Time Series - Difference over time


New Member

I'm new in the time series, so I need some help. I have a short time series (5 quarters), with the proportion of a parameter (public transport-user people). I know there are some effects of TS (trend, seasonal, cyclic and random).

I would like to testing the (significant) difference of two quarters's proportions, such as is there any difference between the proportion of public tranport users of the 4th quarter and the 5th one.

My first question is that sould I firstly test, that my time series is stational in this case.
My second question is that, if it is stational, could I use 'general' significant test?
My third one, if it's not stational, how can I test the differences?

Thanks in advance!


No cake for spunky
As someone who has worked to learn this for years - good luck :p

5 quarters really is not enough data points for time series. The rule of thumb is you need at least 50 points givens issues such as seasonality. If you can run this as days or months that would be much better.

The first thing to test with time series is if you have stationarity. Dickey Fuller is the most common test [all of the stationarity test have power problems so it is often recommended you run a test that the null is stationarity and the null is not stationarity]. I am not sure with so few data points it is even reasonable to test for stationarity.

I have not seen time series used as you are suggesting. That said I would do a Durbin Watson, or the more advanced test for serial correlation. If there is none do a normal statistical test. If there is serial correlation than you have to use an approach such as Regression with correlated error. None of this works with non-stationarity, you have to transform [difference] the data first.
Noetsi-I don't agree with that type of rule of thumb approach. Box-Jenkins said you needed 60 months of data. Makradakis 20 years later said you needed 36. The reality is that it is all about the signal to ratio. 5 quarters is way to short. You should have 3x the seasonality IF there is seasonality.
A stationary time series is one whose statistical properties such as mean, variance, autocorrelation, etc. are all constant over time. Most statistical forecasting methods are based on the assumption that the time series can be rendered approximately stationary (i.e., "stationarized") through the use of mathematical transformations.