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I'm building an Error Correction Model using the Engle-Granger approach with the following interest rates data: Observations: 230 Periodicity: Monthly

I have the following model:

$$\Delta R_t = \sum_{i=1}^{p}\beta_t \Delta R_{t-i} + \sum_{i=0}^{q}\gamma_t \Delta PR_{t-i} + \delta ECT_{t-1} + \varepsilon_t$$

Where R= Interest rate,PR= Policy rate and ECT = error correction term obtained from the long-run model.

I have trouble because of the following tests results:

  1. Jarque-Bera Normality Test rejects normality in residuals.

  2. LM test with 4 lags rejects no autocorrelation in errors.

  3. ARCH-Test with 4 lags rejects null hypothesis.

(I must accept lag selection in these two last tests was based on a rule of thumb, which I feel ends up being arbitrary)

Where should I start looking for errors? Was it lag selection of p and q? Was the specifications set on the tests above? Was the long-run model?

And if I can't solve it how can I "get around" it?

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