Filtering techniques and noise Suppose we have some house price data for 30 years (1970-1999). This is yearly data (30 data points). Suppose some major event $X$ happened on 1980. I want to see whether this event affected prices later on. Is using median filters a good methodology for detecting outliers in later years?
 A: I like the idea of looking for interventions that form level changes in a process.  This can be done using ARIMA models and search for the changepoints. Our friend IrishStat does this with his autobox software as he so nicely demonstated yesterday.
I am sure he will be happy to give you more details and perhaps even do a data analysis for you.
I wouldn't call the level shifts outliers.  There are various types of outliers in time series and numerous ways to try to detect them. We also discussed this either yesterday or today.  Fox identified two type of outliers in his paper from back in the 70s.
A: If you know a priori that a major event occurred at a specific point in time, then one could use a piece of software (that I won't mention because I blush easily!) and specify that this "cause variable" can have contemporaneous and lag structures, THEN a PDL or ADL can be identified to quantify the contemporaneous and lagged structure. This is known as a Transfer Function Model or as an ARMAX model. If you don't have access to this kind of (not-so-expensive) software, then simply lag the indicator/event variable as many times as you think appropriate and estimate the ARMAX model, which of course would include your ARIMA specification and any other indicators reflecting the impact of pulses, level shifts, seasonal pulses and local time trends that were necessary to yield a Gaussian error structure, a.k.a. white noise.
A: The general answer is No, especially, in econometrics. At the very least, you have to use a bunch of control variables: many things impact home prices. Also, you have to be aware of endogeneity: maybe this event was caused by other things, which also had impact on house prices. Establishing causal relationship in econometrics is very tricky.
You may want to look at regression discontinuity literature.
One last point: there's a ton of literature on house prices. You better have a good survey before starting your study.
