Panel ARIMA Model
Panel Autoregressive Integrated Moving Average Model · Also known as: Panel ARIMA, ARIMA for panel data, cross-sectional ARIMA, multi-unit ARIMA
The Panel ARIMA model extends the classical Box-Jenkins ARIMA framework to panel data, fitting autoregressive integrated moving-average dynamics to multiple cross-sectional units observed over time. It accommodates unit-specific short-run dynamics and non-stationarity, making it suitable for forecasting and dynamic analysis when both cross-sectional and temporal dimensions are present.
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When to use it
Use Panel ARIMA when the data form a panel (N units, T periods) and each unit's series exhibits time-series structure — trends, seasonality, or autocorrelation — that a simple pooled cross-sectional regression ignores. It is especially valuable for short-term forecasting at the unit level, for modelling impulse responses to shocks, and when T is long enough (generally T > 20 per unit) to estimate unit-specific ARIMA orders reliably. Avoid Panel ARIMA when T is very short (T < 10) because ARIMA order identification becomes unreliable; in that case a simpler pooled AR or dynamic panel GMM estimator is more appropriate. Also avoid it when the research question concerns long-run equilibrium relationships rather than short-run dynamics — cointegration methods such as Panel VECM or Panel ARDL are better suited there.
Strengths & limitations
- Captures rich unit-specific short-run dynamics including trends, cycles, and shock persistence.
- Handles non-stationary panel series through systematic differencing, avoiding spurious regression.
- Flexible order selection (p, d, q) per unit allows heterogeneous dynamics across cross-sections.
- Well-suited for multi-step-ahead forecasting at the individual unit level.
- Grounded in the mature Box-Jenkins methodology with well-understood identification criteria (ACF, PACF, AIC, BIC).
- Requires moderately long time series per unit (T > 20 recommended) for reliable order identification; short panels make ARIMA fragile.
- Unit-by-unit estimation ignores potential efficiency gains from pooling and can be computationally intensive for large N.
- Does not directly model long-run cointegrating relationships; misses cross-unit equilibria captured by VECM or ARDL.
- Assumes linearity in the ARMA structure; nonlinear dynamics or regime switches require extensions such as TAR or STAR models.
Frequently asked
Should I fit one ARIMA per unit or pool all units?
If T is large (> 30) and theory suggests heterogeneous dynamics, fit unit-specific ARIMA models. If T is short (10–20), pooling with common orders gains efficiency at the cost of imposing homogeneity. Intermediate approaches (grouped estimation, shrinkage) balance both.
How do I choose p, d, q for each unit?
First determine d via unit-root tests (ADF, PP, or panel tests). Then inspect the ACF and PACF of the differenced series, and confirm the order using AIC or BIC. Automated stepwise algorithms (e.g., auto.arima in R) are practical for large N.
What is the difference between Panel ARIMA and Panel VECM?
Panel ARIMA models each unit's differenced series in isolation and is oriented toward short-run dynamics and forecasting. Panel VECM explicitly models long-run cointegrating relationships among variables across units and includes an error-correction term that pulls variables back toward a common equilibrium.
How do I handle cross-sectional dependence?
Test residuals with the Pesaran CD test. If dependence is detected, subtract cross-sectional means (demeaning), use factor-augmented ARIMA, or apply SUR estimation to account for correlated innovations across units.
Is Panel ARIMA the same as a Panel AR model?
No. A Panel AR model includes only autoregressive lags of the dependent variable. Panel ARIMA adds a differencing step (the I component) to handle non-stationarity and a moving-average component (the MA part) to model the shock structure, making it more flexible for integrated series with complex residual autocorrelation patterns.
Sources
- Hsiao, C. (2003). Analysis of Panel Data (2nd ed.). Cambridge University Press. ISBN: 978-0521522717
- Box, G. E. P., Jenkins, G. M., Reinsel, G. C., & Ljung, G. M. (2015). Time Series Analysis: Forecasting and Control (5th ed.). Wiley. ISBN: 978-1118675021
How to cite this page
ScholarGate. (2026, June 3). Panel Autoregressive Integrated Moving Average Model. ScholarGate. https://scholargate.app/en/econometrics/panel-arima-model
Which method?
Set this method beside its closest kin and read them side by side — the library lays the books on the table; the choice is yours.
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