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Unit Root Tests

This study delves into the behavior of macroeconomic variables using integrated process models, specifically examining the ARMA(p,q) framework for time series analysis. We propose two trend models: a fixed trend and a variable trend, analyzing long-run forecasting implications. The fixed model utilizes a constant term, while the variable trend model incorporates dynamic components. We conduct unit root tests to ascertain stationarity in macroeconomic data, providing insights into the nature and predictability of economic trends. The findings highlight the importance of these tests in economic forecasting.

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Unit Root Tests

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  1. Unit Root Tests

  2. Integrated Process • Integrated Process I(1): Yt = Y(t-1) + ARMA(p, q)t • A Key Model (Hypothesis) for Macroeconomic Variables

  3. Behavior of Two Trend Models - Long Run Forecast Implications For t = h (for h=0, Y0=b0) • Fixed Trend Yh = b0 + b1 h + eh eh is WN(0, s) • Variable Trend Yh = Y0 + d h + e1 + e2…. eh… SD of (e1 + e2…. eh) =

  4. Unit Root Test Using t

  5. Unit Root Test Using tm

  6. Unit Root Test Using tt

  7. Unit Root Test - Why So Called? • Note that: Yt - Y(t-1) = (1 - L) Yt = ARMA(p, q)process, i.e.,

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