We estimated ARIMA(0,1,1) instead of MA(1)

General
1

Course Name: Financial Time Series Analysis for Trading, Section No: 15, Unit No: 6, Unit type: Notebook

The notebooks says we fit an MA(1) and obtain the following fitted results:
πœ‡ = -0.21 πœƒ_1 = 0.04

However, this does not correspond to the output of the code, which is:
ma.L1 0.10
sigma2 0.95

Also, in the code, we see the following model:
ARIMA(order = (0,1,1))

That is not an MA(1) on y_t. That is an ARIMA(0,1,1):
(1 βˆ’ L) y_t = Ξ΅_t + θ₁ Ξ΅_{tβˆ’1}
Which means:
Ξ”y_t = Ξ΅_t + θ₁ Ξ΅_{tβˆ’1}
So the MA part applies to first differences, not to levels.

Questions:

  • How are the fitted results πœ‡ = -0.21 πœƒ_1 = 0.04 obtained
  • What is the correct model specification of the MA(1), compared to the ARIMA(order = (0,1,1))?
2

Hi,

The part which was written as β€œπœ‡ = -0.21 πœƒ_1 = 0.04” was a typo and this was corrected and the notebook was updated. As we had directly used the parameter, no other change is required and the performance of the model is the same.
The d parameter is kept as 1, as it is the difference parameter. Later on in section 18, we mention how we are using the β€œd” parameter for the ARIMA model.