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Science Forum Index » Statistics - Math Forum » Determining ARIMA model
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| Guest |
 Posted: Fri Apr 11, 2008 10:45 pm |
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Hi,
I'm new to ARIMA modelling and I'm not sure if I'm determining the
model correctly. Using some stock market data, I obtained the acf and
pacf from the raw data, as shown below. My questions are:
1) Since I've about 2020 data (one standard error is about 0.04),
there are significant acf & pacf terms at lag 33. Do I need to do a
first difference and obtain the acf & pacf? I can't find any reason to
do so as the acf doesn't show the characteristic of a unit root (very
slow damping with the first lag term close to 1), but I'm not entirely
sure.
2) The ACF & PACF doesn't give me a good idea on what model I should
use, so I tested with AR(1) & MA(1) models. Both seemed reasonable
(see further below for results). In this case, which model should I
choose as the forecast? I've tested with ARMA(1,1), AR(2), MA(2)
models but none provide better results. Am I missing any other tests?
ACF PACF Q-Stat Prob
0.087 0.087 15.447 0.000
-0.017 -0.025 16.050 0.000
-0.018 -0.015 16.738 0.001
-0.045 -0.042 20.770 0.000
0.003 0.010 20.784 0.001
0.002 -0.001 20.791 0.002
-0.025 -0.026 22.069 0.002
0.013 0.016 22.427 0.004
0.050 0.048 27.534 0.001
-0.016 -0.025 28.034 0.002
-0.004 -0.001 28.071 0.003
0.018 0.021 28.712 0.004
0.035 0.035 31.170 0.003
0.000 -0.009 31.170 0.005
0.008 0.012 31.308 0.008
0.025 0.029 32.550 0.008
-0.012 -0.017 32.866 0.012
-0.010 -0.010 33.071 0.016
-0.026 -0.021 34.481 0.016
-0.026 -0.019 35.818 0.016
0.017 0.015 36.396 0.020
0.012 0.004 36.671 0.026
-0.001 -0.001 36.671 0.035
0.047 0.045 41.246 0.016
0.028 0.018 42.796 0.015
0.012 0.011 43.091 0.019
-0.026 -0.027 44.470 0.018
-0.005 0.007 44.526 0.025
-0.040 -0.041 47.875 0.015
-0.038 -0.034 50.855 0.010
-0.035 -0.030 53.342 0.008
-0.033 -0.027 55.528 0.006
-0.050 -0.055 60.739 0.002
-0.023 -0.023 61.864 0.002
-0.018 -0.018 62.509 0.003
0.017 0.017 63.136 0.003
Variable Coefficient Std. Error t-Statistic Prob.
C -9.97E-05 0.000163 -0.612198 0.5405
AR(1) 0.087370 0.022152 3.944108 0.0001
Variable Coefficient Std. Error t-Statistic Prob.
C -0.000108 0.000162 -0.665206 0.5060
MA(1) 0.091252 0.022164 4.117132 0.0000
Thank you. |
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| Guest |
| Posted: Sat Apr 12, 2008 3:45 pm |
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On Sat, 12 Apr 2008 01:45:04 -0700 (PDT), thampw@hotmail.com wrote:
Quote: Hi,
I'm new to ARIMA modelling and I'm not sure if I'm determining the
model correctly. Using some stock market data, I obtained the acf and
pacf from the raw data, as shown below. My questions are:
1) Since I've about 2020 data (one standard error is about 0.04),
there are significant acf & pacf terms at lag 33. Do I need to do a
first difference and obtain the acf & pacf? I can't find any reason to
do so as the acf doesn't show the characteristic of a unit root (very
slow damping with the first lag term close to 1), but I'm not entirely
sure.
2) The ACF & PACF doesn't give me a good idea on what model I should
use, so I tested with AR(1) & MA(1) models. Both seemed reasonable
(see further below for results). In this case, which model should I
choose as the forecast? I've tested with ARMA(1,1), AR(2), MA(2)
models but none provide better results. Am I missing any other tests?
snip
You don't say what the stock market data is. Prices? returns?
Individual stocks? An index? What frequency? You might get a better
answer if you could expand a little on this.
-Dick Startz |
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| Guest |
| Posted: Sat Apr 12, 2008 6:46 pm |
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Quote: You don't say what the stock market data is. Prices? returns?
Individual stocks? An index? What frequency? You might get a better
answer if you could expand a little on this.
I didn't know it makes a difference on what stock market data it is.
Anyway, it's a daily return of an index. |
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| Guest |
| Posted: Sun Apr 13, 2008 10:12 am |
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On Sat, 12 Apr 2008 21:46:28 -0700 (PDT), thampw@hotmail.com wrote:
Quote:
You don't say what the stock market data is. Prices? returns?
Individual stocks? An index? What frequency? You might get a better
answer if you could expand a little on this.
I didn't know it makes a difference on what stock market data it is.
Anyway, it's a daily return of an index.
There is a huge amount of research on the behavior of returns on stock
market indices, at least for developed countries. The return is very
close to random, with a distribution that has fat tails. The return is
stationary, so you certainly do not want to first-difference it. At
daily horizons you may find very small amounts of serial correlation,
which it appears you do. Th return is almost completely unpredictable
though. You might look at The Econometrics of Financial Markets, by
Campbell, Lo, and MacKinlay.
-Dick Startz |
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| Guest |
| Posted: Sun Apr 13, 2008 1:53 pm |
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Quote: There is a huge amount of research on the behavior of returns on stock
market indices, at least for developed countries. The return is very
close to random, with a distribution that has fat tails. The return is
stationary, so you certainly do not want to first-difference it. At
daily horizons you may find very small amounts of serial correlation,
which it appears you do. Th return is almost completely unpredictable
though. You might look at The Econometrics of Financial Markets, by
Campbell, Lo, and MacKinlay.
-Dick Startz
Thanks for the advice, Dick. I'll take a look at the book.
Cheers! |
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