Interpreting Panel Data Autocorrelation Von Neumann Ratio Test

[John Riveros]

Greetings Stata Users.

I'm currently analyzing the autocorrelation of a model, in which, I used Panel Data Autocorrelation Von Neumann Ratio Test made by Shehata, Emad Abd Elmessih & Sahra Khaleel A. Mickaiel (2015) in the package: LMAWXT.

The output of the test is this:

==============================================================================
*** Panel Data Autocorrelation Von Neumann Ratio Test
==============================================================================
  Ho: No AR(1) Panel AutoCorrelation - Ha: AR(1) Panel AutoCorrelation

- Panel Rho Value                 =   0.0055
- Von Neumann Ratio Test          =   1.9236     df: (11 , 225)
------------------------------------------------------------------------------

However, I'm not sure how to interpret it, I suspect Panel Rho Value is the calculated test statistic, and the critical value (at some confidence interval) is 1.9236, therefore in this case we're not rejecting the null hypothesis of No AR(1) autocorrelation.

This interpretation is right? or maybe I'm omitting something.

[John Riveros]

Greetings, Well I managed to found the answer by looking for some references. So in order to contribute to the forums, I will post the answer I found.

First of all, some references regarding the use of the Von Neumann's Test of Serial Correlation can be found in Gujarati, (page 491 & 492) Although no wide explanations are given.

Second, in a related explication in R Documentation (N/A), it is stated the following:

"von Neumann et al. (1941) introduced a test for randomness in the context of testing for trend in the mean of a process [...] which is the ratio of the square of successive differences to the usual sums of squared deviations from the mean. This statistic is bounded between 0 and 4, and for a purely random process is symmetric about 2. Small values of this statistic indicate possible positive autocorrelation, and large values of this statistic indicate possible negative autocorrelation. Durbin and Watson (1950, 1951, 1971) proposed using this statistic in the context of checking the independence of residuals from a linear regression model and provided tables for the distribution of this statistic. This statistic is therefore often called the “Durbin-Watson statistic” (Draper and Smith, 1998, p.181)."

Therefore, the explication is that Von Neumann ratio statistic also is bounded between 0 and 4 just like DW. and the symmetric process referred to as about 2, is exactly somewhat closer to the rule of thumb of the DW statistic. Therefore if the Von Neumann ratio statistic is equal or closer to 2, we can't reject the null hypothesis of no serial correlation of first order.

Third. a formal reference which indicates the use of the Von Neumann statistic can be found in an article from Durana et al (2020) where they stated

"We apply the von Neumann test to detect the existence of significant changepoint in the earnings management and parametric standard normal homogeneity test to determine a year when a significant change occurs. Von Neumann’s test is a test using the ratio of mean square successive (year to year) difference to the variance (Von Neumann 1941). [...]

The null hypothesis is that the data are dependent. If the value of N is equal to 2, it means that the sample is homogeneous while the values of N less than 2 indicate that the sample has a breakpoint (Buishand 1982). This test gives no information about the breakpoint." (page, 8).

This confirms that Von Neumann relies on a single statistic similar to DW, and where the absence of serial correlation is given when the statistic is close to 2.

As a concluding remark, in the output presented in the last post, We may say the model estimated for panel data doesn't have a problem of first-order serial correlation.

Bibliography.

Durana et al (2020) Heads and Tails of Earnings Management: Quantitative Analysis in Emerging Countries, Journal "Risks", Vol 8. No. 57 DOI: 10.3390/risks8020057

R Documentation (N/A) Test for the Presence of Serial Correlation, R Documentation. Taken from: http://finzi.psych.upenn.edu/library...ationTest.html