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I have 3 time-series, shown in the plot below:

enter image description here

The plot shows a specific time frame for the 3 time-series data.

I'm aware that some questions were posted around this subject (time-series trend comparison) but I couldn't find a plausible solution for my problem. I'll post some of the links I've used:

How to statistically compare two time series?

Quantifying similarity between two data sets

https://www.researchgate.net/post/How-can-we-statistically-compare-difference-between-two-trends

Quick description of the data:

Both 3 time-series represent NDVI data from an herbaceous layer. The H LINEAR is the NDVI taken from one specific sensor and the others L FOURIER1 and L FOURIER2 are from another sensor. Just to clarify, H LINEAR time series data is from sensor1, and L FOURIER1 and FOURIER2 are from sensor2.

H LINEAR time-series data was linearly interpolated. This data is my core data which I'll be using to validate other data.

L FOURIER1 and L FOURIER2 time series data are data from sensor2 were "Fourier" interpolated to get rid of the noise (measurements from sensor2 inaccurate compared with sensor1)

MY QUESTION IS: What statistical method can I use to compare the trend of H LINEAR with FOURIER 1 and H LINEAR with FOURIER2 in order to understand which time series (L FOURIER1 or L FOURIER2) will better match the trend of H LINEAR?

In other words: Which FOURIER, 1 or 2 time series data can better explain the trend of H LINEAR?

I'm looking for a statistical method that would return one value that will identify a similar trend or not.

I'll post an example of the data below:

dput(head(df1,20))
structure(list(Date = structure(c(15076, 15077, 15078, 15079, 
15080, 15081, 15082, 15083, 15084, 15085, 15086, 15087, 15088, 
15089, 15090, 15091, 15092, 15093, 15094, 15095), class = "Date"), 
    H_LINEAR = c(0.5545, 0.552, 0.5496, 0.5471, 0.5446, 0.5421, 
    0.5396, 0.5371, 0.5346, 0.5322, 0.5297, 0.5272, 0.5247, 0.5222, 
    0.5197, 0.5172, 0.5147, 0.5116, 0.5084, 0.5052), L_FOURIER1 = c(0.5109, 
    0.5105, 0.5101, 0.5097, 0.5094, 0.509, 0.5087, 0.5084, 0.508, 
    0.5077, 0.5074, 0.5071, 0.5068, 0.5065, 0.5062, 0.506, 0.5057, 
    0.5054, 0.5051, 0.5049), L_FOURIER2 = c(0.5368, 0.5365, 0.5361, 
    0.5357, 0.5354, 0.5351, 0.5347, 0.5344, 0.5341, 0.5338, 0.5335, 
    0.5332, 0.533, 0.5327, 0.5324, 0.5321, 0.5319, 0.5316, 0.5313, 
    0.5311)), row.names = 9857:9876, class = "data.frame")

So far I've used the following statistical methods:

  1. correlation coefficient: not suitable since it looks over the values and not the trend

  2. t-test: useful to compare the slope between two time-series but the t-test for this example is not sensitive enough and the p-value is always low (<0.001)

  3. granger test: until now seems the best method for but since this method is used values of series A at time t and predict the values of series B at time t+1, does not give me the confidence to advance

values of series A at time t can predict the values of Series B at time t+1.

NOTE: I have a lot of time-series data from other sensors and visual analysis already made me select a few time-series data but now I need some statistical background to justify my choices.

Sorry if I miss some technical information, I'm quite new to statistics and r programming.

Any help will be much appreciated.

Cláudio Siva
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0 Answers0