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| Edward Jensen... |
 Posted: Mon Nov 02, 2009 6:03 pm |
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Guest
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Hi.
I'm doing some modeling of time series data recorded from a accelerometer at
rest for several hours.
I have the following empirical autocorrelation plot:
http://imageshack.dk/imagesfree/msi02421.png
I get a pretty good fit by taking the first derivative of the series and
fitting a MA(2) model, a ARIMA(0,1,2) model.
My question is: Can you see directly from the autocorrelation plot that this
is an appropriate model?
Thanks in advance. |
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| David Jones... |
| Posted: Tue Nov 03, 2009 5:04 am |
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Guest
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Edward Jensen wrote:
[quote]Hi.
I'm doing some modeling of time series data recorded from a
accelerometer at rest for several hours.
I have the following empirical autocorrelation plot:
http://imageshack.dk/imagesfree/msi02421.png
I get a pretty good fit by taking the first derivative of the series
and fitting a MA(2) model, a ARIMA(0,1,2) model.
My question is: Can you see directly from the autocorrelation plot
that this is an appropriate model?
Thanks in advance.
[/quote]
No. Suggest you do both:
(i) ACF plot of first differences
(ii) ACF plot of residuals from a smooothed trend line.
Also, plot series against time, with smoothed trend lines and a fitted linear trend and use this to help judge and appropriate model.
David Jones |
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| aruzinsky... |
| Posted: Tue Nov 03, 2009 6:01 am |
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Guest
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On Nov 2, 5:03 pm, "Edward Jensen" <edw... at (no spam) jensen.invalid> wrote:
[quote]Hi.
I'm doing some modeling of time series data recorded from a accelerometer at
rest for several hours.
I have the following empirical autocorrelation plot:http://imageshack.dk/imagesfree/msi02421.png
I get a pretty good fit by taking the first derivative of the series and
fitting a MA(2) model, a ARIMA(0,1,2) model.
My question is: Can you see directly from the autocorrelation plot that this
is an appropriate model?
Thanks in advance.
[/quote]
Just out of curiosity,
1. What is the sample mean (average) of the undifferenced data?
2. If the sample mean is not nearly zero, did you forget to subtract
it in calculating autocorrelation and/or model parameters?
3. After subtracting the sample mean, what do you get by LS fit of AR
(1) model, Xk = a1*Xk-1 + Ek, to undifferenced data? If |a1| < 1, you
probably shouldn't take difference the data. |
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| Edward Jensen... |
| Posted: Wed Nov 04, 2009 11:05 am |
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Guest
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"aruzinsky" <aruzinsky at (no spam) general-cathexis.com> wrote in message
news:8955efee-15d9-4e50-a516-1ecfa83cd71f at (no spam) a21g2000yqc.googlegroups.com...
On Nov 2, 5:03 pm, "Edward Jensen" <edw... at (no spam) jensen.invalid> wrote:
[quote]Hi.
I'm doing some modeling of time series data recorded from a accelerometer
at
rest for several hours.
I have the following empirical autocorrelation
plot:http://imageshack.dk/imagesfree/msi02421.png
I get a pretty good fit by taking the first derivative of the series and
fitting a MA(2) model, a ARIMA(0,1,2) model.
My question is: Can you see directly from the autocorrelation plot that
this
is an appropriate model?
Just out of curiosity,
1. What is the sample mean (average) of the undifferenced data?
[/quote]
mean(accelX)
[1] -190.7404
[quote]2. If the sample mean is not nearly zero, did you forget to subtract
it in calculating autocorrelation and/or model parameters?
[/quote]
No.
[quote]3. After subtracting the sample mean, what do you get by LS fit of AR
(1) model, Xk = a1*Xk-1 + Ek, to undifferenced data? If |a1| < 1, you
probably shouldn't take difference the data.
[/quote]
I get a1 = 0.0752
Here a plot of the autocorrelation of the residuals from the AR(1) model:
http://imageshack.dk/imagesfree/0ZN50110.png
Would you say this is good fit?
Based on the autocorrelation plot of the original time series, what made you
think that AR(1) was a good model?
I have read the chapter from Box and Jenkins about model identification.
Their approach is to first study the autocorrelation of the zeroth, first
and second order differenced time series. Based on where the correlations
and partial correlations become zero (or close to) they select an ARMA
model. In my time series the ACF of first order differenced data only show a
significant correlation at lag 1. That's why I tried to model the
differenced data.
Best regards,
Andreas |
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| Edward Jensen... |
| Posted: Wed Nov 04, 2009 11:12 am |
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Guest
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"Edward Jensen" <edward at (no spam) jensen.invalid> wrote in message
news:hcs8o0$seq$1 at (no spam) news.net.uni-c.dk...
[quote]"aruzinsky" <aruzinsky at (no spam) general-cathexis.com> wrote in message
news:8955efee-15d9-4e50-a516-1ecfa83cd71f at (no spam) a21g2000yqc.googlegroups.com...
On Nov 2, 5:03 pm, "Edward Jensen" <edw... at (no spam) jensen.invalid> wrote:
Hi.
I'm doing some modeling of time series data recorded from a
accelerometer at
rest for several hours.
I have the following empirical autocorrelation
plot:http://imageshack.dk/imagesfree/msi02421.png
I get a pretty good fit by taking the first derivative of the series and
fitting a MA(2) model, a ARIMA(0,1,2) model.
My question is: Can you see directly from the autocorrelation plot that
this
is an appropriate model?
Just out of curiosity,
1. What is the sample mean (average) of the undifferenced data?
mean(accelX)
[1] -190.7404
2. If the sample mean is not nearly zero, did you forget to subtract
it in calculating autocorrelation and/or model parameters?
No.
3. After subtracting the sample mean, what do you get by LS fit of AR
(1) model, Xk = a1*Xk-1 + Ek, to undifferenced data? If |a1| < 1, you
probably shouldn't take difference the data.
I get a1 = 0.0752
Here a plot of the autocorrelation of the residuals from the AR(1) model:
http://imageshack.dk/imagesfree/0ZN50110.png
Would you say this is good fit?
Based on the autocorrelation plot of the original time series, what made
you think that AR(1) was a good model?
I have read the chapter from Box and Jenkins about model identification.
Their approach is to first study the autocorrelation of the zeroth, first
and second order differenced time series. Based on where the correlations
and partial correlations become zero (or close to) they select an ARMA
model. In my time series the ACF of first order differenced data only show
a significant correlation at lag 1. That's why I tried to model the
differenced data.
[/quote]
I should also be noted that I have tried fitted AR models of increasing
order but based on AIC, the best model is about p = 190. By including a MA
term, I can get decent fits with just a couple of terms. |
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| aruzinsky... |
| Posted: Wed Nov 11, 2009 6:46 am |
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Guest
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On Nov 4, 10:05 am, "Edward Jensen" <edw... at (no spam) jensen.invalid> wrote:
[quote]"aruzinsky" <aruzin... at (no spam) general-cathexis.com> wrote in message
news:8955efee-15d9-4e50-a516-1ecfa83cd71f at (no spam) a21g2000yqc.googlegroups.com...
On Nov 2, 5:03 pm, "Edward Jensen" <edw... at (no spam) jensen.invalid> wrote:
Hi.
I'm doing some modeling of time series data recorded from a accelerometer
at
rest for several hours.
I have the following empirical autocorrelation
plot:http://imageshack.dk/imagesfree/msi02421.png
I get a pretty good fit by taking the first derivative of the series and
fitting a MA(2) model, a ARIMA(0,1,2) model.
My question is: Can you see directly from the autocorrelation plot that
this
is an appropriate model?
Just out of curiosity,
1. What is the sample mean (average) of the undifferenced data?
mean(accelX)
[1] -190.7404
2. If the sample mean is not nearly zero, did you forget to subtract
it in calculating autocorrelation and/or model parameters?
No.
3. After subtracting the sample mean, what do you get by LS fit of AR
(1) model, Xk = a1*Xk-1 + Ek, to undifferenced data? If |a1| < 1, you
probably shouldn't take difference the data.
I get a1 = 0.0752
Here a plot of the autocorrelation of the residuals from the AR(1) model:http://imageshack.dk/imagesfree/0ZN50110.png
Would you say this is good fit?
Based on the autocorrelation plot of the original time series, what made you
think that AR(1) was a good model?
I have read the chapter from Box and Jenkins about model identification.
Their approach is to first study the autocorrelation of the zeroth, first
and second order differenced time series. Based on where the correlations
and partial correlations become zero (or close to) they select an ARMA
model. In my time series the ACF of first order differenced data only show a
significant correlation at lag 1. That's why I tried to model the
differenced data.
Best regards,
Andreas
[/quote]
I can't be more specific because I haven't been active in time series
analysis for 20 years, but this is what I think I remember:
A little known important fact that is missing from many textbooks is
that Least Squares (LS) is a consistent estimator of both stable and
UNSTABLE AR processes, i.e., with poles inside, on, or outside the
unit circle. For example, if your data is a random walk,
Xk = Xk-1 + Ek,
then Least Squares will give an estimate a1 ~= 1. With your LS
estimate, a1 = 0.0752, your time series is not close to a random walk
therefore you should not difference the data after subtracting the
mean. This does not imply that an AR(1) model is best, it implies
that, after subtracting the mean, you should use an ARMA rather than
an ARIMA model. |
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