<p>In some statistical software (not all), in a correlogram the "zero lag" is also depicted - but the zero lag is just the correlation of a random variable with its own self, so it is by construction equal to unity. This appears to be happening in your first graph where the autocorrelation function is calculated. </p>

<p>The second graph is the partial autocorrelation function which calculates the correlation coefficients after the effect of all "previous" lags (i.e. of lower order) has been removed (by linear projection estimation).</p>

<p>First impression? The process is white noise. What lags appear to exceed the  "statistical significance threshold", they nevertheless indicate <em>very</em> small values, never greater  than $0.05$. This is truly <em>economically negligible</em> correlation even if it exists (irrespective of whether it is "statistically significant"), and most likely is due to "finite-sample variation", rather than indication of any actual relation. </p>

<p>And apart from that, do the lags appearing "significant" <em>make sense</em>? 
It always matters what the process you are examining is, and what is its "typical properties" based on past scientific work (but don't take this to mean that "past typical properties" always carry over to all the realizations of the process).</p>

<p>In any case, it would be instructive to "follow blindly" the Correlograms and see what you get, by trying various combinations based on the lags that appear statistically significant.</p>

CC BY-SA 3.0
2015-12-21T21:18:50.350Z
Thank you so much for your answer :) ! 

I have to say to you that it is the first time I have to interpret an ACF and a PACF plot, and it's not easy for me because it seems to be not "typical" like in what we study, so I am a little lost. 

According to you, if I "follow blindly" the Correlograms and see what I get, are the following combinations true comparing the results given by correlograms ? Can I choose to ignore the lag number 6 in the PACF ?

- ARMA(2,0,0)
- ARMA(3,0,0)
Or can you tell me what combination do you think is also appropriate ... ? 

Thank you in advance.
Marc
CC BY-SA 3.0
2015-12-21T22:08:56.960Z
@MaximeP. As I already wrote in my answer, to me this process looks like simple white noise. So I cannot really pick a combination of lags as more appropriate than another. You should try the various combinations and check the diagnostics for each model, to see which performs better.
Alecos Papadopoulos
CC BY-SA 3.0
2015-12-21T16:23:26.073Z
2015-12-21T16:23:26.073Z
Alecos Papadopoulos
<p>First, I am a French student, so forgive me for my English which can be not clear at all. </p>

<p><a href="https://i.sstatic.net/tX2d0.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/tX2d0.png" alt="difflog values ACF"></a></p>

<p><a href="https://i.sstatic.net/479pN.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/479pN.png" alt="difflog values PACF"></a></p>

<p>I have to analyze a financial series. I have some difficulties to make the second part of the work which focuses on ARMA model. I can't read (interpret?) my Autocorrelation Function (ACF) and Partial Autocorrelation Function (PACF) correlogramm. </p>

<p>To my mind, here we have a MA(0) but I don't know if it's possible. In this case, what does it mean ? </p>

<p>And I don't know also with the PACF graph, if we are in a AR(3) or AR(6). And why the first stick is not over the "confidence level" ? </p>

<p>It is possible that my interpretations are false, please tell me.</p>

CC BY-SA 3.0
2015-12-21T15:48:36.990Z
What software are you using?
Alecos Papadopoulos
CC BY-SA 3.0
2015-12-21T21:19:45.087Z
I am using Rstudio
Marc
<econometrics><financial-economics><applied-econometrics>
Interpretation of ACF and PACF
Marc
# Interpretation of ACF and PACF

(Asked by: username_0 on 2015-12-21)

First, I am a French student, so forgive me for my English which can be not clear at all.

[![difflog values ACF](https://i.sstatic.net/tX2d0.png)](https://i.sstatic.net/tX2d0.png)

[![difflog values PACF](https://i.sstatic.net/479pN.png)](https://i.sstatic.net/479pN.png)

I have to analyze a financial series. I have some difficulties to make the second part of the work which focuses on ARMA model. I can't read (interpret?) my Autocorrelation Function (ACF) and Partial Autocorrelation Function (PACF) correlogramm.

To my mind, here we have a MA(0) but I don't know if it's possible. In this case, what does it mean ?

And I don't know also with the PACF graph, if we are in a AR(3) or AR(6). And why the first stick is not over the "confidence level" ?

It is possible that my interpretations are false, please tell me.

**Tags:** econometrics, financial-economics, applied-econometrics

> **Comments:**
> **username_1**: What software are you using?  
> **username_0**: I am using Rstudio  

---

## 1 answers

### Answer by username_1 on 2015-12-21. Score: 2

In some statistical software (not all), in a correlogram the "zero lag" is also depicted - but the zero lag is just the correlation of a random variable with its own self, so it is by construction equal to unity. This appears to be happening in your first graph where the autocorrelation function is calculated.

The second graph is the partial autocorrelation function which calculates the correlation coefficients after the effect of all "previous" lags (i.e. of lower order) has been removed (by linear projection estimation).

First impression? The process is white noise. What lags appear to exceed the "statistical significance threshold", they nevertheless indicate *very* small values, never greater than $0.05$. This is truly *economically negligible* correlation even if it exists (irrespective of whether it is "statistically significant"), and most likely is due to "finite-sample variation", rather than indication of any actual relation.

And apart from that, do the lags appearing "significant" *make sense*?
It always matters what the process you are examining is, and what is its "typical properties" based on past scientific work (but don't take this to mean that "past typical properties" always carry over to all the realizations of the process).

In any case, it would be instructive to "follow blindly" the Correlograms and see what you get, by trying various combinations based on the lags that appear statistically significant.

> **Comments:**
> **username_0**: Thank you so much for your answer :) !   I have to say to you that it is the first time I have to interpret an ACF and a PACF plot, and it's not easy for me because it seems to be not "typical" like in what we study, so I am a little lost.   According to you, if I "follow blindly" the Correlograms and see what I get, are the following combinations true comparing the results given by correlograms ? Can I choose to ignore the lag number 6 in the PACF ?  - ARMA(2,0,0) - ARMA(3,0,0) Or can you tell me what combination do you think is also appropriate ... ?   Thank you in advance.  
> **username_1**: @MaximeP. As I already wrote in my answer, to me this process looks like simple white noise. So I cannot really pick a combination of lags as more appropriate than another. You should try the various combinations and check the diagnostics for each model, to see which performs better.  

---

