Dear all,
I have trouble finding a correct methodology to investigate if two time series are significantly different.
The data is e.g. two time series vectors with 1000 samples each.
The standard T-Test in R provides reasonable results, however when I use the "paired = TRUE" option, as I should (I guess, as the data is not independent in a time series?), also almost identical time series data is characterized as significantly different:
t = 30.831, df = 1000, p-value < 0.00000000000000022
please point me how to correctly analyze such data :-)
thank you!
Benedikt Gollan The following checklist may help
1. Check for Stationarity: Use the Augmented Dickey-Fuller (ADF) test to ensure both time series are stationary .
2. Differencing: If not stationary, difference the data until stationarity is achieved.
3. Use Appropriate Tests: For comparing time series, consider methods like Dynamic Time Warping (DTW) or the Cross-Correlation Function (CCF) .
4. Avoid Paired T-Test: Standard T-tests assume independence, which is often violated in time series data.
References:
1. Tsay, R. S. (2010). Analysis of Financial Time Series. Wiley.
2. Shumway, R. H., & Stoffer, D. S. (2017). Time Series Analysis and Its Applications: With R Examples. Springer.
3. Chatfield, C. (2003). The Analysis of Time Series: An Introduction. CRC Press.
I would like to add to Muhammad Haroon Shoukat recommendation that the t-test you are using considers only the mean of the two processes supposed to generate your series. Moreover, the test is not valid because you data are not iid? Testing the mean is not the most important. Follow his recommendations and look for tests comparing the autocorrelation functions. My paper with Roch Roy is available on RG.
To investigate if two time series are significantly different, it's crucial to account for their time-dependent structure, making standard t-tests potentially inappropriate. Begin by checking stationarity using the Augmented Dickey-Fuller test with the tseries package (adf.test). If non-stationary, difference the series and re-test. Next, analyze cross-correlation using the ccf function to identify dependencies. Advanced methods include using Dynamic Time Warping (dtw package) for non-linear alignments and fitting models like ARIMA (forecast package) to compare parameters or residuals. These approaches provide a more robust analysis, accounting for time dependencies. For more, see tseries, dtw, and forecast packages.
- Badges
- Science topic
- Similar topics
- Biological Science
- Biochemistry
- Biochemical Techniques
- Analytical Chemistry
- pH