The CADF (Cross-sectional Augmented Dickey-Fuller) test is a unit root test that is commonly used to assess the stationarity of time series data with cross-sectional dependency. Interpreting the results of the CADF test can help determine whether the variables under consideration are stationary or non-stationary.

When interpreting the results of the CADF test in EVIEWS, you would typically look at the t-statistic or p-value associated with the test statistic. The test statistic compares the observed value to a critical value and determines whether the null hypothesis of a unit root (non-stationarity) can be rejected in favor of the alternative hypothesis of stationarity.

Here are some general guidelines for interpreting the results of the CADF test:

If the t-statistic is less than the critical value and the p-value is greater than the significance level (e.g., 0.05), then you would fail to reject the null hypothesis. This suggests that the variable is non-stationary and has a unit root.

If the t-statistic is greater than the critical value and the p-value is less than the significance level, then you would reject the null hypothesis. This suggests that the variable is stationary and does not have a unit root.

If the t-statistic is close to the critical value or the p-value is close to the significance level, then the results may be inconclusive, and further investigation may be required.

When writing about the results of the CADF test in a paper with a large number of cross sections, you can present the test results in a table format. The table can include the variable names, the t-statistic or p-value, and any relevant additional information such as the lag length used in the test. You can also provide a concise summary of the interpretation of the results, highlighting whether the variables are found to be stationary or non-stationary.

It is important to consider the overall context and implications of the test results in your research. Discussing the consequences of non-stationarity or stationarity and considering the potential impact on your analysis and conclusions can help provide a comprehensive interpretation of the results in your paper.

Ajit Singh First i would like to thank you for your answer. Secondly what i mean is how to interpret the result of the following table;

Cross-sectional ADF unit root test

Null hypothesis: Unit root for specified cross-section

Lag selection: AIC with maxlag=9

Test results:

CADF Truncated CADF

Cross-section ADF lags t-stat p-value t-stat p-value

CA01R 8 -1.15613 >=.10 - 1.15613 >=0.10

CA02K 2 -3.23702 =0.10

CA04K 8 -2.18620 >=.10 -2.18620 >=0.10

CA05K 5 -0.38597 >=.10 -0.38597 >=0.10

CA06P 8 -0.95273 >=.10 -0.95273 >=0.10

Based on the provided table, it appears to be the results of a Cross-sectional ADF (Augmented Dickey-Fuller) unit root test. The test is applied to each cross-section separately to assess the presence of a unit root, indicating non-stationarity, in the specified variables.

Here's how to interpret the table:

Null hypothesis: The null hypothesis being tested is that there is a unit root (non-stationarity) for the specified cross-section.

Lag selection: The lag selection method used for the ADF test is AIC (Akaike Information Criterion) with maxlag=9 . This suggests that the lag length for each cross-section was determined using the AIC criterion, considering a maximum lag order of 9.

Test results: The table provides the test results for each cross-section. The columns "ADF lags," "t-stat," and "p-value" represent the lag order used, the test statistic value, and the corresponding p-value, respectively, for the ADF test. The columns "Truncated CADF t-stat" and "Truncated CADF p-value" show the test statistics and p-values for the truncated version of the CADF test.

Interpreting the results:

For each cross-section, compare the t-statistic value to the critical values at a certain significance level (e.g., 0.05) to determine whether to reject the null hypothesis.

If the t-statistic is less than the critical value, or the p-value is greater than the chosen significance level, you would fail to reject the null hypothesis, indicating the presence of a unit root (non-stationarity).

Conversely, if the t-statistic is greater than the critical value, or the p-value is less than the chosen significance level, you would reject the null hypothesis, suggesting the absence of a unit root (stationarity).

Here is an example interpretation for the first cross-section (CA01R):

For CA01R, the ADF test was conducted with 8 lags, resulting in a t-statistic of -1.15613 and a p-value greater than or equal to 0.10.

Since the t-statistic is less than the critical value at the 0.05 significance level, and the p-value is greater than 0.10, we fail to reject the null hypothesis. This indicates that there is evidence of a unit root (non-stationarity) in the CA01R cross-section.

You can apply the same interpretation to the remaining cross-sections in the table.

Remember, the interpretation of the results depends on the chosen significance level and the specific context of your study. It is important to consider the implications of non-stationarity or stationarity in your analysis and draw appropriate conclusions based on the results.

Ajit Singh so the interpretation must be for each cross section right? any suggestions as i do not want to test each station separately. I am analyzing panel data here. Thank you for your time and effort.

Yes, in the context of panel data analysis, the interpretation of unit root tests would typically be conducted for each cross-section or entity separately. This allows for an assessment of the presence or absence of unit roots within each individual entity in the panel.

If you are analyzing panel data and want to avoid testing each station separately, you can consider using panel unit root tests instead of cross-sectional unit root tests. Panel unit root tests take into account the panel structure of the data and allow for testing the presence of unit roots across multiple entities simultaneously.

There are several panel unit root tests available, such as the Levin-Lin-Chu (LLC) test, the Im-Pesaran-Shin (IPS) test, and the Fisher-type tests. These tests consider both the cross-sectional and time-series dimensions of the panel data and can provide more efficient and robust results compared to conducting individual unit root tests for each cross-section.

When using panel unit root tests, you would typically specify the null hypothesis as the presence of a unit root across all entities in the panel. The interpretation would then involve examining the test statistics and p-values to determine whether the null hypothesis can be rejected, indicating the absence of unit roots (stationarity) in the panel.

It's worth noting that the choice of the appropriate panel unit root test may depend on the specific characteristics of your panel data and the assumptions of the underlying model. It's recommended to consult relevant literature or seek expert advice to select the most suitable panel unit root test for your analysis.

Ajit Singh your are right. But I must conduct the second generation unit root test as my panel data have cross section dependence such as CIPS. As far as I know that the 1st generation unit root tests assumes independence of cross sections.

You are correct. The first-generation panel unit root tests assume independence of cross-sections, which may not hold when there is cross-sectional dependence in the panel data . In the presence of cross-sectional dependence, it is recommended to use second-generation panel unit root tests that account for this dependence.

The Cross-sectional Augmented Dickey-Fuller (CADF) test , also known as the Pesaran's CIPS (Cross-sectional Independence Panel Stationarity) test, is one example of a second-generation panel unit root test that considers cross-sectional dependence . The CADF test extends the standard augmented Dickey-Fuller (ADF) test to account for cross-sectional correlation in the panel data.

By using the CADF or other second-generation panel unit root tests , you can properly address cross-sectional dependence in your panel data analysis. These tests provide more reliable results and help avoid potential issues that may arise when using first-generation tests in the presence of cross-sectional dependence.

It's important to note that the choice of the appropriate second-generation panel unit root test may depend on the specific characteristics of your data and the assumptions of the underlying model . Therefore, it's recommended to consult relevant literature or seek expert advice to select the most suitable second-generation panel unit root test for your analysis .