treasury bill to invest in. It will also be useful in the financial markets and the security agencies in the control of the different degrees of liquidity in their securities. 2. Materials and Methods of Analysis We obtained monthly data on the 91-day and 182-day Treasury bills rate from the Bank of Ghana (BoG) from December, 1998 to October, 2012. The rates were modeled using Autoregressive Integrated Moving Average (ARIMA) models. The ARIMA , ,  is a modified form of the Autoregressive Moving Average Model (ARMA ,  model where the times series variable is non-stationary. An ARMA ,  model is the combination of an Autoregressive process and a Moving average process into a compact form in order to reduce