Impulse graph interpretation Answer [closed]

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Impulse graph interpretation Answer [closed]

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#1 by (-1 votes)

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Hello, guys, how are you?

I have a question when interpreting graphs of 'impulse response functions'. I have read a few books, but in none of the ones I consulted is it clearly stated when responses to an impulse may or may not be considered statistically significant. As an example, I put the two graphs below:

I did not just want an interpretation of these specific graphics, but an explanation on how to interpret any graph generated by impulse response functions. Being more specific, what are the criteria that must be observed in order for the response to be statistically significant?

If someone can establish these criteria or indicate some book / post / slides, anything helps. Thanks in advance.

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asked by anonymous 03.02.2017 / 10:15

1 answer

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score -1 · Answer 1

The answers lower were given assuming that y1 and y2 equal zero signify that the response is not meaningful.

Short answer:

Your graphics are from 95% confidence intervals built through bootstrap. A golden rule of statistical inference is:

If 0 (zero) is contained in a confidence interval, then the result is not statistically significant

Since 0 is included in your confidence intervals, which are dashed red lines, none of these ranges are significant.

Long answer:

For the theory of statistical inference, confidence intervals are equivalent to hypothesis testing. It turns out that hypothesis tests give you a binary answer: either the null hypothesis was rejected, or the null hypothesis was not rejected.

On the other hand, confidence intervals give you an interval at which the actual population parameter may be. Note, in the figures, that 0 (zero) is contained in all intervals. Therefore, 0 is a possible result for the response variable. Therefore, we can not reject the null hypothesis in these cases.

References:

1) Bussab, W. de O. and Morettin, P.A. (2013). Basic Statistics. Editora Saraiva, São Paulo, 8th edition.

2) Any other basic statistical book dealing with confidence intervals and hypothesis testing