Unit Root Tests

Due to the stochastic nature of time series variables (i.e. the tendencies of the mean of the series to oscillate in a seemingly unpredictable “random

68 The cointegration test adopted for the purpose of this study is Johansen (1988) cointegration test.

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walk” over time (Dougherty, 1992), the use of a unit root test becomes inevitable within the context of the theory of unit-root econometrics (Asteriou and Hall, 2007). As a condition for a univariate analysis, a series must be stationary⁶⁹ for unique dynamics to be properly explored. Unit root test is carried out on each of the included variables in VAR for any joint significance tests to be observed on the lags of such variables (Brooks, 2008). In the event a non-stationary series (i.e. with the presence of unit roots) exists, the outcome from ordinary classical regression analysis will remain invalid, therefore resulting in “spurious regressions”⁷⁰ (Asteriou and Hall, 2007;

Brooks, 2008). As part of the tests on the properties of time series, a unit root test is carried out in order to establish stationarity or non-stationarity in the series (Brooks, 2008; Asteriou and Hall, 2007). Therefore, the null hypothesis test is carried out to establish whether each series is integrated of order one (i.e. Yt= I(1)) which simply implies that there is a presence of a unit root in each of the series.

Furthermore, Brooks (2008) noted two major important reasons why the stationarity checks should be carried out on a series: First, there is a clear distinction on the effect of ‘shocks’ between stationary and non-stationary data. Whereas in stationary series, ‘shocks’ during time t will continue to have a reduced effect as time changes from one period to another (t to t + 1, and from t + 1 to t + 2, and so on); but the persistence of the shocks in non-stationary series moves towards infinity, which interprets that the ‘shocks’ in period t will not have a lower effect in t + 1, and subsequent t + 2 and so on.

Second, relates much to the fear of spurious regressions as a result of applying classical regressions to non-stationary data, which might produce a very high R2 and significant coefficient estimates, therefore producing invalid results.

Therefore, depending on “the order of integration of a series”⁷¹, various tests are applicable in the course of examining stability in the series in relation to

69 Stationary series is such series “...with a constant mean, constant variance and constant autocovariances for each given lag.” (see, Brooks, 2008).

70 Spurious regression is such which employs classical regression analysis on series that appears to be non-stationary, therefore producing invalid results (Asteriou and Hall, 2007).

71 According to Asteriou and Hall (2007), “the order of integration of a series” is assumed as a general rule to be the size a series is differenced for it to become a stationary one. In this regard, it is similar to the number of unit roots.

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constant mean and variance (popularly known as ‘stationary series’). A series Yt integrated of order d is denoted by Yt = I(d). Therefore, a series with unit-root problem, which is integrated of order 1 [i.e. denoted I(1)], can be filtered at a first-difference (i.e. (∆𝑌_𝑡= 𝑌_𝑡− 𝑌_𝑡−1) to generate a stationary series with a constant mean and variance. This is one of the crucial property test for time series model such as VAR to be estimated. The various approaches to investigating stationarity properties (i.e. performing the unit-root tests) include Augmented Dickey-Fuller (ADF); Dickey-Fuller GLS (ERS);

Phillips-Perron (PP); Kwiatkowski-Phillips-Schmidt-Shin (KPSS); Elliot-Rthenberg-Stock Point-Optimal (ERSO); and Ng-Perron (NP) test. However, the most famous among them are usually two (i.e. the Augmented Dickey-Fuller (ADF), the Phillips-Perron) which have enjoyed widespread application⁷² in the fields of Economics, Accounting and Finance.

Similarly, in line with the previous studies’ practices, this study employs Augmented Dickey and Fuller and Phillips and Perron for unit roots tests in an effort to ensure consistency and allow for comparison with the previous studies. Furthermore, it allows for comparison between parametric and non-parametric tools in time series analysis and other various unit – root tests⁷³. 5.5.3.5 Cointegration Tests

Cointegration,⁷⁴ being a statistical tool through which co-movement of non-stationary economic variables or series can be described, has been employed in the previous literature to test long term relationships between variables in Accounting, Finance and Economics disciplines most particularly where oil prices are involved. For example, cointegration was used to test long run relationship between oil prices and global economic activity (Lardic and Mignon, 2008; He et al., 2010), other commodity prices such as gold (Zhang and Wei, 2010), evidence of collusion and cartel behaviour (Gülen, 1996).

Two or more non-stationary time series data are considered to be cointegrated “if a linear combination of the terms results in a stationary time

72 Some of the studies that employ or propagate the popularity of the two tests include but not limited to the followings: Zuniga (2005); Asteriou and Hall (2007); Farzanegan (2011); Brooks (2008);

73 For further references about the tests, refer to Gülen (1996), Zuniga (2005).

74 This is a process through which long-run comovement of non-stationary variables are evaluated and described. It has been used in many OPEC studies (see Gülen, 1996; Kaufmann et al., 2004).

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series” (Zuniga, 2005). It is important to note that for cointegration to take effect, all the included variables in VAR models must be of the same order of integration. Evidence of cointegration between variables has been interpreted as presence of long run relationship which enables the estimation of VECM (see Gülen, 1996).

A number of approaches are available in the economic literature which includes: Engle-Granger (Engle and Granger, 1987) two-step test, the Johansen cointegration test and Phillips-Ouliaris cointegration test. However, despite the shortcomings of each of the approaches, the most popular one in social sciences⁷⁵ is the one developed by Johansen (1988). Johansen’s system cointegration method introduces two tests statistics, namely the Trace and Lambda Max tests. The null hypothesis usually states there is no cointegrating equation in the system. Under both trace and Max statistics, the null hypothesis can be rejected or fail to reject on two bases, namely: excess of the trace or Max statistics over the critical values or simply the significance level. In view of the fact that evidence of cointegration might suggest application of the vector error correction models (VECM), the long run dynamics existing within the variables might be observed subject to any restriction in the model.