Recurrence Quantification Analysis will allow you to look for the most relevant periods present in your data without imposing any stationarity constraint or continuous assumption directly in the time (not frequency !!!) space in terms of periods of recurrence. Moreover you can easily detect singularities, trends, laminarities, phase transitions and correlate these events with any external variables, look at the Norbert Marwan's website on recurrences where you can find many tutorials, even in my RG site you can download many papers on this technique.

Dear Milan,

Adding to the above,Standard approach to modeling event count data is to use a Poisson distribution.Poisson regression models are limited because they assume events are independent. Alternative models assume dependence: negative binomial and generalized event count (GEC). GEC and negative binomial are not appropriate for time series data. The current practices for time series count data are

PEWMA: Poisson Exponentially Weighted Moving Average Models a moving mean for persistent event count data.

PAR(p): Poisson Auto regressive Model of Order p Models a linear auto regressive, mean reverting event count series.

Thanks to both Alessandro and Venkata,

Alessandro - great suggestions, I'm not that familiar with RQA, particularly around inference wrt external variable, but I think a recurrence plot could be a very helpful visuallizaton in this case.

I had played with an R package for RQA a few years ago, but can't remember the name - do you have any software recommendations? I still need to check out your site, so forgive me if the info is right there...

Venkata,

Thank you, I'm not familiar with PEWMA or PAR but will look into these methods - can you recommend software (preferably R package)?. Of course my preference would be to simply use Poisson regression, if I can convince myself (and of course stat reviewer ultimately) that adjusting for fixed effects (weekday, month, year) will produce independent, or largely uncorelated poission distributed residuals. I'd been using autocorrelation plots to try to make this assessment, but I'm not sure about what cutoff to apply. Is there a rule of thumb?

FYI - I found the discussion thread at:

http://stats.stackexchange.com/questions/50677/testing-independent-of-data-assumption-before-doing-poisson-regression

This was very helpful - great idea to use the Durbin-Watson test statistic to assess correlation in residuals, using a bootstrap to avoid assuming normality. Nice approach, and I implemented it easily, but I totally agree with one of the helpful commentators in the thread Glen W that graphical methods are generally more useful. Bootstrap DW p-value for my dataset was .49, so good news, I also found an recurrence plot implementation in the R package "tseriesChaos" which I'm looking at right now...

Dear Milan,

you can use RQA descriptors to make inferences and correlation with any other variables, see for example:

http://www.biomedcentral.com/1472-6807/9/48

or the attached file

Thank you Jose,

I will try to take a look at the reference - I'm still working on understanding/implementing CAR and SAR spatial models so it may take me a while to work up to it.

Thanks to everyone who has contributed to this thread.

Ultimately, for the primary analysis we chose to use a Negative Binomial regression model, deciding that the assumption of serial independence was reasonable based on the Durbin Watson test (null distribution obtained by bootstrap) and examination of auto-correlation function plots. As a secondary sensitivity analysis, I fitted a simple AR(7) model (after trend/seasonality adjustment with NB regression) assuming normality, evaluating normality assumption with QQ plots and Kolmogarov-Smirnov test. Both approaches yielded consistent results. I'd like to explore other methods going forward and would appreciate any advice or comments.

The paper should be available online within the next week or so:

Sandhu A, Seth M, Gurm HS. Daylight savings time and myocardial

infarction. Open Heart 2014;1:e000019. doi:10.1136/openhrt-2013-

000019

Thanks again for all of the comments and advice, I don't usually work with time-series data so it was very helpful to hear different perspectives.