# Vector Autoregressive Models

#### noetsi

##### Fortran must die
I know this is not causality in the classic sense. Say you two variables x and y. If you reject the null so that x granger causes y does this automatically mean that Y granger causes X or do you have to test this. Does "causality' flow both ways automatically in this or you need to test it both ways?

#### hlsmith

##### Not a robit
Not overly familiar with the granger causality material, but wonder if this is were study content knowledge comes into play and temporality.

#### noetsi

##### Fortran must die
Well it would if causality does not automatically go both ways. Then you could model X > Y versus Y > X based on theory.

In my research area, vocational administration services, I don't think there is any theory to build on. Time series analysis rarely occurs.

I don't think there is anyone left on this board who works a lot in time series.

#### hlsmith

##### Not a robit
Well causality doesn't go both ways but if you have 2 variables a statistic model doesnt know which came first.

#### noetsi

##### Fortran must die
I am not sure causality can not go to ways. That is what a feedback loop is. X influences Y and then Y influences X. I suspect this occurs often in economic and financial analysis.

#### noetsi

##### Fortran must die
Since I can no longer figure out how to rename this thread, I am changing the topic to vector autoregressive models.

Is Item Response Functions and Variance Decomposition limited to structural models or can you apply it to recursive models that set no limits on parameters.

#### Miner

##### TS Contributor
I am not sure causality can not go to ways. That is what a feedback loop is. X influences Y and then Y influences X. I suspect this occurs often in economic and financial analysis.
I thought I would throw this in from a course I teach in problem solving. There should be some overlap in statistics.

Three rules of causality:
• A correlation or association exists between the hypothesized cause and the effect
• Cause must precede effect in time
• The mechanism linking cause to effect must be identified
When the linking mechanism is unknown, people will tend to infer causality whether it exists or not.

Causes of false causality:
• Contiguity - Perceiving something close in time or space as the cause
• Similarity - Perceiving something sharing a similarity with the effect (e.g., appearance, intensity) as the cause
• Regularity or correlation - If "A" is followed regularly by "B", and "B" has seldom occurred in the absence of "A", we are likely to perceive a casual relationship
Possible causes for correlation:
• A causes B
• B causes A
• A and B partially cause each other (your feedback loop is one example)
• A causes C, which causes B
• A and B are both caused by C
• Under reported data for A or B (i.e., only exceptions are reported)
• The observed correlation was due purely to chance

#### Attachments

• 35.3 KB Views: 1

#### hlsmith

##### Not a robit
As for your feedback loop, well yeah you can have one but time has elapsed and now you are in the future. So it is not the same model but a new t+1 model, (t=time).

So you can have X1 -> Y1, then have Y1 -> X2 and X2 ->Y2, where Y2 is probably independent of Y1 given you are controlling for X2, this is because of Markovian independence. This continues on in the same format into the future.

#### noetsi

##### Fortran must die
Well the type of models we are talking about have multiple lags built into them.

#### noetsi

##### Fortran must die
For impulse response functions you can generate simple ones, or orthogonal ones, or cumulative ones. I understand the theoretical difference. What is the practical difference?