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Confidence intervals for autocorrelation function
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Given a time series data sample I have computed autocorrelation coefficients for various lags, the result looks something like this
How do I compute the confidence intervals around the sample autocorrelation curve?
The reason for that is to see if another autocorrelation curve computed from samples generated by some model is within those confidence intervals.
confidence-interval autocorrelation
asked 7 hours ago
Anya
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up vote
2
down vote
favorite
Given a time series data sample I have computed autocorrelation coefficients for various lags, the result looks something like this
How do I compute the confidence intervals around the sample autocorrelation curve?
The reason for that is to see if another autocorrelation curve computed from samples generated by some model is within those confidence intervals.
confidence-interval autocorrelation
asked 7 hours ago
Anya
132
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Anya is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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Maybe try with a bootstrap method.
– user2974951
7 hours ago
@user2974951 thanks for your suggestion, I will try that. However, I was hoping to find out if some asymptotic approximation formula was available.
– Anya
6 hours ago
add a comment |Â
up vote
2
down vote
favorite
up vote
2
down vote
favorite
Given a time series data sample I have computed autocorrelation coefficients for various lags, the result looks something like this
How do I compute the confidence intervals around the sample autocorrelation curve?
The reason for that is to see if another autocorrelation curve computed from samples generated by some model is within those confidence intervals.
confidence-interval autocorrelation
asked 7 hours ago
Anya
132
New contributor
Anya is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Given a time series data sample I have computed autocorrelation coefficients for various lags, the result looks something like this
How do I compute the confidence intervals around the sample autocorrelation curve?
The reason for that is to see if another autocorrelation curve computed from samples generated by some model is within those confidence intervals.
confidence-interval autocorrelation
confidence-interval autocorrelation
asked 7 hours ago
Anya
132
New contributor
Anya is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 7 hours ago
Anya
132
New contributor
Anya is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 7 hours ago
Anya
132
New contributor
Anya is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 7 hours ago
Anya
132
asked 7 hours ago
Anya
132
132
New contributor
Anya is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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New contributor
Anya is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
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Check out our Code of Conduct.
Maybe try with a bootstrap method.
– user2974951
7 hours ago
@user2974951 thanks for your suggestion, I will try that. However, I was hoping to find out if some asymptotic approximation formula was available.
– Anya
6 hours ago
add a comment |Â
Maybe try with a bootstrap method.
– user2974951
7 hours ago
@user2974951 thanks for your suggestion, I will try that. However, I was hoping to find out if some asymptotic approximation formula was available.
– Anya
6 hours ago
Maybe try with a bootstrap method.
– user2974951
7 hours ago
Maybe try with a bootstrap method.
– user2974951
7 hours ago
@user2974951 thanks for your suggestion, I will try that. However, I was hoping to find out if some asymptotic approximation formula was available.
– Anya
6 hours ago
@user2974951 thanks for your suggestion, I will try that. However, I was hoping to find out if some asymptotic approximation formula was available.
– Anya
6 hours ago
add a comment |Â
2 Answers
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A quick google search with "confidence intervals for acfs" yielded
Janet M. Box-Steffensmeier, John R. Freeman, Matthew P. Hitt, Jon C. W. Pevehouse: Time Series Analysis for the Social Sciences.
In there, on page 38, the standard error of an AC estimator at lag k is stated to be
$AC_SE,k = sqrtN^-1left(1+2sum_i=1^k[AC_i^2] right)$
where $AC_i$ is the AC esimate at lag i and N is the number of time steps in your sample. This is assuming that the true underlying process is actually MA. Assuming asympotic normality of the AC estimator, you can calculate the confidence intervals at each lag then as
$CI_AC_k = [AC_k - 1.96timesdfracAC_SE,ksqrtN, AC_k + 1.96timesdfracAC_SE,ksqrtN]$.
For some further info, see also this and this.
answered 4 hours ago
samtt
403
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up vote
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When the ACF is estimated from data I think also the error should be directly computed from the same data. I think that is generally the safest and most conservative approach. I would just store the resulting products of the signal with itself after each shift in the row of a matrix. Then you have the full distribution of values at each shift. Computing the column-wise average and the std/sem gives you a estimate of the AC and its variation. Bootstrapping and other resampling procedures on that matrix enable you to estimate the confidence intervals. This has the advantage that there are no special assumptions to be made and it can always be made compatible with your specific AC computation (normalization, padding etc.).
answered 1 hour ago
Jojo
664
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2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
2
down vote
accepted
A quick google search with "confidence intervals for acfs" yielded
Janet M. Box-Steffensmeier, John R. Freeman, Matthew P. Hitt, Jon C. W. Pevehouse: Time Series Analysis for the Social Sciences.
In there, on page 38, the standard error of an AC estimator at lag k is stated to be
$AC_SE,k = sqrtN^-1left(1+2sum_i=1^k[AC_i^2] right)$
where $AC_i$ is the AC esimate at lag i and N is the number of time steps in your sample. This is assuming that the true underlying process is actually MA. Assuming asympotic normality of the AC estimator, you can calculate the confidence intervals at each lag then as
$CI_AC_k = [AC_k - 1.96timesdfracAC_SE,ksqrtN, AC_k + 1.96timesdfracAC_SE,ksqrtN]$.
For some further info, see also this and this.
answered 4 hours ago
samtt
403
New contributor
samtt is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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up vote
2
down vote
accepted
A quick google search with "confidence intervals for acfs" yielded
Janet M. Box-Steffensmeier, John R. Freeman, Matthew P. Hitt, Jon C. W. Pevehouse: Time Series Analysis for the Social Sciences.
In there, on page 38, the standard error of an AC estimator at lag k is stated to be
$AC_SE,k = sqrtN^-1left(1+2sum_i=1^k[AC_i^2] right)$
where $AC_i$ is the AC esimate at lag i and N is the number of time steps in your sample. This is assuming that the true underlying process is actually MA. Assuming asympotic normality of the AC estimator, you can calculate the confidence intervals at each lag then as
$CI_AC_k = [AC_k - 1.96timesdfracAC_SE,ksqrtN, AC_k + 1.96timesdfracAC_SE,ksqrtN]$.
For some further info, see also this and this.
answered 4 hours ago
samtt
403
New contributor
samtt is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
add a comment |Â
up vote
2
down vote
accepted
up vote
2
down vote
accepted
A quick google search with "confidence intervals for acfs" yielded
Janet M. Box-Steffensmeier, John R. Freeman, Matthew P. Hitt, Jon C. W. Pevehouse: Time Series Analysis for the Social Sciences.
In there, on page 38, the standard error of an AC estimator at lag k is stated to be
$AC_SE,k = sqrtN^-1left(1+2sum_i=1^k[AC_i^2] right)$
where $AC_i$ is the AC esimate at lag i and N is the number of time steps in your sample. This is assuming that the true underlying process is actually MA. Assuming asympotic normality of the AC estimator, you can calculate the confidence intervals at each lag then as
$CI_AC_k = [AC_k - 1.96timesdfracAC_SE,ksqrtN, AC_k + 1.96timesdfracAC_SE,ksqrtN]$.
For some further info, see also this and this.
answered 4 hours ago
samtt
403
New contributor
samtt is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
A quick google search with "confidence intervals for acfs" yielded
Janet M. Box-Steffensmeier, John R. Freeman, Matthew P. Hitt, Jon C. W. Pevehouse: Time Series Analysis for the Social Sciences.
In there, on page 38, the standard error of an AC estimator at lag k is stated to be
$AC_SE,k = sqrtN^-1left(1+2sum_i=1^k[AC_i^2] right)$
where $AC_i$ is the AC esimate at lag i and N is the number of time steps in your sample. This is assuming that the true underlying process is actually MA. Assuming asympotic normality of the AC estimator, you can calculate the confidence intervals at each lag then as
$CI_AC_k = [AC_k - 1.96timesdfracAC_SE,ksqrtN, AC_k + 1.96timesdfracAC_SE,ksqrtN]$.
For some further info, see also this and this.
answered 4 hours ago
samtt
403
New contributor
samtt is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
answered 4 hours ago
samtt
403
New contributor
samtt is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
answered 4 hours ago
samtt
403
answered 4 hours ago
samtt
403
403
New contributor
samtt is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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New contributor
samtt is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
samtt is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
add a comment |Â
add a comment |Â
up vote
1
down vote
When the ACF is estimated from data I think also the error should be directly computed from the same data. I think that is generally the safest and most conservative approach. I would just store the resulting products of the signal with itself after each shift in the row of a matrix. Then you have the full distribution of values at each shift. Computing the column-wise average and the std/sem gives you a estimate of the AC and its variation. Bootstrapping and other resampling procedures on that matrix enable you to estimate the confidence intervals. This has the advantage that there are no special assumptions to be made and it can always be made compatible with your specific AC computation (normalization, padding etc.).
answered 1 hour ago
Jojo
664
add a comment |Â
up vote
1
down vote
When the ACF is estimated from data I think also the error should be directly computed from the same data. I think that is generally the safest and most conservative approach. I would just store the resulting products of the signal with itself after each shift in the row of a matrix. Then you have the full distribution of values at each shift. Computing the column-wise average and the std/sem gives you a estimate of the AC and its variation. Bootstrapping and other resampling procedures on that matrix enable you to estimate the confidence intervals. This has the advantage that there are no special assumptions to be made and it can always be made compatible with your specific AC computation (normalization, padding etc.).
answered 1 hour ago
Jojo
664
add a comment |Â
up vote
1
down vote
up vote
1
down vote
When the ACF is estimated from data I think also the error should be directly computed from the same data. I think that is generally the safest and most conservative approach. I would just store the resulting products of the signal with itself after each shift in the row of a matrix. Then you have the full distribution of values at each shift. Computing the column-wise average and the std/sem gives you a estimate of the AC and its variation. Bootstrapping and other resampling procedures on that matrix enable you to estimate the confidence intervals. This has the advantage that there are no special assumptions to be made and it can always be made compatible with your specific AC computation (normalization, padding etc.).
answered 1 hour ago
Jojo
664
When the ACF is estimated from data I think also the error should be directly computed from the same data. I think that is generally the safest and most conservative approach. I would just store the resulting products of the signal with itself after each shift in the row of a matrix. Then you have the full distribution of values at each shift. Computing the column-wise average and the std/sem gives you a estimate of the AC and its variation. Bootstrapping and other resampling procedures on that matrix enable you to estimate the confidence intervals. This has the advantage that there are no special assumptions to be made and it can always be made compatible with your specific AC computation (normalization, padding etc.).
answered 1 hour ago
Jojo
664
answered 1 hour ago
Jojo
664
answered 1 hour ago
Jojo
664
answered 1 hour ago
Jojo
664
664
add a comment |Â
add a comment |Â
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Maybe try with a bootstrap method.
– user2974951
7 hours ago
@user2974951 thanks for your suggestion, I will try that. However, I was hoping to find out if some asymptotic approximation formula was available.
– Anya
6 hours ago