INTERNATIONAL JOURNAL OF SCIENTIFIC & TECHNOLOGY RESEARCH VOLUME 2, ISSUE 6, JUNE 2013 ISSN 2277-8616
177
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Multivariate Jackknife Delete-5 Algorithm On The
Effect Of Nigeria Foreign Trade On Foreign
Exchange Rates Of Naira (1960-2010).
Obiora-Ilouno H. O., Mbegbu J. I.
Abstract: In this paper we presented the multivariate extension of multiple linear regression using Jackknife techniques in modeling the relationship
between m set of responses
1 2
, , ,
m
YY Y and a single set of r regressors
1 2
, , ,
m
Z Z Z . The responses are Oil Import
1
( ), Y Non-Oil Import
2
( ), Y Oil Export
3
( ), Y Non-Oil Export
4
( ) Y which is classified as Nigeria Foreign Trade, while the regressors are Exchange Rate of US Dollar
1
( ), Z and Exchange Rate of Pounds sterling’s
2
( ) Z which are classified as Foreign Exchange Rate. We proposed new algorithm for estimating the
parameters of multivariate linear regression using the jackknife technique. The results obtained using Jackknife delete-5 algorithm competes favorably
with the existing methods. Consequently Time Series approach was adopted for future prediction of the Nigeria Foreign Trade from year 2011 to 2020.
Evidently, the time series plot depicts an increase of exchange rate of US Dollar and Pounds Sterling over the years under consideration. Thus, this will
definitely affect Nigeria Foreign Trade negatively which could be harmful to the Nigeria’s economy.
Keywords: multivariate, Jackknife, delete-5, foreign trade, foreign exchange rate, linear regression.
————————————————————
Introduction:
Adebiyi et al [1] estimated the effects of oil price stocks and
exchange rate on the real stock returns in Nigeria over
1985-2008 using a multivariate VAR analysis. Variables
ranging from real oil prices, real stock returns, and index of
industrial production to three types of oil specifications were
employed. Also, the study further classified oil price stocks
into sub-samples: for a first subsample (1985-1999), for a
second sub-sample (2000-2004) and for a third sub-sample
(2005-2008). Empirical results showed an immediate and
significant negative real stock return on oil price stock in
Nigeria. The Granger causality test employed indicated that
causation run from oil price stocks to stock returns, implying
that variation in stock market is explained by oil price
volatility. [6] proposed functional multivariate regression
modeling by estimating the model using a regularized
maximum likelihood method. This paper presents a
multivariate jackknife delete-5 algorithm on the effect of
foreign trade on foreign exchange rates of naira (1960-
2010).
1.0 MATERIALS AND METHODS
1.1 General form of Multivariate Linear Regression
Model
According to [5], multivariate linear regression model
defines the relationship between m responses
1 2
, , ,
m
YY Y and a single set of r predictors,
1 2
, , , .
r
Z Z Z
1 01 11 1 21 2 1 1
2 02 12 1 22 2 2 2
0 1 1 2 2
(1)
r r
r r
m m m m rm r r
Y Z Z Z
Y Z Z Z
Y Z Z Z
The expectation and variance of error term
are
1
2
()
m
E E
and
2
Var
respectively.
Let
0 1
, , ,
j j jr
Z Z Z
denote the values of the predictor
variables for the
th
j trial. Let
'
1 2
, , ,
j j j jm
Y Y Y Y
be
the responses, let
1 2
, ,
j j jm
be the errors for
th
j
trial Thus we have ( 1) n r design matrix
______________________
Obiora-Ilouno H. O., Mbegbu J. I.
Nnamdi Azikiwe University, Awka, Nigeria,
e-mail: obiorallouaoho@yahoo.com ,
Phone no: +2348060518823
Department of Mathematics , University of Benin,
Benin City, Edo State, Nigeria.
e-mail: julian.mbegbu@yahoo.com
Phone no: +2348020740989
Corresponding author,
e-mail: obiorallouaoho@yahoo.com