QUESTION:

  allstat-request@mailbase.ac.uk Precedence: list Hello All, I hope this question isn't too easy for

you, but my knowledge of statistics is not particularly broad. I'm having some problems trying to

calculate confidence intervals for a 12 month moving average rate calculation for vehicle failure rates.

The calculation is based on a 12 month return figure divided by a 12 month moving average of the vehicle

registrations with an appropriate lag incorporated for the amount of time involved in processing the

information. I have tried using a the Binomial distribution as a model, giving 95% confidence intervals of

p+/-1.96*sqrt(p*q/n). np5 Is this correct with n as the 12 month moving average figure ? Can anyone can

point me to some literature on this ? Thanks Duncan Griffiths

ANSWER:

A twelve month moving average is a particular form of an ARIMA or Box-Jenkins model where a 12

period lag or a pure autoregressive structure is assumed. Furthermore, the parameters are constrained

to be equal ( 1/12 th for each and every one). This double assumption ( i.e. the form of the model and the

equality of the coefficients) can be overcome by time series modelling. In general the user should be

aware of any violation of the Gaussian assumptions and use software/procedures which are robust to

these and other proven violations. Some of the violations that are readily dealt with are

Constancy of the mean of the residuals ( via intervention detection providing in-line identification

of pulses,seasonal pulses, level shifts and local time trends). The mean of the residuals has to be

zero everywhere or at least proven to be not significantly different from zero.

Constancy of the variance of the process ( via either power transforms, log, square-root etc. or variance

change detection procedures leading to weighted estimation, akin to weighted least squares)

Constancy of parameters (via either Chow tests of Tong-like SETAR procedures) At the end of the day you

can use programs for ARIMA modelling , free CDC programs are hot-linked via http://www.autobox.com

like AUTOBOX or free ARIMA programs from the CDC. Please visit http://www.autobox.com for more

information and for the CDC website info. AUTOBOX allows you to constrain both model form and

parameters such that you can compute confidence limits from the model that you have assumed, always

dangerous even for Econometricians and others. Note that some work has been done using bootstrapping

essentially resampling the residuals to compute confidence limits. I would be grateful for any feedback

from the list on this topic.