CPI Time-Series Forecasting Using ARIMA(5,1,0)

Overview

This repository presents a rigorous univariate time-series forecasting study of the Consumer Price Index (CPI) using an ARIMA(5,1,0) specification.

The objective is to:

• Implement statistically disciplined out-of-sample validation
• Benchmark against a naive persistence model
• Generate a forward 12-month CPI projection
• Demonstrate leakage-safe forecasting methodology

This project emphasizes methodological correctness rather than purely predictive performance.

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Dataset

• Frequency: Monthly
• Total observations: 190 months (~15.8 years)
• Target variable: CPI index level

The dataset was chronologically indexed and strictly partitioned prior to model estimation.

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Methodology

1. Stationarity and Differencing

To remove long-run trend and induce stationarity, first differencing was applied:

$$ y'_t = y_t - y_{t-1} $$

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2. Model Specification

An ARIMA(5,1,0) model was selected:

• ( d = 1 ) → First differencing
• ( p = 5 ) → Five autoregressive lags
• ( q = 0 ) → No moving-average component

The differenced model is defined as:

$$ y'_t = c + \phi_1 y'_{t-1} + \phi_2 y'_{t-2} + \phi_3 y'_{t-3} + \phi_4 y'_{t-4} + \phi_5 y'_{t-5} + \varepsilon_t $$

where:

• ( c ) = constant
• ( \phi_i ) = autoregressive coefficients
• ( \varepsilon_t ) = white noise error term

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3. Validation Design (Leakage-Safe)

To simulate realistic forecasting conditions:

• Training set: First 178 months
• Test set: Final 12 months (strictly held out)

The model was fit exclusively on training data and used to forecast the unseen 12-month horizon.

No future information was used during estimation.

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4. Benchmark Model

A naive persistence forecast was implemented as a baseline:

$$ \hat{y}_{t+1} = y_t $$

This establishes a minimal predictive benchmark.

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Evaluation Metrics

Performance was assessed using standard out-of-sample error measures.

Root Mean Squared Error (RMSE)

$$ RMSE = \sqrt{\frac{1}{n} \sum_{i=1}^{n} (y_i - \hat{y}_i)^2} $$

Mean Absolute Error (MAE)

$$ MAE = \frac{1}{n} \sum_{i=1}^{n} |y_i - \hat{y}_i| $$

Mean Absolute Percentage Error (MAPE)

$$ MAPE = \frac{100}{n} \sum_{i=1}^{n} \left| \frac{y_i - \hat{y}_i}{y_i} \right| $$

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Out-of-Sample Results

Metric	ARIMA	Naive
RMSE	0.8921	5.3743
MAE	0.6927	4.7434
MAPE	0.21%	—

The ARIMA model substantially outperforms the naive persistence benchmark, demonstrating strong short-term predictive accuracy under proper validation.

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Outputs

• validation_plot.png — 12-month holdout comparison (ARIMA vs Naive)
• future_forecast.png — Forward 12-month CPI projection
• validation_metrics.md — Numerical performance summary

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Forecast Interpretation

The forward 12-month projection suggests continued CPI momentum consistent with recent inflation dynamics.

Forecast uncertainty increases with horizon length due to recursive error propagation.

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Limitations

• Linear structure assumption (may underperform during structural macroeconomic shocks)
• No explicit seasonal modeling (SARIMA extension could be explored)
• Optimized for short-term forecasting performance

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Author

Meherab Hossain Shafin

Independent time-series forecasting study demonstrating statistically disciplined model validation and benchmark comparison for applied macroeconomic forecasting.

Reproducibility

Install dependencies:

pip install pandas numpy matplotlib statsmodels scikit-learn
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