Kuliah 12: Model Autoregresif dan Distributed Lag

Introduction

In this tutorial, we will explore the concepts of autoregressive models and distributed lag models, which are crucial in econometrics. These models help us understand how predictor variables affect a response variable over time, rather than instantaneously. This guide is based on the teachings from a lecture by I Wayan Sumarjaya and is designed to help you grasp these important econometric concepts.

Step 1: Understand Autoregressive Models

Autoregressive (AR) models are used to predict future values based on past values of the same variable. Here’s how to approach them:

• Definition: An autoregressive model uses the relationship between an observation and a number of lagged observations (previous time periods).

• Model Specification: The general form of an AR model can be expressed as:

  Y_t = c + φ_1Y_{t-1} + φ_2Y_{t-2} + ... + φ_pY_{t-p} + ε_t
  

  Where:

  • Y_t is the current value,
  • c is a constant,
  • φ represents the coefficients,
  • ε_t is the error term,
  • p is the order of the model (number of lagged terms).

• Practical Advice:

  • Analyze historical data to determine the appropriate lag length (p).
  • Use statistical software to estimate the coefficients (φ values) for your model.

Step 2: Explore Distributed Lag Models

Distributed lag models help in understanding how the impact of predictor variables is distributed over time. Here’s how to work with them:

• Definition: These models consider the effects of an independent variable not just at the current time but also at previous time periods.

• Model Specification: A simple form of a distributed lag model can be represented as:

  Y_t = c + β_0X_t + β_1X_{t-1} + β_2X_{t-2} + ... + β_qX_{t-q} + ε_t
  

  Where:

  • X represents the predictor variable,
  • β represents the coefficients for each lagged predictor.

• Practical Advice:

  • Identify the relevant predictor variables that might influence the response variable over time.
  • Estimate the lag structure using techniques such as the Almon method or polynomial distributed lags.

Step 3: Estimate and Validate the Models

After specifying your models, it’s essential to estimate and validate them.

• Estimation:

  • Use statistical software packages (like R, Python, or Stata) to fit your autoregressive and distributed lag models.
  • Check for stationarity in your time series data using tests such as the Augmented Dickey-Fuller test.

• Validation:

  • Assess the model fit using R-squared, AIC, or BIC.
  • Perform residual analysis to check for autocorrelation and ensure the assumptions of the model are met.

Conclusion

Understanding autoregressive and distributed lag models is vital for analyzing time series data in econometrics. By following the steps outlined above, you can effectively model and interpret the dynamics between variables over time. Start by practicing with real datasets, applying these models, and validating your findings to enhance your econometric skills. Next, consider exploring advanced topics such as cointegration and error correction models for deeper insights into time series analysis.