Modelling and predicting the Consumer Price Index in Saudi Arabia

The study addresses inflation dynamics in Saudi Arabia by modeling and forecasting the Consumer Price Index (CPI), a standard measure for inflation. Stable, low inflation supports investment, employment, and currency stability, while volatility undermines confidence and economic activity. Recent increases in Saudi inflation, potentially due to VAT and administrative fee changes, motivate analysis of CPI behavior to inform policy. The research uses monthly CPI data (Jan 2013–May 2020; 89 observations) to build an econometric time series model capable of capturing seasonal patterns and producing reliable short-term forecasts for policy use.

The literature on CPI modeling in Saudi Arabia is limited. Globally, various time series models—AR, MA, ARIMA/SARIMA, ES, ARCH/GARCH, VARCH, and hybrids—have been applied. Adams et al. (2014) found ARIMA(1,2,1) best for Nigeria’s CPI. Ashuri and Lu (2010) showed SARIMA excels in in-sample CCI forecasting; Holt–Winters performs well out-of-sample. Mordi et al. (2012) forecasted CPI via disaggregated components. Zhang et al. (2013) used ARMA for China’s CPI; Akhter (2013) used SARIMA for Bangladesh; Norbert (2016) modeled Rwanda; Nyoni (2019) predicted Saudi CPI with ARIMA; Ji et al. (2020) proposed GSTARI outperforming ARIMA by incorporating space-time effects. Other applications include Indonesia ARIMA models (Ahmar et al., 2018) and comparisons of machine learning versus time series for inflation forecasting. Additional related time series applications (e.g., ANN, ARIMA-GARCH hybrids) demonstrate broader forecasting advancements. Collectively, findings stress selecting models suited to economy-specific dynamics and seasonality.

Data: Monthly CPI for Saudi Arabia from the General Authority for Statistics, January 2013–May 2020 (89 observations). Summary statistics: mean 97.08, SD 2.10, min 92.70 (2013M01), max 100.90 (2018M01); skewness −0.50; kurtosis 2.55. Software: MS Excel 2010, EViews 8.1. Stationarity testing: Visual inspection (time plot and correlogram) and Augmented Dickey–Fuller (ADF) tests. At levels, CPI is nonstationary (ADF t = −2.02, p = 0.28; critical values: −3.51, −2.89, −2.58 at 1%, 5%, 10%). First differencing yields stationarity (ADF t = −8.24, p = 0.00). ACF/PACF of differenced series show seasonal patterns (annual periodicity), motivating a seasonal model. Model identification and specification: Box–Jenkins framework applied. ACF/PACF behavior used to identify potential SARMA/SARIMA structures. Candidate models included SARMA (0,1,0)(12,0,12), ARMA (1,1,1)(12,0,12), SARMA (1,1,0)(12,0,12), SARMA (0,1,1)(12,0,12), and reduced seasonal specifications. Estimation: Parameters estimated via least squares in EViews for differenced CPI D(CPI). The preferred model SARMA (0,1,0)(12,0,12) includes seasonal AR(12) and seasonal MA(12) on the differenced series and a constant. Convergence achieved after 24 iterations; MA backcast used. Model selection: Compared models using sum of squared residuals (SQR), Akaike Information Criterion (AIC), Schwarz Bayesian Criterion (SBC), Theil’s Inequality Coefficient, and RMSE. SARMA (0,1,0)(12,0,12) minimized all metrics among candidates. Diagnostics: Residual correlogram and Ljung-Box Q-statistics indicate white-noise residuals (autocorrelations within ±2SE, p-values high). Residual stationarity confirmed by ADF under various exogenous specifications (constant; constant+trend; none), all strongly rejecting unit root. Inverted AR/MA roots indicate stability/invertibility. Forecasting: Using the selected SARMA model, one-year-ahead forecasts produced for 2020M06–2021M06. Forecast accuracy assessed via RMSE and Theil’s inequality coefficient, both lowest for the selected model among candidates.

- Nonstationarity at levels: ADF t = −2.02, p = 0.28 (fail to reject unit root); stationarity after first differencing: ADF t = −8.24, p = 0.00. - Seasonal dynamics present (annual periodicity in ACF/PACF), necessitating seasonal model components. - Model selection (Table 4): SARMA (0,1,0) (12,0,12) outperforms alternatives with SQR = 15.79699, AIC = 1.345911, SBC = 1.43791, Theil’s I.C. = 0.00233, RMSE = 0.45591. - Estimated model (D(CPI) as dependent variable): Constant = 0.062020 (Prob ≈ 0.0207), SAR(12) = −0.775836 (p < 0.0001), SMA(12) = 0.957902 (p < 0.0001); R² = 0.2621; Adj. R² = 0.2419; DW = 1.8118. - Residual diagnostics: Correlogram within ±2SE; Ljung–Box p-values large; ADF on residuals strongly rejects unit root across specifications (e.g., t ≈ −8.64 to −8.70, p = 0.000), indicating white-noise, stationary residuals and adequate model fit. - Forecasts (selected): 2020M06 = 98.7; 2020M07 = 98.6; 2020M08 = 98.6; 2020M09 = 98.6; 2020M10 = 98.7; 2020M11 = 98.8; 2020M12 = 98.9; 2021M01 = 99.0; 2021M02 = 99.0; 2021M03 = 99.0; 2021M04 = 99.1; 2021M05 = 99.3; 2021M06 = 99.4, indicating a gradual upward trajectory.

The study finds that Saudi Arabia’s CPI exhibits nonstationarity at levels with clear seasonal patterns, aligning with economic realities such as VAT changes and administrative fee adjustments. Applying the Box–Jenkins approach, the SARMA (0,1,0)(12,0,12) model effectively captures the annual seasonality and short-run dynamics after first differencing. Diagnostics confirm white-noise, stationary residuals and model stability, supporting the model’s adequacy. The model’s superior information criteria, low RMSE, and very low Theil’s inequality coefficient indicate strong in-sample performance and credible short-term forecasting capability. The resulting forecasts show a steady monthly CPI increase from mid-2020 through mid-2021, consistent with ongoing inflationary pressures. These insights directly support the research aim by providing an empirically validated tool to anticipate CPI paths, thereby informing timely monetary and fiscal policy responses and planning by stakeholders.

The SARMA (0,1,0) (12,0,12) model best represents Saudi Arabia’s monthly CPI dynamics from 2013–2020, successfully accounting for nonstationarity through differencing and capturing pronounced seasonality. Model diagnostics validate adequacy and stability, and out-of-sample forecasts for June 2020–June 2021 indicate a gradual upward CPI trend, offering actionable insights for policymakers. Future research should enhance robustness by exploring richer specifications (e.g., SARIMA with exogenous regressors), hybrid and machine learning models, and frameworks addressing structural breaks, outliers, and regime shifts to further improve forecast accuracy and resilience.

- The CPI series is nonstationary at levels, requiring differencing; this challenges some standard modeling assumptions and may limit interpretability of levels dynamics. - Limited sample (89 monthly observations, Jan 2013–May 2020) may constrain model generalizability and structural break detection. - Potential unmodeled structural changes (e.g., tax policy shifts, COVID-19 shocks) and outliers could affect forecast accuracy. - Forecasts are subject to uncertainty and may be impacted by unforeseen economic events; no external regressors were included to capture such shocks.