Tag Archives: PACF

Modeling Inflation Rates in Nigeria: Box-Jenkins’ Approach (Published)

This study modeled the inflation rates in Nigeria using Box Jenkins’ time series approach. The data used for the work ware yearly collected data between 1961 and 2013. The empirical study revealed that the most adequate model for the inflation rates is ARIMA (0, 0, 1). The fitted Model was used to forecast the Nigerian inflation rates for a period of 12 years.  Based on these results, we recommend effective fiscal policies aimed at monitoring Nigeria’s inflationary trend to avoid damaging consequences on the economy.

Keywords: ACF, ARIMA, Forecasting, Inflation, PACF


This paper fit a time series model to the consumer price index (CPI) in Nigeria’s Inflation rate between 1980 and 2010 and provided five years forecast for the expected CPI in Nigeria. The Box-Jenkins Autoregressive Integrated Moving Average (ARIMA) models was estimated and the best fitting ARIMA model was used to obtain the post-sample forecasts. It was discovered that the best fitted model is ARIMA (1, 2, 1), Normalized Bayesian Information Criteria (BIC) was 3.788, stationary R2 = 0.767 and Maximum likelihood estimate of 45.911. The model was further validated by Ljung-Box test (Q = 19.105 and p>.01) with no significant autocorrelation between residuals at different lag times. Finally, the five years forecast was made, which showed an average increment of about 2.4% between 2011 and 2015 with the highest CPI being estimated as 279.90 in the 4th quarter of the year 2015.

Keywords: ACF, ARIMA, Box and Jenkins, CBN, CPI, PACF

Modelling to Anticipate World Price of Each Ounce of Gold in International Markets (Published)

Any change in sale price may affect customers, distributers and sellers. Anticipating future prices is one of the best ways to face appropriately such these price changes in the market. Time series have wide range of application in various fields such as economy, management and marketing. Time series is a very important tool to analyze a collection of observations which are recorded as daily, weekly, monthly and annually reports. In this paper, the world price of each ounce of gold during 338 continuous months are considered (Average per month) and the target is to assess the behavior of data and to release a suitable model for this data to anticipate world price of each ounce of gold during upcoming months by means of analysis of time series. The first step to analyze time series is to draw data. Next step is to recognize effective parameters on the series (trend, cycle and seasonal) and to remove them from time series and at last to process a static model on time series. We drew autocorrelation function (ACF) and partial autocorrelation function (PACF) for data. Auto-regression model (AR), moving average model (MA) and a combination of AR and MA models (ARIMA, ARMA) were selected as the grade of recognition model and appropriate model. After all stages to analyze time series and creation of remained parameters and after consideration of fitness of represented model, anticipation of world price of gold for each ounce will take place. In this regard, the result of considering the data in this paper produces information for future to make appropriate and profitable decision based on current data. The process is done by means of MINITAB software.

Keywords: ACF, ARIMA, Forecast, PACF, Time Series