Need urgent help using Variance Ratio test

[Maurelius]

Hi!

I'm doing a study on whether a stock market is under random walk or mean reverting. I've heard that the variance ratio test is a great tool to help you with this. The only problem I have is how to choose the "Test periods". The default is "2 4 8 16". How do I decide this? Worth mentioning is that I have time-series with around 3500 observations in them.

Regards,

Maurelius

[EViews Glenn]

There is no correct answer to the observation periods at which to examine the variance ratios. The defaults correspond to the original Lo and MacKinlay paper, but others do tests examining longer memory aggregates. If you have specific views about relevant intervals, you may use those as well.

[Maurelius]

Thanks for the answer.

Since I'm all new to this, would you care to explain more in detail and easy reading what these "Test periods" actually are?

Would really appreciate it.

[EViews Glenn]

From the first paragraph of the EViews documentation:

One popular approach to answering this question, the Lo and MacKinlay (1988, 1989) overlapping variance ratio test, examines the predictability of time series data by comparing variances of differences of the data (returns) calculated over different intervals. If we assume the data follow a random walk, the variance of a q-period difference should be q times the variance of the one-period difference. Evaluating the empirical evidence for or against this restriction is the basis of the variance ratio test.

The test periods correspond to different choices for q.

[Maurelius]

Thanks for your reply.

I have a few follow-up questions;

1. To calculate variance ratio test do we need to have the daily data return instead of daily closing price?

2. Do we need to logarithm the daily prices to perform the variance ratio test?

[EViews Glenn]

1. Either, you just choose the corresponding data specification (e.g., if you use the price, then you want to choose Random Walk, we'll then difference the data).
2. If you choose exponential random walk, we'll dlog.

[Maurelius]

Thank you so much for your help EViews Glenn,

One last thing. Would you care to help me interpret this variance ratio test result?

Null Hypothesis: Log ATLAS_COPCO_B is a martingale
Date: 04/23/14 Time: 09:59
Sample: 1 3560
Included observations: 3557 (after adjustments)
Heteroskedasticity robust standard error estimates
User-specified lags: 2 4 8 16 32 64 128 256 512 1024 2048

Joint Tests Value df Probability
Max |z| (at period 8 )* 3.512812 3557 0.0049

Individual Tests
Period Var. Ratio Std. Error z-Statistic Probability
2 0.975649 0.012201 -1.995725 0.0460
4 0.919689 0.024988 -3.213969 0.0013
8 0.860181 0.039803 -3.512812 0.0004
16 0.817295 0.059156 -3.088548 0.0020
32 0.758616 0.087961 -2.744210 0.0061
64 0.691390 0.125045 -2.467993 0.0136
128 0.673462 0.175052 -1.865377 0.0621
256 0.546667 0.243526 -1.861542 0.0627
512 0.507272 0.353126 -1.395330 0.1629
1024 0.566261 0.566964 -0.765020 0.4443
2048 0.304430 0.823484 -0.844667 0.3983

Have I understood this correctly that the observed time series is mean reverting? If so, how can I tell in how many test periods this i significant? E.g is it mean reverting in a period of 64 to 512 periods.

[EViews Glenn]

1. I prefer to think of it as we reject the hypothesis that the innovations to the process are a Martingale. You are free to interpret that as mean-reverting or not.

2. You tested "User-specified lags: 2 4 8 16 32 64 128 256 512 1024 2048". All that the test results say is that the variance ratio is violated for one of these intervals. That said, the individual statistic results suggest (this is not a formal statement) that the strongest rejections occur in the 4, 8, 16, and 32 range. Again, that's an informal diagnostic.

[Maurelius]

Thank you so much for this EViews Glenn!

You are right, you can't really say that it's mean-reverting just because the null hypothesis of a Martingale is rejected.

But when judging by the result, are you looking at the probability-values or variance ratios? I for one thought that the variance ratio was the important thing here. A variance ratio of 1 equals random walk, variance ratio > 1 is trending (positive autocorrelation) and variance ratio < 1 is mean reverting (negative autocorrelation).

What are the important variables to focus on at a variance ratio test?

[EViews Glenn]

I'm looking at p-values for the informal analysis.

[Maurelius]

OK. So first, when the p-values are under 5% significance you can reject that it is a Martingale. Second, you look at the variance ratio and see if it's greater or less than one to interpret it as mean reverting or mean averting?

[zahrakhawaja]

hi i am doing thesis on the topic dynamic effects of trade openness on financial development: evidence from Asia i have applied variance ratio test on all the variables i have selected i want to know that some of the variables probability are insignificant how can i make them significant using user specified is there any particular criteria for selecting the user specified