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SARIMAX (ARIMA(2,1,2)) Model Results for GDP Growth (%)

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Collins Odhiambo

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Source: Finance & Economics Dataset (2000 – 2025), estimated in Python (statsmodels SARIMAX).

| Parameter | Coefficient | Std. Error | z-Statistic | P >| z | | 95% Confidence Interval |
|————|————–|————|————-|——-|—————————|
| AR(1) | -0.9939 | 0.019 | -51.18 | 0.000 | [-1.032, -0.956] |
| AR(2) | 0.0058 | 0.018 | 0.32 | 0.753 | [-0.030, 0.042] |
| MA(1) | -0.0009 | 16.239 | ≈ 0.00 | 1.000 | [-31.829, 31.828] |
| MA(2) | -0.9991 | 16.226 | -0.06 | 0.951 | [-32.801, 30.802] |
| σ² | 18.3716 | 298.365 | 0.06 | 0.951 | [-566.413, 603.157] |

Model Fit Statistics

Metric Value Interpretation
Log-Likelihood -8624.27 Model likelihood under estimated parameters
AIC 17258.55 Used for model comparison (lower = better fit)
BIC 17288.58 Penalizes model complexity
HQIC 17269.35 Balanced criterion between AIC and BIC
Ljung-Box (Q) p-value 0.98 Residuals ≈ white noise (no autocorrelation)
Jarque-Bera p-value 0.00 Residuals are non-normal (light tails)
Heteroskedasticity (H) p-value 0.43 No significant variance instability detected

Interpretation

  1. Model Structure

    • The best-fit model is ARIMA(2, 1, 2), implying:

      • p = 2: Two autoregressive lags capture persistence in GDP growth.

      • d = 1: first differencing removes trend, making the series stationary.

      • q = 2: Two moving-average terms account for short-term shocks.

  2. Significance

    • Only AR(1) is statistically significant (p < 0.001), suggesting that last-period growth is the main driver of current growth movements.

    • Other lags and MA terms are statistically insignificant, indicating a limited contribution to model performance.

  3. Goodness of Fit

    • AIC ≈ 17 258 and BIC ≈ 17 289 show moderate fit.
      Despite residual non-normality (JB p < 0.01), the absence of autocorrelation (Q p ≈ 0.98) confirms dynamic adequacy.

  4. Variance & Stability

    • The estimated σ² ≈ 18.37 suggests mild volatility.
      Low heteroskedasticity implies a stable conditional variance across the sample.

Economic Insight

  • The strongly negative AR(1) (-0.99) reveals a mean-reverting behavior—periods of above-average growth tend to be followed by slowdowns and vice versa.

  • This aligns with the classical business-cycle mechanism: expansions naturally self-correct as inflationary or structural pressures accumulate.

  • Insignificant MA terms indicate that random shocks (policy announcements, external demand changes) do not systematically persist beyond one period.

  • In practical terms, the economy appears to be cyclically stable, with growth responding more to its own history than to stochastic disturbances.

Policy Implications

Aspect Interpretation Policy Recommendation
Cyclical Persistence GDP growth reacts primarily to previous values Maintain counter-cyclical policies to avoid overshooting.
Shock Absorption Limited MA effect → quick dissipation of random disturbances Build fiscal buffers to stabilize unexpected fluctuations.
Variance Stability Homoscedastic residuals Continue a consistent monetary policy to preserve volatility control.
Forecasting Reliability Model captures trend but underestimates tail events Integrate volatility extensions (ARCH/GARCH) for risk assessment.

Technical Summary

Specification Value
Model Type SARIMAX / ARIMA(2, 1, 2)
Dependent Variable GDP Growth (%)
Estimation Method Maximum Likelihood Estimation (MLE)
Sample Period 2000 – 2008 (3000 observations)
Software Python (statsmodels v0.14)
Transformation First Difference (ΔGDP Growth)
Diagnostics Ljung-Box and Jarque-Bera tests applied to residuals

Acknowledgment

Prepared by: Collins Odhiambo Owino
Institution: DatalytIQs Academy — Division of Econometrics & Financial Analytics
Software: Python (statsmodels, matplotlib)
Dataset: Finance & Economics Dataset (2000 – 2025), Kaggle.
License: Educational Research License — DatalytIQs Open Repository Initiative

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