Dear Academics,
I have two times series with 12 observations for each. Both are yearly quantitive data for last 12 years. I presented as graphs and it seems they have negative correlation.
How can I show the relationship between them statistically (first series effect on second or at least correlation)? Which tests should I perform?
Datas are non-stationary.
One thing to remember in research and statistics is that correlation is not always a sign of causation, which means that although two variables might be correlated to one another, one may not necessarily having a significant effect on the other.
If you want to test for correlation, you could either opt for Pearson's correlation (if both variables are continuous in nature and the data is normally distributed)- https://www.youtube.com/watch?v=S9j-wuPf1sI
Or, if the data is ordinal in nature, you could opt for Spearman's Rank Correlation- https://www.youtube.com/watch?v=SZoT95D9bBQ&t=12s
If you are convinced that one of the variables is surely having a significant impact on the other, then you could opt for regression analysis.
To statistically analyze the relationship between your two non-stationary time series with 12 observations each, you can follow these simplified steps:
1. Check for Stationarity: Use the Augmented Dickey-Fuller test to check each series for stationarity.
2. Make Data Stationary: If the series are non-stationary, difference them (subtract each value from its predecessor) to stabilize the mean and variance.
3. Correlation Analysis: Once the series are stationary:
- Pearson Correlation Coefficient: If the data seem normally distributed.
- Spearman's Rank Correlation: If the relationship doesn’t seem linear.
4. *Causality Test: If you're interested in how one series might influence another:
- Granger Causality Test: This assesses if past values of one series can predict future values of another.
5. Regression Analysis: Consider a simple linear regression if you're exploring how changes in one series potentially affect changes in the other, but check for autocorrelation in residuals.
These steps will help you establish both correlation and potential causal relationships in a statistically sound manner.
Hi Cem Avcı
Some information from RG:
https://www.researchgate.net/post/How_to_assess_synchrony_between_time_series
https://www.researchgate.net/post/Multiple-cross-correlation-function
However, as you said, the observations are few …
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