This is How to Specify ARDL Models #ardl #ecm #boundstest #cointegration #lags

Introduction

This tutorial provides a step-by-step guide on specifying Autoregressive Distributed Lag (ARDL) models and understanding the outcomes of the bounds cointegration test. It's essential for econometric analysis, especially when dealing with time series data. By following these steps, you'll learn how to determine which model to use based on cointegration results and how to specify the ARDL framework effectively.

Step 1: Perform the Bounds Cointegration Test

Before specifying a model, you need to check if your variables are cointegrated.

• Gather your data: Ensure you have the time series data for the variables you want to analyze.
• Run the bounds test: This involves using statistical software (like Stata or EViews) to perform the test.
• Interpret the results:
  • If the test indicates cointegration, proceed to the next step for specifying the appropriate model.
  • If there is no cointegration, you will focus on the short-run model specification.

Step 2: Specify the ARDL Model for Non-Cointegrated Variables

If the bounds test shows that the variables are not cointegrated, specify the ARDL model as follows:

• Select the appropriate lags:

  • Use criteria such as AIC or BIC to determine the optimal number of lags for each variable.

• Structure the model:

  • The basic form of the ARDL model is given by:

    Y_t = c + ∑(β_i * Y_(t-i)) + ∑(γ_j * X_(t-j)) + ε_t
    

    Where:

    • Y_t is the dependent variable.
    • X represents the independent variables.
    • β and γ are coefficients for the lags.
    • c is a constant.

• Estimate the model: Use your software to estimate the parameters of the ARDL model.

Step 3: Specify the ECM/VECM for Cointegrated Variables

If the bounds test indicates cointegration, you should specify the Error Correction Model (ECM) or Vector Error Correction Model (VECM).

• Determine the cointegration rank: This helps to identify the number of cointegrating relationships in your data.

• Specify the VECM structure:

  • The general form is:

    ΔY_t = α + ∑(β_i * ΔY_(t-i)) + ∑(γ_j * ΔX_(t-j)) + λ * (Y_(t-1) - θ'X_(t-1)) + ε_t
    

    Where:

    • Δ indicates the first difference.
    • α is a constant.
    • λ represents the error correction term.
    • θ'X_(t-1) captures the long-run equilibrium relationship.

• Estimate the model: Use statistical software to estimate the parameters and evaluate the model fit.

Step 4: Evaluate Your Model

Regardless of which model you use, evaluating its performance is crucial.

• Check the residuals: Ensure they are normally distributed and homoscedastic.
• Conduct diagnostic tests: Perform tests for autocorrelation and model stability.
• Validate the model: Use out-of-sample forecasting to test the predictive capability of your model.

Conclusion

In this tutorial, you learned how to specify ARDL models based on the outcomes of the bounds cointegration test. Remember, if your variables are not cointegrated, you will specify an ARDL model, whereas cointegrated variables require an ECM or VECM specification. Regular evaluation of your model is vital to ensure its reliability and effectiveness. For further learning, consider exploring additional resources or tutorials on econometric modeling techniques.