In Table 1, the model specified for the Gross Domestic Product (GDP) is reported as ARIMA(1, 0, 2). This parameterization, with an integration order of d=0, indicates that the GDP series was treated as a stationary process.
This is highly problematic from both a theoretical and empirical standpoint!!
Theoretical Non-Stationarity: GDP is a canonical example of a macroeconomic series that exhibits a stochastic trend. It is widely accepted in the econometrics literature that such series are non-stationary in levels (i.e., they are integrated of order 1, I(1), or higher). Fitting an ARMA model (which is equivalent to ARIMA(p,0,q)) to a non-stationary series is a classic case of spurious regression. The model may produce seemingly good in-sample fit and high R² values, but the parameter estimates are inconsistent, and the out-of-sample forecasts are unreliable.
1. The paper correctly states on Page 3: “The ARMA model can only be used on stationary data. In practice, many time series are non-stationary… it is necessary to differentiate the data series.” The application of d=0 to GDP directly contradicts this stated principle.
2. The manuscript does not report the results of standard unit root tests (e.g., Augmented Dickey-Fuller, KPSS) to justify the stationarity of the GDP series. Without this critical diagnostic step, the choice of d=0 appears unsupported and is likely incorrect.
3. The reported forecast accuracy for GDP (MAPE of 9.16%) is potentially misleading. The model is likely capturing the inherent trend in an invalid way, and its predictive performance for turning points or future periods would be highly questionable. Since GDP is a primary driver of economic health and a key variable in the analysis, this specification error casts doubt on the broader findings and policy implications that rely on the GDP forecasts.
I would be very interested to hear the authors’ justification for treating the GDP series as stationary. Could they provide the results of the unit root tests conducted during the model identification phase? A re-specification of the GDP model with an appropriate d>0 would be essential to validate this part of the study’s conclusions.