First, I advise you to formulate clear hypotheses that you want to test. These are not accessible from your question alone.

Then, I recommend you test for autocorrelation in the data and choose an appropriate test.

Hope this helps.

Dear Dr. Heiko Balzter,

I want to perform trend analysis on Rainfall time series to check whether there is a trend in Monthly, seasonal or Annual time series.

From Literature, I came to know that the data may have the problem of Auto-correlation.

there are three phases of my intended research.

1. To check if the data is having the problem of auto correlated data?

In this case null hypothesis is that There is no Auto-correlation! and alternate hypothesis is the data is auto-correlated.

2.To check the seasonality in time series?

In this case null hypothesis is that There is no Trend! and alternate hypothesis is there is trend.

3.Find magnitude of the trend and change point analysis.

One of my colleague suggested me that on-ground rainfall data observation may not be correlated as they are individual observations at various time intervals. Is it true? Can I skip the test for auto correlation?

Or if I have to test for auto-correlation, what are the tests to be used?

For trend analyses, focus is increasingly being directed towards the consideration of long-range dependence than serial auto correlation in data. In other words, there are other critical issues to consider for more realistic change analyses than simply conducting the Mann-Kendall test.

Some of the issues may include:

1.  investigation of short-durational sub-trends alongside long-term trends

2. both method- and data-related uncertainty in trend analyses

3. influence of spatial heterogeneity and irregularity in data periods at different stations on trend results

For the above issues (as well as others), you can use the recently developed robust method for analyses of trend and sub-trends using the freely downloadable tool "CRD-NAIM" as well as the supporting documents or papers from the links below:

 https://www.researchgate.net/publication/309695087

https://www.researchgate.net/publication/305386142

https://www.researchgate.net/publication/275462047

https://www.researchgate.net/publication/303813632

https://www.researchgate.net/publication/283301923

https://sites.google.com/site/conyutha/tools-to-download 

Article Statistical Uncertainty in Hydrometeorological Trend Analyses

Article Statistical analyses of potential evapotranspiration changes...

Article Identification of sub-trends from hydro-meteorological series

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Article Analyses of rainfall trends in the Nile River Basin