Tag Archives: Time Series

Application of Cube Root Transformation of Error Component of Multiplicative Time Series Model (Published)

This paper makes use of cube transformation of the error component of multiplicative time series model. Data from federal road safety commission (FRSC) Nigeria on road accident were collected and analyzed by fitting the regression line of log mean (logmean) against log standard deviation (logstdev). This gave a fitted slope  which agrees with the required value of 0.6666 this gives a transformation of 1-0.666977= 0.333023 (1- which is the cube root transformation.  Data were later decomposed into time series components.  Recommendations on areas of application of cube root transformation were equally given.

Keywords: Components, Cube Transformation, Logmean, Multiplicative, Time Series

The Effect of Fiscal Policy on Financial Sector Development in Sierra Leone: A Time Series Approach (Published)

This study investigates fiscal policy impact on financial sector development in Sierra Leone between 1980 and 2015. The objective of the study is to establish the long run relationship between fiscal policy variable and financial sector development.  The study used a quantitative approach; the model was formulated with Private sector credit used as a proxy variable for financial sector development.  This was regressed against gross domestic product, money supply, real interest rates, inflation and total tax revenue.  The study used error correction model to estimate both long term and short term effects of the explanatory variables on the dependent variables in the empirical functions.  The unit root tests shows that variables in the equations were I(1) variables, meaning they were stationed at first difference using both the Augmented Dickey Fuller  and Philip Pheron tests. The Johansson co integration tests concludes that there are more than one co-integrating factors in each empirical function, therefore a long run relationship exists between private sector credit and its explanatory variables.   To validate the quality of the data for the use of vector auto regression, all of the tests were conducted including; lag length criteria test, serial correlation test, normality test, stability test.  The result from the private sector credit and fiscal and non-fiscal variables in Sierra Leone contradicts most of the theoretical and empirical literature on financial sector development. The conclusion is that even when we are expecting a negative relationship between private sector credit and money supply, real interest rates, total tax revenue and inflation, the results all came out positively and significantly in long run financial economic analysis.  This study shows that the private sector is willing to borrow regardless of the interest rate in the economy and the level of taxation.  Basically the risk appetite in the private sector shows the level of desperation of private institution to access short to medium term capital.  This might explain the reason for the high non-performing loans (NPL) in the economy of Sierra Leone.

Keywords: Fiscal Policy, Sierra Leone, Time Series, financial policies

Autoregressive Integrated Moving Average (Arima) Model for the Major Airline Disasters in the World from 1960 Through 2013 (Published)

This research fit a univariate time series model to the major Airline Disasters in the world from 1960 through 2013. The Box-Jenkins Autoregressive Integrated Moving Average (ARIMA) model was estimated and the best fitting ARIMA model was used to obtain the post-sample forecasts for five years. The fitted model was ARIMA (0,1,1) with Akaike Information Criteria (AIC) of 323.14, Normalized Bayesian Information Criteria (BIC) of 327.04, Stationary R2 of 0.348.This model was further validated by Ljung-Box test with no significant Autocorrelation between the residuals at different lag times and subsequently by white noise of residuals from the diagnostic checks performed which clearly portray randomness of the standard error of the residuals, no significant spike in the residual plots of ACF and PACF. The forecasts value indicates that Airline Disasters will increase slightly with almost equal number of cases for the next five years (2014-2018).

Keywords: ARIMA, Airline Disasters, Box- Jenkins, Forecast, Ljung-Box, Stationarity, Time Series, Unit Root

Statistical Analysis of Non-Communicable Diseases in a Health Facility in Takoradi, Ghana (Published)

Current trends indicate that global Non-Communicable Diseases (NCD) accounts for about 60% of deaths and will increase by 17% over the next 10 years with poor and disadvantaged populations disproportionately affected, widening health disparities between and within countries. It is against these challenges that “Statistical Analysis of Non-Communicable diseases” was undertaken. The main objective of this paper was to determine the age groups that are affected most and also to determine the trend of each of the selected Non-Communicable Diseases. To achieve this, a five-year data set was collected from Takoradi Hospital. Results of the analysis of the data depict that, females dominate those who are suffering from Non-Communicable Diseases. Also, people within 20 to 34 year group are mostly affected by Non-Communicable Diseases. It also reveals that the number of cases of the Non-Communicable Diseases analyzed have declining trend with the exception of anemia. It was therefore recommended that, people from all walks of life must give due consideration to their diet and thus eat balanced diet and do regular exercise to keep them healthy.

Keywords: Forecast, Health Facility, Non-Communicable Disease, Takoradi-Ghana., Time Series

On The Tractability of Some Discordancy Statistics for Modelling Outliers in a Univariate Time Series (Published)

This paper compares the tractability of four discordancy statistics for modelling outliers based on extremeness. They are: the Generlaized Extreme Studentized Deviate (ESD), Grubb’s test, Hampel’s method and the quartile method. The last two methods are seen to detect outliers even for datasets that are not approximately normal, although Hampel outperforms the quartile method in some cases. However, a multiplier effect of 2.2 is proposed for the quartile method in addition to the robust statistics for accommodating the outliers.

Keywords: Autocorrelation function (ACF)., Generalized Extreme Studentized Deviate (ESD), Outliers, Time Series


Motor accident is a major cause of mortality and disability in Nigeria, which
explains the reason for the establishment of Federal Road Safety Commission in 1988 to address
the carnage and maiming on the highways and roads. This paper employed Time Series statistical
tools to build model, and examine seasonality pattern of the number of cases of motor accident
recorded at the Federal Road Safety Commission, Osun Sector command using secondary data
collected from the record section of the command from 2006 to 2012. Autoregressive Integrated
Moving Average (ARIMA) depicts reduction in the recorded number of cases recorded. This result
was corroborated by Least Squares trend with quarterly decline of six (6) cases of motor accident.
The seasonal pattern clearly portrayed quarter four (October, November, and December) as the
season with high prevalence of motor accident. It was finally concluded that the Federal Road
Safety Commission has been performing to expectation in the manner it discharges her duties by
adjuring from the results of the analyses

Keywords: Model, Time Series, Trend, accident, road safety, seasonal

Effects of Exchange Rate Liberalization on French Beans Exports in Kenya (Review Completed - Accepted)

The exports of French beans are one of the leading contributors to foreign exchange earnings in Kenya. Nevertheless, the economic impacts of exchange rate liberalization on French beans exports in Kenya are unclear. The purpose of this paper is to evaluate the magnitude and direction of the effects of exchange rate liberalization on French beans exports from Kenya to its major trading partners in the European Union. Monthly data for a fixed exchange regime represented by the period from 1990- 1993 and a flexible regime represented by the period from 1994-2011 was used in the estimation of an export demand model. The empirical results show that the liberalization of the exchange rate led to an increase in the French beans export volumes from Kenya to the European Union. The paper recommends maintenance of a competitive exchange rate and export promotion in order to boost Kenya’s French beans exports.

Keywords: Exchange Rate, Exports, Liberalization, Time Series

Informality and Domestic Savings in Nigeria: Lessons from Time Series Analysis (Published)

Following the dearth of empirical evidence on the response of domestic savings to informality in Nigeria, this study examined the impact of informality on domestic savings in Nigeria for the period 1970 to 2011 as a means of providing evidence based policies that will enhance the growth and development of the Nigerian economy. The study employed time series analysis using the OLS estimation procedure. The estimation results of the long run model indicate that informality hinders the growth of domestic savings, while the degree of financial depth impacts significantly and positively on domestic savings in Nigeria. It was also found that the growth rate of real per capita income impacts positively on domestic savings, even though it is not statistically significant in the long run. Based on these findings, we recommended that policy makers and the government should seek to improve the linkage between the formal and informal sectors in Nigeria as this would have a strong positive impact on domestic savings. Deposit money banks and the monetary authority should evolve policies aimed at reaching the unbanked informal sector agents, especially the rural households and the urban informal production units in order to deepen the financial sector and assist in mobilizing the much needed savings that will engender investment and growth in Nigeria. Also, development policy in Nigeria should focus on increasing the productive base of the economy in order to promote real income per capita growth and reduce unemployment.

Keywords: CBN, Domestic Savings, Informality, Nigeria, Time Series

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