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Autocorrelation and lags definition

1

$begingroup$

I'm looking for a way to define lags in autocorrelation graphs / corellograms. I understand how to interpret such a graph but can't define a lag in a clear concise manner. Does a definition for this concept already exist? If not, what would be a good way to construct it?

statistics stochastic-processes terminology definition correlation

share|cite|improve this question

edited Apr 6 at 20:27

Alexander Gruber♦

20.1k25103174

asked Apr 3 at 16:36

Sammy.dSammy.d

467

$endgroup$

add a comment | 

1

$begingroup$

I'm looking for a way to define lags in autocorrelation graphs / corellograms. I understand how to interpret such a graph but can't define a lag in a clear concise manner. Does a definition for this concept already exist? If not, what would be a good way to construct it?

statistics stochastic-processes terminology definition correlation

share|cite|improve this question

edited Apr 6 at 20:27

Alexander Gruber♦

20.1k25103174

asked Apr 3 at 16:36

Sammy.dSammy.d

467

$endgroup$

add a comment | 

$begingroup$

I'm looking for a way to define lags in autocorrelation graphs / corellograms. I understand how to interpret such a graph but can't define a lag in a clear concise manner. Does a definition for this concept already exist? If not, what would be a good way to construct it?

statistics stochastic-processes terminology definition correlation

share|cite|improve this question

edited Apr 6 at 20:27

Alexander Gruber♦

20.1k25103174

asked Apr 3 at 16:36

Sammy.dSammy.d

467

$endgroup$

share|cite|improve this question

edited Apr 6 at 20:27

Alexander Gruber♦

20.1k25103174

asked Apr 3 at 16:36

Sammy.dSammy.d

467

share|cite|improve this question

edited Apr 6 at 20:27

Alexander Gruber♦

20.1k25103174

asked Apr 3 at 16:36

Sammy.dSammy.d

467

edited Apr 6 at 20:27

Alexander Gruber♦

20.1k25103174

edited Apr 6 at 20:27

Alexander Gruber♦

20.1k25103174

asked Apr 3 at 16:36

Sammy.dSammy.d

467

asked Apr 3 at 16:36

Sammy.dSammy.d

467

1 Answer
1

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oldest

votes

1

$begingroup$

You have a time series variable, $X$, with realizations at discrete points in time indexed by $t$, so the time series data is $x_1,x_2,ldots,x_T$.

An autocorrelation asks to what degree realizations with a certain time difference - a lag - co-move. For example, the autocorrelation with a lag of 1 would compute the correlation of the following pairs: $(x_1,x_2)$; $(x_2,x_3)$; $(x_3,x_4)$, and so on. Formally, the lag $l$ defines $Corr(x_t,x_t+l)$. Informally, the lag defines the time-distance for which you compare realizations of the time series.

An autocorrelation graph usually plots these correlations for different values of $l$, starting from $1$ to, say, $10$ (depends on context).

For example, $x_t$ could denote the price of Microsoft at the end of day $t$, and the autocorrelation with lag $l=1$ tells you how much the stock price co-moves from day to day. The lag $l=365$ tells you how much the stock price today co-moves with the stock price next year.

share|cite|improve this answer

answered Apr 3 at 22:35

NamelessNameless

2,7531333

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Thank you so much! You've put it so clearly.
  $endgroup$
  – Sammy.d
  Apr 6 at 8:46
  

  
  
  
  

add a comment | 

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1

$begingroup$

You have a time series variable, $X$, with realizations at discrete points in time indexed by $t$, so the time series data is $x_1,x_2,ldots,x_T$.

An autocorrelation asks to what degree realizations with a certain time difference - a lag - co-move. For example, the autocorrelation with a lag of 1 would compute the correlation of the following pairs: $(x_1,x_2)$; $(x_2,x_3)$; $(x_3,x_4)$, and so on. Formally, the lag $l$ defines $Corr(x_t,x_t+l)$. Informally, the lag defines the time-distance for which you compare realizations of the time series.

An autocorrelation graph usually plots these correlations for different values of $l$, starting from $1$ to, say, $10$ (depends on context).

For example, $x_t$ could denote the price of Microsoft at the end of day $t$, and the autocorrelation with lag $l=1$ tells you how much the stock price co-moves from day to day. The lag $l=365$ tells you how much the stock price today co-moves with the stock price next year.

share|cite|improve this answer

answered Apr 3 at 22:35

NamelessNameless

2,7531333

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Thank you so much! You've put it so clearly.
  $endgroup$
  – Sammy.d
  Apr 6 at 8:46
  

  
  
  
  

add a comment | 

1

$begingroup$

You have a time series variable, $X$, with realizations at discrete points in time indexed by $t$, so the time series data is $x_1,x_2,ldots,x_T$.

An autocorrelation asks to what degree realizations with a certain time difference - a lag - co-move. For example, the autocorrelation with a lag of 1 would compute the correlation of the following pairs: $(x_1,x_2)$; $(x_2,x_3)$; $(x_3,x_4)$, and so on. Formally, the lag $l$ defines $Corr(x_t,x_t+l)$. Informally, the lag defines the time-distance for which you compare realizations of the time series.

An autocorrelation graph usually plots these correlations for different values of $l$, starting from $1$ to, say, $10$ (depends on context).

For example, $x_t$ could denote the price of Microsoft at the end of day $t$, and the autocorrelation with lag $l=1$ tells you how much the stock price co-moves from day to day. The lag $l=365$ tells you how much the stock price today co-moves with the stock price next year.

share|cite|improve this answer

answered Apr 3 at 22:35

NamelessNameless

2,7531333

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Thank you so much! You've put it so clearly.
  $endgroup$
  – Sammy.d
  Apr 6 at 8:46
  

  
  
  
  

add a comment | 

$begingroup$

You have a time series variable, $X$, with realizations at discrete points in time indexed by $t$, so the time series data is $x_1,x_2,ldots,x_T$.

An autocorrelation asks to what degree realizations with a certain time difference - a lag - co-move. For example, the autocorrelation with a lag of 1 would compute the correlation of the following pairs: $(x_1,x_2)$; $(x_2,x_3)$; $(x_3,x_4)$, and so on. Formally, the lag $l$ defines $Corr(x_t,x_t+l)$. Informally, the lag defines the time-distance for which you compare realizations of the time series.

An autocorrelation graph usually plots these correlations for different values of $l$, starting from $1$ to, say, $10$ (depends on context).

For example, $x_t$ could denote the price of Microsoft at the end of day $t$, and the autocorrelation with lag $l=1$ tells you how much the stock price co-moves from day to day. The lag $l=365$ tells you how much the stock price today co-moves with the stock price next year.

share|cite|improve this answer

answered Apr 3 at 22:35

NamelessNameless

2,7531333

$endgroup$

share|cite|improve this answer

answered Apr 3 at 22:35

NamelessNameless

2,7531333

answered Apr 3 at 22:35

NamelessNameless

2,7531333

answered Apr 3 at 22:35

NamelessNameless

2,7531333