Time Series Analysis: time lag and decomposition

Hi everyone,

currently I'm working on a project where I want to test effects of external indicators on internal sales data.
So I already collected a lot of data and now want to compare two time series. But there are some things I'm not sure about:

  1. Is it recommendable to decompose each time series in advance? So basically I would test the random component of time series 1 against the random part of time series 2? Thus I dont attribute an effect to the "predictor" that is just based on high seasonality / trend for both time series?
  2. If some data is only available on a quarterly basis, is it ok from a statistical point of view to divide that time series by 3 in order to get monthly data?
  3. When data preprocessing is done: I'd conduct a cross correlation test to account for time-shifted correlation, what measurements should I take to ensure those findings are valid (ACF, PACF)?
Thanks in advance! If there is any literature especially on 1., I'd be super happy for you to share it with me.

Best regards,


Less is more. Stay pure. Stay poor.
I am not well versed in time series, so I will contribute what I can.

#1, yes it would seem advantageous to, at the bare minimum, decompose each to understand its trend, seasonality, and irregularity aspects.

#2, What would be the purpose of dividing it into months, getting more observations? There would be obvious risks in doing this, for example you can look at annual data for a time series and not see any seasonality when it actually exists. So if you had annual data and you turned it into 12 observations you would lose that important feature and its variability would be misrepresented. The same thing could happen in your example, your series would seem like it has less variability than it truly may have and there could be a true trend within the quarter that you are now assuming is stationary since you would have four congruent values.

#3, What would be the difference in what you are doing and in ACF? Not quite following.


No cake for spunky
There are many types of time series methods and what is recommended depends on which method you use.

"If some data is only available on a quarterly basis, is it ok from a statistical point of view to divide that time series by 3 in order to get monthly data?"

Although I have never seen that question raised almost certainly not. For one thing this would likely distort if seasonality or Stationarity exists since you are artificially splitting the data evenly and assigning it to the 3 periods - when in fact the data can not be assumed to be even across periods. If the data would have been 4,3,2 making it 3,3,3 will distort the results.

This would be particularly critical in an approach like ESM or (because it is searching for AR or MA patterns) ARIMA.

I am not sure what you mean by 3. You use ACF or PACF to suggest serial correlation in your data that you then remove in ARIMA>