The I(2) or mixed of them, which is precondition

The data of most time series
economic variable show a trend and therefore in most cases are non-stationary, it rarely stationary in
level forms. Regression involving non-stationary time series often lead to the
problem of spurious regression. The
other necessary condition for testing unit root test before applying a model is
to check whether the variables enter in the regression are order of  I(0), I(1), I(2) or mixed of them, which is
precondition in model selection. As a result, before running further regression
analysis of the variables, it required to ensure stationary properties of the
variables. It must be transformed to a
stationary series before models are fitted. The unit-root tests
are first performed to examine and observe the stationary properties of the
model variables.

Taking the log of the series
variable may result in stationarity. If the series has a trend over time,
seasonality or some other non-stationarity pattern, the usual solution is to
take the difference of the series from one period to the next period or to
introduce an appropriate explanatory variable if the trend and seasonal effects
are very regular. If the series needs to be differenced at lags greater than
one period in order to have stationarity properties.  At this time, we will have carried out
the Augmented Dickey and Fuller (ADF), and Phillips and Perron (1988) (PP) test
to examine the stationary property of the variables. To ensure reliable result
of test for stationarity, this study employs both Augmented Dickey-Fuller (ADF)
test and Philip-Perron (PP) tests.  The
null hypothesis in these two tests is that there exists Non-stationarity or
unit root in the variable. Additionally, The Augmented Dickey-Fuller (ADF) and
Phillips-Perron (PP) unit root tests use intercept and trend and test for
variables’ stationarity at levels and first differences.

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3.3.1. Augmented Dickey-Fuller (ADF) Test

It is widely used stationarity
test in time series analysis, and was developed from the Dickey-Fuller (DF)
test (Dickey and Fuller, 1979), which directly testing the null
hypothesis of the unit root (non-stationarity). The Dickey-Fuller (DF) test is work
based on autoregressive of order one, AR (1) method with a white-noise error
terms. This indicates DF test regression does not include values of variables more
than one lag, the error terms may be serially correlatedwith further lags. As a
result the results such AF tests may be biased and are not valid (Davidson and
Mackinnon, 1999; Gujarati, 2004; and Kirchgassner and Wolters, 2007). The ADF
test avoids this problem because it corrects for serial correlation by adding
lagged-difference terms (Greene, 2003). The ADF test includes extra lagged
terms of the dependent and independent variables to eliminate autocorrelation. ADF test consists of three different regression
equations to test the presence of a unit root.

The general form ADF equation in which no intercept term and
time trend.

Yt = ?Yt-1+

t-i+1

t………………………………………………………………………

ADF equation with the auto regression includes only intercept

Yt =

0
+ ?Yt-1+

t-i+1

t…………………………………………………………………….

ADF equation, when the auto regression includes the intercept and a
trend, the equation form:

Yt =

0
+ ?Yt-1+

t-i+1

1t  

t……………………………………………………………..3.4

Where
Yt is any variable in the model to be tested for stationarity at time t, ?t
is an error term, t is a time trend variable; ? denotes the first
difference operator and p is the optimal lag length of each
variable chosen such that first-differenced terms make a white noise. In the
above three equations, the null hypothesis of ADF is ?=0 and the alternative is
that ?

x

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