This paper explores the stationarity of price movements, dividend yields, and earnings yields for stock market indices and individual stocks within the broader context of the random walk hypothesis. This argument supporting the random walk hypothesis is supported by many economic researchers and financial economists. The absence of unit roots implies that the series are stationary, leading to the inference of probability of asset price predictability and therefore weaker support for the random walk hypothesis.
After obtaining consistent results from their series of tests, Tas and Dursunoglu decisively reject the random walk hypothesis for the ISE. Many of the aforementioned studies rely on unit root tests (with small deviations) to determine whether the used macroeconomic and/or financial data follow a random walk.
Identifying the Presence of Unit Roots in Global Market Indices
The unit root test will be used to determine whether the panel of underlying stocks that make up each index has a unit root. As shown in the table above, for all investigated stock indices excluding the Dow Jones Industrial Average, the null hypothesis cannot be rejected at the 10% critical value level. Having a unit root implies non-stationarity, which leads to the preliminary conclusion that these indices behave like a random walk.
However, this test says little to nothing about the stationarity of the indices' underlying components or the stationarity of the panel of underlying components. The DJIA is the lone index for which one can reject the null hypothesis at the 5% critical value level. This means that according to the data collected and can be confirmed at the 5% level, the DJIA time series does not possess a unit root.
Therefore, it follows that it is likely that the closing values of the DJIA do have a stationary relationship over the period for which the data is collected. While it would be presumptuous to automatically conclude from this test that the movements of the DJIA over time do not follow a random walk, it provides an interesting. Reasons that could potentially lead to false conclusions include the relatively smaller size of the DJIA in terms of components compared to many of the other indices, the specific data set used in my particular investigation, and the imperfect correlation between stationarity and randomness .
Compared to the other data sets for which the presence of unit roots has been tested, the DJIA data set is the most comprehensive, going back to 1928.
The Stationarity of Stock Prices 1. The Dow Jones Industrial Average
However, when the aggregated conclusions of the unit root tests are presented graphically rather than numerically, a compelling story emerges. In order to reject the null hypothesis at least at the 10% critical value level, the test statistic of the ADF tests must be at least less than -3.12 and at most less than -3.151. The results of each of the individual root tests of the ADF units are summarized in Figure 4.1.1.
Each test statistic is listed in the appropriate range; intervals are listed in increments of 0.1. The red line in the plot above marks the range -3.12 to -3.151 below which the test statistic from each ADF test must fall in order to reject the null hypothesis at the 10% critical value level. As can be seen in the figure, most of the components of the DJIA can be shown not to have a unit root at various confidence levels.
To be specific, between 53 and 57% of the test results show a rejection of the null hypothesis of the ADF test at least at the 10% level.
Statistic Distribution of DJIA Augmented Dickey-Fuller Unit Root Tests on Individual Components
We can reject the null hypothesis of the Im-Pesaran-Shin unit root test, which states that all panels have unit roots. In addition, the null hypotheses of the Breitung and Levin-Lin-Chu unit root tests, which also state that all series contain unit roots, can be rejected. This result is also consistent with previous test results that showed variability in the ability to reject the null hypothesis of the unit root test.
It is important to note that one of the assumptions inherent in ADF unit root tests is that the time series exhibit stability. Regarding this, the issue is where the strength of the panel unit root test lies. Therefore, to take advantage of the strength of the panel unit root test versus the individual ADF unit root test, it is useful to examine its results over short time periods, i.e.
Following the same process as examining the Dow, ADF unit root tests were performed individually on each of the 500 components of the S&P 500 index. However, it is important to note the overall trend of the results found from these tests. The red line approximates the -3.12 to -3.24 range, the comprehensive range below which the null hypothesis of the ADF unit root test can be rejected at least at the 10% critical value level.
In contrast to the results obtained from the data used for the components of the.
Statistic Distribution of S&P 500 Augmented Dickey-Fuller Unit Root Tests on Individual Components
The Stationarity of Dividend Yields
Based on John Cochrane's studies in “Permanent and Transitory Components of GNP and Stock Price,” this study continues by analyzing the stationarity of the relationship between dividends and stock prices for the components of the DJIA and the S&P 500. Although preliminary results to Given the conclusion that the DJIA's price movements are potentially stationary while those of the S&P 500 are most likely non-stationary, many believe in the likely non-stationarity of stock prices in general. To test the stationarity of the dividend yields of the underlying components of the DJIA and the S&P 500, the ADF unit root test is further used.
These tests regress the logarithm of the ratio of the sum of the dividends in the given half-year period to the closing price at the beginning of the half-year period, as a percentage, on time. Unlike the study of price stationarity, panel unit root tests are not performed on dividend yields. This is because the length of the majority of yield datasets is insufficient to.
Due to the variability in the results of the ADF unit root tests on the dividend yields of the underlying components of the DJIA, it is useful to graph the aggregated results in Figure 5.1.1, which shows the distribution of the test statistics of the twenty-nine ADF tests grouped into 0.119 increments. As can be visually concluded from the graph, it appears that a minority of dividend yields reject the null hypothesis that the time series has a unit root. In particular, the dividend yields of three companies, or about 10.34% of the evaluated companies, do not have unit roots and thus exhibit stationary behavior.
Due to data limitations, the results of the ADF tests on the dividend yields of 382 of the 500 companies that make up the S&P 500 index are shown in the same way as Figure 5.1.1 in Figure 5.2.1 below.
The Stationarity of Earnings Yields
Statistic Distribution of S&P 500 Augmented Dickey-Fuller Unit Root Tests on Dividend Yields for Individual Components
To compare the results of the ADF tests on earnings yields with those on dividend yields, panel unit root tests are not performed. The red line approximates the range of -2.604 to -2.63, within or below which the test statistic must fall to lead to rejection of the null hypothesis that the time series possesses a unit root with a critical value level of at least 10%. The results show that for the DJIA, a much higher percentage of corporate earnings yields compared to dividend yields behave stationary.
Statistic Distribution of DJIA Augmented Dickey-Fuller Unit Root Tests on Earnings Yields for Individual Components
Conclusion
It can be concluded that the price movements of the Dow Jones Industrial Average are generally more stationary than the S&P 500 index in recent history. This difference in behavior is likely to be largely due to the relatively high level of corporate synchronicity in the components underlying the DJIA. Interpreting the results of the ADF unit root tests on dividend yields for the companies underlying the DJIA and S&P 500 does not lead to the conclusion that dividend yields are stationary, contrary to my preliminary hypothesis and previous studies using older data.
Only about 10% of the companies comprising the DJIA were shown to reject the null hypothesis of the unit root test and therefore do not have unit roots for dividend-price ratios. In addition, it was found that only 5-10% more of the companies comprising the S&P 500 rejected the null hypothesis of the unit root test for dividend data than for price data. Instead of paying dividends to investors, growth stocks typically prefer to reinvest retained earnings in projects that contribute to the company's.
Finally, based on the results from ADF's tests of earnings yields for DJIA components, it can be concluded that earnings yields are likely to be a more stationary process than dividend yields. Although this segment of the investigation was conducted only for companies within the DJIA, judging by the relatively similar null hypothesis rejection rates of the ADF unit root test of dividend yields for the DJIA and the S&P 500 when compared to the rejection rates The null hypothesis of the ADF test for prices can be assumed to be the same for earnings yields on the S&P 500. As a result, due to the significantly higher proportion of fixed income yields , it may make more sense for financial data analysts to shift their focus away from dividend yields and toward price-earnings ratios when considering data sets primarily from the 1990s and 2000s.
In order to firmly grasp the full weight of this claim, an investigation into the stationarity of earnings returns for the companies that make up the S&P 500 would be a useful addition to this study. Tables A.2 to A.9: Panel unit root test results for the Dow Jones Industrial Average using one-year periods. Tables B.2 to B.4: Panel unit root test results for the S&P 500 index using one-year periods.
