QUESTION:

If anybody has a handy way of dealing with this problem please let me know (with references please).

I thought this would be straightforward, but everybody I talk to gives me a different answer. I have two

short time series (of say 15 points) x and y and I want to test the significance of a regression of y on x.

I need to correct for the inflated degrees of freedom caused by the non-independence of the data.

The series are too short for ARIMA modeling, and I don't want to use first differences or detrended series

because that will eliminate most of the signal I am trying to capture. Any hints how to do this ? Also, what

can I do if one or both series has missing data, or if one of the series consists of only a fraction of the

points contained in the other.

ANSWER:

AFS has spent considerable time and interest in the problem you refer to. Our time series work uses the

tools of Transfer Functions to identify the form of the relationship. We extend the Transfer Function to

detect pulses, level shifts, seasonal pulses and time trends. Furthermore assumptions regarding

constancy of variance of the errors is tested and the analysis modified to reflect the results of the

hypothesis testing. Finally, gulp !, we speak to the issue of constancy of model/parameters leading to final

models. I suggest that you download the data for the CASE STUDY and attempt to use whatever

spreadsheet tool or limited time series tool like SAS or RATS or SHAZAM that you have access to.

These products have serious limitations as they relate or don't relate to your problem. AUTOBOX is

geared and focused directly on the problem you refer to. My opinions are somewhat biased but reflect 30

years of work in time series analysis and some 21 years of developing expert systems to aid users like

yourself. With respect to the paucity of data (15 values), I would like to say that you might do well by

setting up a starting model and allowing AUTOBOX to evolve from there by its rigorous tests of

necessity and sufficiency. When the number of values are small it sometimes is impossible to be purely

empirical and things can go better with a nudge in the right direction.

P.S. If you have missing data this can be treated via INTERVENTION DETECTION or OUTLIER ANALYSIS.

P.S.S The need for differencing and or time trends can be identified as part

P.S.S.S. There is no need to adjust for inflated degrees of freedom as the model ultimately incorporates a

gaussian process thus all Central Chi-Square tests follow.

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