I would like to understand relationships between variables by which cross-correlation function, that means what is the extent one variable influence the other one.
ARMA model is used to fit two variables with time series structure. We know that the model requires the data to be stationary. Normally, we check the pattern by plotting the data. If a series is deemed nonstationary, we use differencing to make it stationary.
I also saw that there is a way to decompose the time series, and the residual time series from the seasonal decomposition is used as the starting point rather than the differenced series. See Worrall & Burt "Time series analysis of long-term river dissolved organic carbon records" (2004).
Any comments to help me understand the method will be appreciated.
I would like to spell the question with the example (Worrall.et.al 2004). Specifically, the step of the method and my understanding. If I were misunderstood, please feel free to correct me.
Step 1，decompose time series (TS) of color and TS of flow with function decompose() respectively, which to exact deflow$residuals, that the stationary of data is achieved.
Step 2, derive ARMA model for deflow$residuals with function arma() , that is describe the behavior of the flow TS.
Step 3, the ARMA of color TS be used to filter the color TS, that is describe the behavior of the color TS. But I don't understand why do not directly derive ARMA model fitting decolor$residuals? And which function for "filter"?
Step 4, calculating the residuals between of the floe and color with function cor(), which to represent how an unpredicted flow influences the color. Here confused, that the author expect influence on the color and why decompose color firstly?
Thanks for your patience upon my unmatured question.