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))?