Re: goodness of fit test for data over time
- From: dave@xxxxxxxxxxx
- Date: 11 Jul 2006 12:45:37 -0700
jl wrote:
I have a set of measurements taken over a period of time, {(x1,
t1),...,(xn, tn)} where xi was the measurement at time ti and the ti
are evenly spaced times. There is clearly some trend in the data, say
it is parabolic, decreasing at earlier ti and increasing at later ti.
So I fit some polynomials to this data, say a quadratic f1(t), and then
a quartic f2(t).
I would like a goodness of fit test that will spit out a test statistic
that will allow me to test the hypothesis that the data set {(x1,
t1),...,(xn, tn)} follows the curve f1.
Ultimately the goal would be to use the test statistic to tell me
whether f1 is a better fit than f2.
Can anyone direct me to such a method for comparing fitted curves (in
general and not just for this specific case)?
Thanks,
JL
JL ..
Characterizing a set of equally spaced values can be approached by
fitting high order polynomials and then after insuring the residuals
are free of any autocorrelative structure, any anomalies such as
Pulses, Level Shifts, Seasonal Pulses and or Local Time Trends, and
that the variance of the errors is constant over time and that the
parameters of the model are invariant over time ....one could then
compute ( and believe ! ) t values in order to assess model adequacy.
The practice of fitting high order polynomials has long since been
discarded by statisticians in favor of developing hybrid models which
explicitely take into account previous values vua autoegressive
structure and any necessary dterministic structure such as level shifts
and time trends ( both linear , quadratic etc as needed ). Test s of
necessity and sufficiency are accomplished yielding a parsimonious
model.
This is done for all other parallel time series.
Tests of commonality of parameters yields a conclusion about any
statistically significant difference between series. THis is known in
the literature as ppoled cross-sectional time series analysis.
We at AFS have implemened such tests in our award winning software (
AUTOBOX / FreeFore)
You can download a Freeware Version from http://www.autobox.com which
will allow you to analyze each series separately. To actually perform
the test for commonality of coefficients over the series will require
you to purchase a professional version.
If you want to chat about time series ..please feel free to call .
Dave Reilly
Automatic Forecasting Systems
http://www.autobox.com
215-675-0652
.
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