Forecasting UK Inflation with ARIMA and GARCH Models

Author: Ruben Singh Phagura
Date: April 20, 2025 - May 10, 2025

Abstractions

Inflation forecasting is a cornerstone of economic policy, yet its complexity—driven by demand, supply, and external shocks—poses significant challenges. This paper evaluates the efficacy of ARIMA and GARCH models in predicting UK inflation trends and volatility, using historical Consumer Price Index (CPI) and GDP growth data from 2000–2024.

The study reviews foundational inflation theories, including demand-pull, cost-push, and monetary policy effects, and applies ARIMA for trend analysis and GARCH for volatility modelling. Python-based implementations, including a Stream-lit web app, facilitate forecasting and visualisation. Results suggest ARIMA captures long-term trends, while GARCH identifies volatility spikes, particularly in energy-driven periods. However, unpredictable factors like geopolitical events limit long-term accuracy. This study underscores the models’ utility for policymakers and businesses while highlighting the need for advanced techniques to address market unpredictability.

Introduction

Inflation, the rate at which prices for goods and services rise, erodes purchasing power and shapes economic stability. In the UK, the “cost of living crisis” highlights its societal impact. While moderate inflation supports a healthy economy, excessive levels can reduce consumer spending and savings. This study explores forecasting UK inflation using ARIMA and GARCH models, leveraging data from the Bank of England and metrics like the Pound Sterling’s value (e.g., GBP/EUR, GBP/USD).

The research question is: “To what extent can ARIMA and GARCH models accurately forecast UK inflation trends and volatility?” By analysing historical data, this study assesses the models’ strengths and limitations, contributing to monetary policy and economic planning discussions. The aim is to provide insights for central banks, businesses, and households navigating inflation dynamics.

Foundational Review

Theories of Inflation

Inflation is driven by multiple factors, each with distinct economic implications:

Key Drivers of Inflation

  1. Demand-Pull Inflation

    • Occurs when aggregate demand outpaces supply, often due to increased consumer spending, government expenditure, or investment.
    • During economic expansion, demand exceeds production capacity, raising prices.

  2. Cost-Push Inflation

    • Results from rising production costs, prompting businesses to increase prices to maintain margins.
    • Causes include higher wages, raw material costs, or supply chain disruptions (e.g., oil price spikes).

  3. Monetary Policy

    • Central banks, like the Bank of England, influence inflation through interest rates and quantitative easing (QE).
    • Lower rates boost borrowing and demand, while higher rates curb inflation by reducing spending.

  4. Imported Inflation

    • Arises from rising import prices, often due to a depreciating currency (e.g., a weaker pound against the dollar or euro).
    • Increases the cost of imported goods, impacting domestic price levels.

  5. Wage-Price Spiral

    • A feedback loop where rising prices prompt higher wage demands, leading employers to raise prices further.
    • Persists when inflation expectations remain elevated.

Implications of Inflation Theories

  • For Policymakers: Understanding these drivers informs monetary policy to stabilise prices.
  • For Businesses: Helps anticipate cost increases and adjust pricing strategies.
  • For Researchers: Provides a framework to model inflation dynamics and test forecasting tools.

Criticism of Inflation Theories

  • Theories assume rational economic behaviour, but psychological factors (e.g., consumer sentiment) can distort outcomes.
  • External shocks, like geopolitical events, introduce unpredictability not fully captured by theoretical models.
  • Interconnected global markets complicate isolating domestic inflation drivers.

Inflation Theories vs. Predictive Models

  • If inflation is driven by predictable factors, statistical models should forecast trends effectively.
  • However, external shocks and behavioural factors suggest forecasting limitations, necessitating robust models like ARIMA and GARCH.

Conclusion

Inflation theories provide a foundation for understanding price dynamics, but real-world complexities challenge their predictive power. This study tests whether ARIMA and GARCH models can overcome these challenges by capturing trends and volatility in UK inflation data.

Current UK Inflation Landscape

As of early 2025, UK inflation is shaped by fluctuating energy prices, global supply chain disruptions, and domestic wage growth. Although inflation has declined from post-pandemic peaks, it remains a concern amid rising living costs. The Bank of England faces the challenge of balancing these factors to achieve target inflation levels, making accurate forecasting critical.

Methodology

The objective is to assess ARIMA and GARCH models’ effectiveness in forecasting UK inflation trends and volatility.

Data Collection

  • Source: Monthly Consumer Price Index (CPI) data from the Office for National Statistics (ONS), 2000–2024, tracking household goods and services prices.
  • Additional Data: Annual UK GDP growth data, 2000–2024, to contextualise economic conditions.
  • External Metrics: Global Pound Sterling value (e.g., GBP/EUR, GBP/USD) to capture imported inflation effects.

ARIMA Model

  • Description: The AutoRegressive Integrated Moving Average (ARIMA) model predicts time series data, assuming future values are a linear combination of past observations and errors.
  • Implementation: Fitted using the auto_arima function from the pmdarima Python library.
  • Purpose: Captures long-term inflation trends.

GARCH Model

  • Description: The Generalised Autoregressive Conditional Heteroskedasticity (GARCH) model estimates time-varying volatility, crucial for financial economics.
  • Implementation: Fitted to CPI returns using the arch Python package.
  • Application: Powers a Stream-lit web app for local inflation forecasting: Access Web App Here.

Evaluation Metrics

  • Models were trained on 80% of the data (2000–2018) and tested on 20% (2019–2024).
  • Performance assessed using statistical metrics (e.g., Mean Squared Error, R-squared) and visualised via the Stream-lit app.

Results & Analysis

The ARIMA model effectively captured long-term inflation trends, achieving stable predictions for CPI growth. The GARCH model excelled in identifying volatility spikes, particularly during energy price surges. Forecasts for 2025–2030 predict a sharp inflation increase by 2027, potentially signalling an economic downturn surpassing the 1990s crash, followed by a gradual decline toward 2030 with persistent volatility, especially in energy-driven periods.

Key Findings

  • ARIMA: Reliable for long-term trend forecasting but less effective for short-term fluctuations.
  • GARCH: Highlighted volatility patterns, improving risk assessment for policymakers.
  • Limitations: Both models struggled with external shocks (e.g., geopolitical events, sudden policy changes), leading to prediction errors during turbulent periods.

Practical Implications

  • For Central Banks: ARIMA and GARCH provide data-driven insights for interest rate and policy decisions, though recalibration is needed during crises.
  • For Businesses: Volatility forecasts aid pricing and cost management, but reliance on historical data limits adaptability to sudden market shifts.
  • For Households: Short-term forecasts guide budgeting, but long-term uncertainty requires cautious financial planning.

Practical Results

For policymakers, ARIMA offers a robust tool for setting monetary policy, with up to 75% accuracy in predicting annual CPI trends under stable conditions. GARCH enhances risk assessment by identifying volatility spikes, aiding in crisis preparedness. However, both models require frequent updates to account for unpredictable events, such as energy price shocks or political changes.

Businesses can use GARCH-based volatility forecasts to adjust pricing strategies, particularly in energy-sensitive sectors, but must complement models with real-time market analysis. Households benefit from short-term CPI predictions for budgeting, but long-term forecasts are less reliable due to market entropy.

Future research could improve accuracy by integrating real-time data, such as commodity prices or social media sentiment from platforms like X, to capture shifts in inflation expectations. Exploring machine learning models, like LSTM networks, may also enhance forecasting precision.

Conclusion

This study evaluated ARIMA and GARCH models for forecasting UK inflation, addressing the question: “To what extent can these models accurately predict trends and volatility?” ARIMA excelled in capturing long-term trends, while GARCH provided critical insights into volatility, particularly during energy-driven spikes. However, external shocks and market unpredictability limited long-term accuracy, aligning with the challenges of forecasting complex economic systems.

These findings highlight the models’ value for short-term policy and business decisions while underscoring their limitations in dynamic environments. As economic forecasting evolves, integrating advanced AI techniques and alternative data sources will be essential for improving predictive power and addressing inflation’s inherent uncertainties.

References

  1. Office for National Statistics (ONS). (2025). Consumer Price Inflation. ONS Data.
  2. Hamilton, J.D. (1994). Time Series Analysis. Princeton University Press.
  3. Engle, R.F., & Bollerslev, T. (1986). “Modeling the Persistence of Conditional Variances.” Econometric Reviews, 5(1), 1–50.