Time series data

#1
Hi. I'm trying to see if there is a relationship between fire safety input to residents and real data about the number of fires, casualties and the severity of fire. Just thinking about the number of fires, I used a simple regression model. The number of visits per month is the independent variable and the number of fires per month is the dependent variable. I used data from April 2015 to April 2019. The model indicated there was no correlation or relationship between the two. But then I started thinking that the effect of the visit might not be immediate. The household may have a fire, but months or years down the line. Should I just accept that regression isn't the way to look at this or is there something I can do to better use time series data like this. I was hoping to see evidence that our fire safety visits reduce fires and casualties or reduce fire severity. I'm very new to this so don't have a great understanding of which models work for which problem. I'd be grateful for being put on the right path. I've tried googling this but not found the answer.
 

noetsi

Fortran must die
#2
All the multivariate time series methods are extremely complicated. You should spend a fair amount of time reading them before you pursue that (I have spent over 5 years doing so and essentially have given up because of the complexity of the issues and the lack of good sources to consult in time series on disputed points). For example if the different series/variables are integrated of a different order how do you address this (or even can you, there is disagreement on this topic ). How do you address cointegration which will influence the method you chose to analyze data with?

One example of the difficulty is that there is not a single person on this board who would claim to be an expert on this topic :)
 
#3
All the multivariate time series methods are extremely complicated. You should spend a fair amount of time reading them before you pursue that (I have spent over 5 years doing so and essentially have given up because of the complexity of the issues and the lack of good sources to consult in time series on disputed points). For example if the different series/variables are integrated of a different order how do you address this (or even can you, there is disagreement on this topic ). How do you address cointegration which will influence the method you chose to analyze data with?

One example of the difficulty is that there is not a single person on this board who would claim to be an expert on this topic :)

Thanks for the response, even if I didn't get the answer I sought (though I did in a way - don't spend anymore time torturing myself! Which is very helpful). This would probably explain why no one has ever published anything that links fire safety input to reduced fires or fire severity. I'll stick to the qualitative research I think!
 

noetsi

Fortran must die
#4
To me, admittedly not a statistician, multivariate time series is as complex as it gets. And the fact that, as on this board, so few are expert in it tends to support this view. Univariate time series, like exponential smoothing and ARIMA, while not simple are a lot easier to use. But they don't help when you want to use multiple variables.

Vector Autoregressive Models (or with Cointegration Vector Error Correction models) are the state of the art as far as I know if you do chose to pursue that. Another thing you could try is regression with ARMA error. Be warned that such models tend to have lags of Y and if you use lags of Y autocorrelation (contrary to what you might read) will cause bias. So you need to do something like Breusch Pagan test to check for this (not Durbin Watson which is in all the text but is decades out of date).