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Page 1 of 6

Journal for Studies in Management and Planning

Available at http://internationaljournalofresearch.org/index.php/JSMaP

e-ISSN: 2395-0463

Volume 01 Issue 02

March 2015

P a g e | 230 Available online: http://internationaljournalofresearch.org/

Forecast of Adult Literacy in Sudan

Dr. Elfarazdag Mahjoub Mohammed Hussein,

Department of Statistics-Faculty of Science-Tabuk University (KSA), Sudan

Abstract:

The main objective of this paper is to

find out a time series model to monitor

and forecast the Adult Literacy rate in

Sudan. To achieve this objective, a

series of Adult Literacy ranged from

1990 to 2009 was obtained from the

Sudan Central Bureau of statistics and

United Nation Annual Reports, time

series analysis technique mainly box

and Jenkins were used to find the

required model .Analysis done by e- views package. The paper conclude

that The most proper time series

model to forecast the Adult Literacy

rate in Sudan is the ARIMA model,

The general trend of Adult Literacy is

an increasing trend with annual

increase Less than 3%.

Keywords: Adult Literacy, box and

Jenkins, auto regressive moving average,

Sudan.

Literacy is typically described as the ability to

read and write. It is a concept claimed and

defined by a range of different theoretical

fields. The United Nations Educational,

Scientific and Cultural Organization

(UNESCO) provides a useful and reasonably

definition of literacy, it is defined as the

"ability to identify, understand, interpret,

create, communicate, compute and use printed

and written materials associated with varying

contexts. Literacy involves a continuum of

learning in enabling individuals to achieve

their goals, to develop their knowledge and

potential, and to participate fully in their

community and wider society."

The aim of the study is to find out a time series

model based on annual basis for the Adult

Literacy rate in Sudan for the period 1990-

2009.

The importance of this study concentrated at

the serious need of constructing a time series

model for the future forecast to detect the

pattern of change in Adult Literacy which

helps for the future planning.

The used Adult literacy data was compiled

from the annual United Nations Development

Program Reports starting from 1990 up to 2009

will be used.

2. Theoretical framework

Time series analysis techniques, namely Box

and Jenkins technique was used, the series

extends over the period 1990-2013, which is

fairly long; Autoregressive Integrated Moving

Average (ARIMA) was chose for the analysis.

2.1 Time Series Components

Time series consists of several components,

which are:

(A) Trend

(B) Cyclical Variations.

(D) Irregular fluctuations.

2.2 Time Series Decomposition Model

If a time series exhibits trend effects and

seasonal effects, it can be useful to decompose

it in order to isolate these effects. One model

that allows us to do this is the multiplicative

decomposition model, it’s the most popular

decomposition model, and it’s expressed as

Page 2 of 6

Journal for Studies in Management and Planning

Available at http://internationaljournalofresearch.org/index.php/JSMaP

e-ISSN: 2395-0463

Volume 01 Issue 02

March 2015

P a g e | 231 Available online: http://internationaljournalofresearch.org/

follows:

t t t t t Y = T * S * C * I

Also there is decomposition model known as

the additive model, which expressed as

follows:

t t t t t Y = T + S + C + I

Where:

Yt: The observed value of the time series in

time period t.

Tt: The trend components in time period t.

St: The seasonal components in time period t.

Ct: The cyclical components in time period t.

It: The erratic components in time period t.

2. 3 Forecasting Methods

There are many forecasting methods that can

be divided into two basic types which are:

(A) Qualitative Forecasting Methods

Qualitative forecasting methods generally use

the opinion of the expert to subjectively predict

future events.

(B) Quantitative Forecasting Methods

Quantitative forecasting models are grouped

into two main models, which are:

(I) Univariate Models

Univariate models predict the future events of

time series on the basis of the past values of the

time series (Powerman, 1979) .When a

univariate model is used; historical data are

analyzed in an attempt to identify a data

pattern, then assuming that it will continue in

the future. Univariate forecasting models are

most useful when conditions are expected to

remain the same.

(II) Causal Models

The use of such models involves the

identification of other variables that are related

to the variable to be predicted, once these

related variables have been identified, a

statistical model that describes the

relationships between these variables and the

variable to be forecasted is developed. The

statistical relationship derived is then used for

forecasting the variable of interest.

Generally we can say that quantitative

forecasting methods are used when historical

data are available univariate models predict

future values of the variable of interest on the

basis of historical pattern of that variable,

assuming the historical pattern will continue;

causal models predict future values of the

variable of interest based on the relation

between that variable and other variables.

Qualitative forecasting techniques are used

when historical data are scarce or not available

at all and depend on the opinions of experts

2.4 Choosing the Forecast Technique

In choosing the forecasting technique the

forecaster must consider the following factors

1. The nature of the study variable.

2. The time frame.

3. The pattern of data.

4. The cost of forecasting.

5. The accuracy desired.

6. The availability of data.

7. The ease of operation and understanding.

The first factor to be considered in choosing a

forecasting method is the form in which the

forecast is desired i.e. determine whether the

forecaster will use point or interval forecast.

The second factor that can influence the choice

of forecasting method is the time frame of the

forecasting situation. Forecast are generated for

point in time may be a number of days , weeks,

months, quarters or years in the future. This

Page 3 of 6

Journal for Studies in Management and Planning

Available at http://internationaljournalofresearch.org/index.php/JSMaP

e-ISSN: 2395-0463

Volume 01 Issue 02

March 2015

P a g e | 232 Available online: http://internationaljournalofresearch.org/

length of time is called the time frame; the

length of the time frame is usually categorized

as follows:

1. Immediate less than month.

2. Short term more than three months to less

than two years.

3. Long term two years or more.

The length of the time frame influence the

choice of forecasting technique, typically a

longer time frame makes accurate forecasting

more difficult.

The pattern of data must also be considered

when choosing forecasting model. Thus, it is

important to identify the existing data pattern.

One of the most important factor that affect the

choice of forecasting technique is the desired

accuracy of the forecast, the availability of

information and last the ease with which the

forecasting method is operated and understood

is important.

2.5 The Box-Jenkins Methodology

This methodology developed by G. E. P. Box

and G. M. Jenkins, consists of four basic steps.

The first step, called tentative identification

step, involves tentatively identifying a model.

Once a model has been identified, we estimate

the model parameters in the second step that

called the estimation step. The third step is

called the diagnostic checking step, here we

check the adequacy of the model, if the model

proves to be inadequate, it must be modified.

When a final model is determined, we use the

model to forecast future time series values; this

fourth step is called the forecasting step.

There are many Box-Jenkins models; these

models can be grouped into the following three

basic classes:

(A) Autoregressive models.

(B) Moving average models.

models.

Box-Jenkins models are often called ARIMA

models [Autoregressive Integrated Moving

Average]. The Univariate Box – Jenkins

models have proven to provide accurate

forecast in short term forecasting applications.

2.6 Stationary and Non-Stationary Time

Series

The classical Box – Jenkins models describe

stationary time series, thus in order to

tentatively identify a Box – Jenkins models, we

must first determine whether or not a time

series under investigation is stationary, if it is

not, we must transform it into a series of

stationary time series values either by using the

log or the reciprocal. A time series is said to be

stationary if the statistical properties such as

mean and variance of time series are constant

through time , if we have observed n values y1,

y2, y3, ...., yn , of a time series, we can use a

plot of these values against time to help us to

determine whether the time series is stationary

or not. If the n values seem to fluctuate with

constant variation around a constant mean,

then it is reasonable to believe that the time

series is stationary, if the n values do not

fluctuate with constant variation, then it is

reasonable to believe that the time series is no

stationary. If we decided that the time series is

not stationary we can transform it from non- stationary to stationary by taking the first

differences of the non-stationary time series.

2.7Unit Root Test -Augmented Dickey- Fuller (DF) Test

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