5. RESULTADOS Y DISCUSIONES
5.4. Conversión alimenticia
5.4.2. Conversión alimenticia en la etapa acabado (29 - 42 días)
To investigate the existence of stochastic non-stationary in the time series and ensure that all variables are stationary, which means that they have a constant mean and variance. Therefore, in order to determine the order of integration of the variables, two unit root tests are applied. These are the Augmented Dickey-Fuller (ADF), the Phillip-Peron. The time series are (SSM, DSM and KSM), and the (SABIC, STC, NCCY, Al Rajhi Bank and Electricity company). However, a differencing technique was needed to transform this into a stationary series, because the time series has trending movement and was not stationary in all plots and statistical tests in figure 3.1 taken from chapter 5, so the differenced series was applied to the model. The differenced times series is denoted as follow:
Rt = Pt — Pt-q (6.2.1.1) Therefore, the time series Pt represents the general share index value or share price for today, Pt-q is the previous day of the general index value or the previous share price. When the times series in not stationary or has a unit root the ADF and PP unit root tests give a null hypothesis, but if the series is stationary the hypothesis is the opposite. The ADF and PP test should be significant and show stationary series at the first difference or take the second difference. Thus, the hypothesis for the test is depicted below:
• H0: Variables are not stationary or got unit root • H1: Variables are stationary.
The Augmented Dickey-Fuller (ADF) test results are shown in table 6.1, and the Phillips- Perron. Tests are shown in table 6.2 for the gathered data.
Table 6. 1: First Difference and logarithmic level of ADF, ADF drift and ADF With trend and drift test
ADF ADF drift ADF With trend and drift
Statistics Test Statistic Significan
t level Critical Value Statistic Test Significant level Critical Value Statistic Test Significant level Critical Value
SSM
-29.348*** 1% -3.430 -29.348*** 1% -2.328 -29.344*** 1% -3.960
-lag 2 5% -2.860 Lag2 5% -1.645 Lag2 5% -3.410
- 10% -2.570 - 10% -1.282 - 10% -3.120
DSM
-4.555*** 1% -3.553 -4.555*** 1% -2.378 -4.560*** 1% -4.108
Lag4 5% -2.915 Lag4 5% -1.669 Lag4 5% -3.481
10% -2.592 10% -1.295 10% -3.169
KSM -11.304*** Lag3 1% 5% -3.430 -2.860 11.304*** Lag3 5% 1% -2.333 -1.648 -11.355*** Lag3 5% 1% -3.960 -3.410
- 10% -2.570 - 10% -1.283 - 10% -3.120
SABIC -55.701*** Lag0 1% 5% -3.430 -2.860 -55.701*** Lag0 5% 1% -2.328 -1.645 -20.253*** Lag2 5% 1% -3.960 -3.410
- 10% -2.570 - 10% -1.282 - 10% -3.120
STC -40.069 1% -3.430 -40.069*** 1% -2.328 32.784*** 1% -3.960
Lag1 5% -2.860 Lag3 5% -1.645 Lag2 5% -3.410
- 10% -2.570 - 10% -1.282 10% -3.120
NCCY 29.898*** 1% -3.430 -37.955*** 1% -2.328 -26.847*** 1% -3.960
Lag2 5% -2.860 Lag1 5% -1.645 Lag3 5% -3.410
- 10% -2.570 - 10% -1.282 10% -3.120
Al-Rajhi bank
-30.570*** 1% -3.430 -30.570*** 1% -2.328 -26.666*** 1% -3.960
Lag2 5% -2.860 Lag2 5% -1.645 Lag3 5% -3.410
- 10% -2.570 - 10% -1.282 10% -3.120
Electricity company
-26.246*** 1% -3.430 -26.246*** 1% -2.328 26.286*** 1% -3.960
Lag3 5% -2.860 Lag3 5% -1.645 Lag3 5% -3.410
- 10% -2.570 - 10% -1.282 10% -3.120
Note: Numbers in parentheses corresponding to ADF test statistics are the optimal lags, chosen based on Akaike Information Criterion (AIC).
*, **, *** denote the rejection of the null hypothesis of a unit root at 10%, 5% and 1% respectively Source: Author’s calculation
The table (6-1) show the result of the ADF test for the log levels and first difference for the time series SSM, DSM and KSM as general index, and SABIC, NCCY, STC, Alrajhi Bank and Electricity Company as individual companies.
The results for Saudi Dubai and Kuwait stock market indicate that all the series are of integrated order one I (1). That is all the series are stationary at first difference due to the test statistic being larger than the critical value at the 1% level of significance. For example, Saudi stock market with a Statistic of (-29.348) is greater than the Critical Value of (-3.430) at significant 1% level.
The results for the individual companies (SABIC, NCCY, STC, Alrajhi Bank and Electricity Company as individual companies) reveal that the null hypothesis can be rejected for the unit root and accepted for the alternative hypotheses at a significance level of 1% for all the variables, because at 1%, 5% and 10% levels, t-statistics values are more negative than ADF critical values. For example, SABIC approximate critical value is (-3.430) and the test statistic is (-55.701) so the researcher would reject the null hypothesis and accept the alternative hypothesis.
Table 6. 2: First Difference at logarithmic level of test PP, PP drift and PP With trend and drift
PP PP with Drift PP with drift and trend
Statistics Test
Statistic Significant level Critical Value Statistic Test Significant level Critical Value Test Statistic Significant level Critical Value
PP PP drift PP With trend
SSM
-29.348*** 1% -3.430 -29.348*** 1% -2.328 -29.344*** 1% -3.960
-lag 2 5% -2.860 Lag2 5% -1.645 Lag2 5% -3.410
- 10% -2.570 - 10% -1.282 - 10% -3.120
DSM
-4.555*** 1% -3.553 -4.555*** 1% -2.378 -4.560*** 1% -4.108
Lag4 5% -2.915 Lag4 5% -1.669 Lag4 5% -3.481
10% -2.592 10% -1.295 10% -3.169
KSM -11.304*** Lag3 1% 5% -3.430 -2.860 11.304*** Lag3 5% 1% -2.333 -1.648 -11.355*** Lag3 5% 1% -3.960 -3.410
- 10% -2.570 - 10% -1.283 - 10% -3.120
SABIC -55.701*** Lag0 1% 5% -3.430 -2.860 -55.701*** Lag0 5% 1% -2.328 -1.645 -20.253*** Lag2 5% 1% -3.960 -3.410
- 10% -2.570 - 10% -1.282 - 10% -3.120
STC -40.069 Lag1 1% 5% -3.430 -2.860 -40.069*** Lag1 5% 1% -2.328 -1.645 32.784*** Lag2 5% 1% -3.960 -3.410
10% -2.570 10% -1.282 10% -3.120
NCCY 29.898*** Lag2 1% 5% -3.430 -2.860 -37.955*** Lag1 5% 1% -2.328 -1.645 -26.847*** Lag3 5% 1% -3.960 -3.410
10% -2.570 10% -1.282 10% -3.120
Al-Rajhi bank
-30.570*** 1% -3.430 -30.570*** 1% -2.328 -26.666*** 1% -3.960
Lag2 5% -2.860 Lag2 5% -1.645 Lag3 5% -3.410
10% -2.570 10% -1.282 10% -3.120
Electricity company
-26.246*** 1% -3.430 -26.246*** 1% -2.328 26.286*** 1% -3.960
Lag3 5% -2.860 Lag3 5% -1.645 Lag3 5% -3.410
10% -2.570 10% -1.282 10% -3.120
Note: Numbers in parentheses corresponding to PP test statistics are the optimal lags, chosen based on Akaike Information Criterion (AIC).
*, ** and *** *, imply 10%, 5% and 1% levels of significance respectively. Source: Author’s own calculations
The table (6-2) present the result of the PP test for the log levels and first difference for the time series (SSM, DSM and KSM), and (SABIC, NCCY, STC, Alrajhi Bank and Electricity Company).
The PP unit root test for all selected capital markets and individual companies, and the result are reported in table 6-2. It is clear that, the null hypothesis of unit root (non-stationary) is rejected, as the value of test statistic is more negative than the critical value in each country and individual company’s case. Thus, the result indicate that the capital markets and the stock price in select companies and developing markets do not follow random walk hence, market are not weak-form efficient.
The results for SSM, DSM and KSM, and SABIC, NCCY, STC, Alrajhi Bank and Electricity Company as individual companies indicated to be stationary after taking the first difference at log level. The result goes into the negative direction, the basic logic is to reject the null hypothesis if the test statistic is sufficiently extreme. For example, Al-Rajhi bank at (significant level 10%, critical value -2.570) is larger and more positive than (5% significant level and critical value at -2.860) and 1% critical value more extreme than 5% and is lower at (-3.430). However, the actual test statistic is (-30.570), this is an extreme than the conventional 1% value and even the 5% and 10% value because it is more negative than -3.430 (and even - 2.860 and -2.570. Therefore, the researcher does reject the null hypothesis of unit root at 1% significance levels.
The results confirmed that all the time series for the period 2005-2016 are of integrated order one I (1). That is all the series are non-stationary after taking into account that the first difference of time series are stationary. Therefore, the first difference time series passes the Phillips-Perron PP test and Augmented Dickey-Fuller ADF test with 99% confidence, has an approximate constant variance and a constant mean.