Correlation between an event and a time series I have a time series, e.g. the daily number of visitors on my blog. I have a set of events of some class, like the days when I made a new posting. I want to measure the effect of a new posting on the visitors. However, the effect of a new posting is not limited to the same day the posting was made. It could be days later.
So to generalize it: There is a (either discrete time or continous time) series of data points. There is a set of events given by their time instants. All events are believed to have a similar effect on the series, beginning from the event time and lasting for some time t_L.
Is there a statictical method to approach this problem? Am I missing some assumptions?
 A: This probably belongs on CrossValidated.  It seems like a reasonable question but not quite as easy as you might like to answer (without shortcuts).
A statistician's model of this would probably start with a Poisson-distributed response (reasonable for count data). It is most straightforward to assume that posting has an effect on the log-density of the Poisson response for each days.  So let's say we count the number of postings on the same day, one day before, two days before, $i$ days before, as $k_i$.  Then we could say something like
$$
\begin{split}
y_i & \sim \textrm{Poisson}(\eta) \\
\eta & = \exp\left(\beta_0 + \beta_1 \sum_{i=0}^{t_L} k_i \beta_2^i\right)
\end{split}
$$
That is, the effect of postings on the log-density declines geometrically with time since posting (set $\beta_2=1$ if you want the effects to remain constant over time until $t_L$ at which time they disappear, but this seems less realistic ...)
You could then estimate the parameters by maximum likelihood estimation (write computer code to compute the probability $L$ of the observed outcomes for a given set of parameters $\{\beta_j\}$, then find $\textrm{argmax}_{\{\beta_j\}} L$.
Some of the biggest things left out here:


*

*possibility of overdispersion, i.e. there is more variability in the daily counts than expected from the Poisson distribution, even after accounting for the posting pattern.  Using a negative binomial rather than a Poisson response is fairly straightforward.

*temporal autocorrelation.  This is a big one; we are implicitly assuming that the $y_i$ are conditionally independent. To allow for autocorrelation we would either have to add a (probably Gaussian) latent variable, or figure out what the marginal variance-covariance matrix would look like in the presence of autocorrelation ...

