I need to determine whether climatic data from two geographical location are similar or not, and explore the relation between this difference and the occurrence of particular disease in one location than the other in the framework of ecological research. My data are time-series of 3 year of historical climatic information from those locations (4 locations with a latitude gradient). Now I compared the with paired t-test, but I feel like this is not the suitable test to use. And, this test will not actually give me seasonality of data or give the relation between some events (occurrence of outbreak) and a peak of temperature or drought for example. I use SPSS and Matlab. Is there any routine to solve this issue?
One way to know if two series has similar temporal variability patterns is to perform a crosscorrelation analysis.
Previusly to this kind of test you must remove the autocorrelation of your time series to avoid spurious relationships. ARIMA is a good method to do this. You can obtain similar results removing the autocorrelation sources by mean of a deterministic models fitting linear trends, periodic trends, etc. obtainig stationary time series.
The problem of this kind of methods is that are very laborious and if you have not got experience working with them is difficult to obtain results with sense.
Is poisble perform these kind of analysis with SPSS and Matlab
One way to know if two series has similar temporal variability patterns is to perform a crosscorrelation analysis.
Previusly to this kind of test you must remove the autocorrelation of your time series to avoid spurious relationships. ARIMA is a good method to do this. You can obtain similar results removing the autocorrelation sources by mean of a deterministic models fitting linear trends, periodic trends, etc. obtainig stationary time series.
The problem of this kind of methods is that are very laborious and if you have not got experience working with them is difficult to obtain results with sense.
Is poisble perform these kind of analysis with SPSS and Matlab
Following a double - mass analysis it seems to be much simplier
If you are data are complete, then you can use dynamic time-warping algorithm (after removing noise) to determine where they correspond to each other and where they differ. Depending upon their score, you need to fix a threshold to determine if two of the time series comes have similar seasonality. You can even avoid deriving your own threshold by using some clustering algorithm. Kmeans is already available in MATLAB.
However, none of the methods would work, if your data is discontinuous....
I think you can use seasonal models for high frequency data. Spline functions could be a useful tool. Recently, we have proposed some procedures to compare seasonal patterns in daily price series. The paper is as follows:
Martín Rodríguez, G. y J.J. Cáceres Hernández (2013) Canary tomato export prices: comparison and relationships between daily seasonal patterns. Spanish Journal of Agricultural Research, 11(4): 882-893.
You can use a wavelet transform. I often applied it to different timeseries. Please see http://noc.ac.uk/using-science/crosswavelet-wavelet-coherence
kindly conduct independent T-test, to compare for the association if the sample size more than 90, if not up to 90 u do Rank Sum, or Wilcox Test
A different approach is to use an adaptive Wiener filter. It extracts the correlated part of the two time series and removes the uncorrelated part as noise. See attachment, which is from my texbook "MATLAB Recipes for Earth Sciences, 3rd Edition" (Springer, 2010), which you should use as the reference when using it.
Hi Oliver.
You have an interesting problem and has multiple edges because it includes many varables simultaneously from two different geographical areas. I propose two ways:
A) If you want to compare whether there are differences varable variable can use the t-student, or an analysis of variance either single or double.
B) But if you want to compare the influence of all variables at the same time, my recommendation is the multivariate statistics. In particular I suggest the Hotelling T2. I am attaching a function in Matlab that I use for this.
If you have any problems do not hesitate to contact me using it.
Best regards, Evelio
Olivier. I suggest this preliminar approach: 1) Choose your main variable, 2) Get small seasonal data sets for each region. 3) For each region-season separate the media value from the distribution structure. 4) Compare media estimates between two years. 5) Compare distribution structure variations between two years. Apply your experience at the moment of interpretation.
This surely takes a long time effort. So it helps to simplify and limit the context (years, regions, seasons, measured variables ..) to keep your research under control..
In general it is necessary to study first each context data with respect to itself -for just one variable- and then proceed to make other comparisons: inter-regional, inter-seasonal, inter-year, etc.
The last step is to enter multivariable analysis, which has also its big risks. OK, best wishes, emilio
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