I would like to perform a time series analysis on two countries. To be more precise, I would like to discuss the effect of an event in country 1 on country 2. I was thinking about using GDP growth or exports to analyse the effects. However, I am not sure if this will be sufficient. Furthermore, I am also wondering which statistical technique I could use in this case.

A more concrete example would be: I want to determine the effect of a crisis in Argentina on Brazil. Let's say I determine this using the data on Foreign Direct Investment. I then want to research the effect of the crisis of 2001 in Argentina on the GDP of Brazil. What technique could I use?

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    $\begingroup$ regression might be good to start off with $\endgroup$
    – Taylor
    Oct 18 '17 at 15:41
  • $\begingroup$ change-point detection, or intervention analysis $\endgroup$ Oct 18 '17 at 15:44

You will want to build a regression model for this. The proper way is to use a Transfer Function modelling process as described in Chapter 11 of the Box-Jenkins textbook.

I can summarize for you.....

The procedure for transfer function model identification outlined by Box and Jenkins uses the cross correlations between two prewhitened series to tentatively identify model form. The first step to this process is to develop an ARIMA model for each of the user-specified input time series in the equation. Each series must then be made stationary by applying the appropriate differencing and transformation parameters from its ARIMA model. The stationary time series are, in turn, "prewhitened". Prewhitening refers to the process of applying a given set of autoregressive and moving average factors to a stationary series. The stationary output series is prewhitened by the input series AR and MA factors. If there is more than one input series, then the stationary output series is prewhitened once for each different input. Prewhitening is necessary because it removes the intrarelationship in the individual series. This allows you to more accurately assess the interrelationship between the input and the output series. The cross correlations between the prewhitened input and output reveal the extent of this interrelationship. The cross correlations can be converted to estimates of the impulse response weights or regression weights. The pattern in the impulse response weights indicate can suggest a tentative transfer function model. By applying these impulse response weights to the input series to predict the output series,one can generate a preliminary estimate of the noise series. Following the rules for ARIMA model identification, the patterns in the autocorrelations and partial autocorrelations of the tentative noise process give clues as to the initial form of the noise model. Given the identified transfer function and noise model, one can proceed to the model estimation/diagnostic checking phase.

  • $\begingroup$ First of all thank you a lot for the comment. The method you suggest seems the correct one and I will look into it and try to apply it to my problem. However, I was wondering about the use of cointegration, Granger Causality and an Error correcting model. Would these methods also be a valid way to analyze my problem? $\endgroup$ Oct 20 '17 at 10:48

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