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How should I interpret a symmetrical autocorrelation plot?
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I have plotted a time series using pandas autocorrelation_plot and mathplotlibs acorr.
Notice that the above mathplotlibs image is symmetrical, what would this mean?
time-series forecasting autocorrelation
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Jim
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up vote
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I have plotted a time series using pandas autocorrelation_plot and mathplotlibs acorr.
Notice that the above mathplotlibs image is symmetrical, what would this mean?
time-series forecasting autocorrelation
asked 2 hours ago
Jim
1084
New contributor
Jim 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
1
down vote
favorite
up vote
1
down vote
favorite
I have plotted a time series using pandas autocorrelation_plot and mathplotlibs acorr.
Notice that the above mathplotlibs image is symmetrical, what would this mean?
time-series forecasting autocorrelation
asked 2 hours ago
Jim
1084
New contributor
Jim is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
I have plotted a time series using pandas autocorrelation_plot and mathplotlibs acorr.
Notice that the above mathplotlibs image is symmetrical, what would this mean?
time-series forecasting autocorrelation
time-series forecasting autocorrelation
asked 2 hours ago
Jim
1084
New contributor
Jim is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 2 hours ago
Jim
1084
New contributor
Jim is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited 3 mins ago
asked 2 hours ago
Jim
1084
New contributor
Jim is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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asked 2 hours ago
Jim
1084
asked 2 hours ago
Jim
1084
1084
New contributor
Jim is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
Jim is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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1 Answer
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The autocorrelation is the cross correlation of a signal with itself. Unlike the cross correlation between two different signals, the autocorrelation is always symmetric about zero (i.e. equal at lags $+tau$ and $-tau$). Because the positive and negative halves of the autocorrelation function are redundant, sometimes only the positive half is plotted, as in your first plot. If you plotted the negative half as well, it would be symmetric like your second plot.
answered 33 mins ago
user20160
14.4k12351
Clear and concise answer, thank you!
– Jim
13 mins ago
1
(+1) Otherwise put, the correlation between some $x$ at time $t$ and at time $t + tau$ is identical to the correlation between those quantities the other way round, just as the correlation between $x$ and $y$ is the same as that between $y$ and $x$. The detail that there are some $t$ without a corresponding $t + tau$ is solved by the correlation being defined only when both values are present (as is also true for $x$ and $y$, as in real datasets missing values are always possible). It's the same story if you think in terms of $t$ and $t - tau$.
– Nick Cox
7 mins ago
add a comment |Â
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
2
down vote
accepted
The autocorrelation is the cross correlation of a signal with itself. Unlike the cross correlation between two different signals, the autocorrelation is always symmetric about zero (i.e. equal at lags $+tau$ and $-tau$). Because the positive and negative halves of the autocorrelation function are redundant, sometimes only the positive half is plotted, as in your first plot. If you plotted the negative half as well, it would be symmetric like your second plot.
answered 33 mins ago
user20160
14.4k12351
Clear and concise answer, thank you!
– Jim
13 mins ago
1
(+1) Otherwise put, the correlation between some $x$ at time $t$ and at time $t + tau$ is identical to the correlation between those quantities the other way round, just as the correlation between $x$ and $y$ is the same as that between $y$ and $x$. The detail that there are some $t$ without a corresponding $t + tau$ is solved by the correlation being defined only when both values are present (as is also true for $x$ and $y$, as in real datasets missing values are always possible). It's the same story if you think in terms of $t$ and $t - tau$.
– Nick Cox
7 mins ago
add a comment |Â
up vote
2
down vote
accepted
The autocorrelation is the cross correlation of a signal with itself. Unlike the cross correlation between two different signals, the autocorrelation is always symmetric about zero (i.e. equal at lags $+tau$ and $-tau$). Because the positive and negative halves of the autocorrelation function are redundant, sometimes only the positive half is plotted, as in your first plot. If you plotted the negative half as well, it would be symmetric like your second plot.
answered 33 mins ago
user20160
14.4k12351
Clear and concise answer, thank you!
– Jim
13 mins ago
1
(+1) Otherwise put, the correlation between some $x$ at time $t$ and at time $t + tau$ is identical to the correlation between those quantities the other way round, just as the correlation between $x$ and $y$ is the same as that between $y$ and $x$. The detail that there are some $t$ without a corresponding $t + tau$ is solved by the correlation being defined only when both values are present (as is also true for $x$ and $y$, as in real datasets missing values are always possible). It's the same story if you think in terms of $t$ and $t - tau$.
– Nick Cox
7 mins ago
add a comment |Â
up vote
2
down vote
accepted
up vote
2
down vote
accepted
The autocorrelation is the cross correlation of a signal with itself. Unlike the cross correlation between two different signals, the autocorrelation is always symmetric about zero (i.e. equal at lags $+tau$ and $-tau$). Because the positive and negative halves of the autocorrelation function are redundant, sometimes only the positive half is plotted, as in your first plot. If you plotted the negative half as well, it would be symmetric like your second plot.
answered 33 mins ago
user20160
14.4k12351
The autocorrelation is the cross correlation of a signal with itself. Unlike the cross correlation between two different signals, the autocorrelation is always symmetric about zero (i.e. equal at lags $+tau$ and $-tau$). Because the positive and negative halves of the autocorrelation function are redundant, sometimes only the positive half is plotted, as in your first plot. If you plotted the negative half as well, it would be symmetric like your second plot.
answered 33 mins ago
user20160
14.4k12351
answered 33 mins ago
user20160
14.4k12351
answered 33 mins ago
user20160
14.4k12351
answered 33 mins ago
user20160
14.4k12351
14.4k12351
Clear and concise answer, thank you!
– Jim
13 mins ago
1
(+1) Otherwise put, the correlation between some $x$ at time $t$ and at time $t + tau$ is identical to the correlation between those quantities the other way round, just as the correlation between $x$ and $y$ is the same as that between $y$ and $x$. The detail that there are some $t$ without a corresponding $t + tau$ is solved by the correlation being defined only when both values are present (as is also true for $x$ and $y$, as in real datasets missing values are always possible). It's the same story if you think in terms of $t$ and $t - tau$.
– Nick Cox
7 mins ago
add a comment |Â
Clear and concise answer, thank you!
– Jim
13 mins ago
1
(+1) Otherwise put, the correlation between some $x$ at time $t$ and at time $t + tau$ is identical to the correlation between those quantities the other way round, just as the correlation between $x$ and $y$ is the same as that between $y$ and $x$. The detail that there are some $t$ without a corresponding $t + tau$ is solved by the correlation being defined only when both values are present (as is also true for $x$ and $y$, as in real datasets missing values are always possible). It's the same story if you think in terms of $t$ and $t - tau$.
– Nick Cox
7 mins ago
Clear and concise answer, thank you!
– Jim
13 mins ago
Clear and concise answer, thank you!
– Jim
13 mins ago
1
1
(+1) Otherwise put, the correlation between some $x$ at time $t$ and at time $t + tau$ is identical to the correlation between those quantities the other way round, just as the correlation between $x$ and $y$ is the same as that between $y$ and $x$. The detail that there are some $t$ without a corresponding $t + tau$ is solved by the correlation being defined only when both values are present (as is also true for $x$ and $y$, as in real datasets missing values are always possible). It's the same story if you think in terms of $t$ and $t - tau$.
– Nick Cox
7 mins ago
(+1) Otherwise put, the correlation between some $x$ at time $t$ and at time $t + tau$ is identical to the correlation between those quantities the other way round, just as the correlation between $x$ and $y$ is the same as that between $y$ and $x$. The detail that there are some $t$ without a corresponding $t + tau$ is solved by the correlation being defined only when both values are present (as is also true for $x$ and $y$, as in real datasets missing values are always possible). It's the same story if you think in terms of $t$ and $t - tau$.
– Nick Cox
7 mins ago
add a comment |Â
Jim is a new contributor. Be nice, and check out our Code of Conduct.
Jim is a new contributor. Be nice, and check out our Code of Conduct.
Jim is a new contributor. Be nice, and check out our Code of Conduct.
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