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Regression with Time Series Data

Explore the concepts of polynomial distributed lag models, geometric lag impact multiplier, Koyck transformation, ARDL models, and understanding stationarity in time series data for accurate regression analysis.

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Regression with Time Series Data

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  1. Regression with Time Series Data Judge et al Chapter 15 and 16

  2. Distributed Lag

  3. Polynomial distributed lag

  4. Estimating a polynomial distributed lag

  5. Geometric Lag Impact Multiplier: change in ytwhen xtchanges by one unit: If change in xt is sustained for another period: Long-run multiplier:

  6. The Koyck Transformation

  7. Autoregressive distributed lag ARDL(1,1) ARDL(p,q) Represents an infinite distributed lag with weights: Approximates an infinite lag of any shape when p and q are large.

  8. Stationarity • The usual properties of the least squares estimator in a regression using time series data depend on the assumption that the variables involved are stationary stochastic processes. • A series is stationary if its mean and variance are constant over time, and the covariance between two values depends only on the length of time separating the two values

  9. Stationary Processes

  10. Non-stationary processes

  11. Non-stationary processes with drift

  12. Summary of time series processes • AR(1) • Random walk • Random walk with drift • Deterministic trend

  13. Trends • Stochastic trend • Random walk • Series has a unit root • Series is integrated I(1) • Can be made stationary only by first differencing • Deterministic trend • Series can be made stationary either by first differencing or by subtracting a deterministic trend.

  14. Real data

  15. Spurious correlation

  16. Spurious regression R2 0.7495 D-W 0.0305

  17. Checking/testing for stationarity • Correlogram • Shows partial correlation observations at increasing intervals. • If stationary these die away. • Box-Pierce • Ljung-Box • Unit root tests

  18. Unit root test

  19. Dickey Fuller Tests • Allow for a number of possible models • Drift • Deterministic trend • Account for serial correlation Drift Drift against deterministic trend Adjusting for serial correlation (ADF)

  20. Critical values

  21. Example of a Dickey Fuller Test

  22. Cointegration • In general non-stationary variables should not be used in regression. • In general a linear combination of I(1) series, eg: is I(1). • If etis I(0) xtand yt are cointegrated and the regression is not spurious • et can be interpreted as the error in a long-run equilibrium.

  23. Example of a cointegration test

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