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Econ 240C

Econ 240C. Lecture 18. Review. 2002 Final Ideas that are transcending p. 15 Economic Models of Time Series Symbolic Summary. 2. Review. 2. Ideas That Are Transcending. Use the Past to Predict the Future. A. Applications Trend Analysis linear trend quadratic trend exponential trend

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Econ 240C

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  1. Econ 240C Lecture 18

  2. Review • 2002 Final • Ideas that are transcending p. 15 • Economic Models of Time Series • Symbolic Summary

  3. 2

  4. Review • 2. Ideas That Are Transcending

  5. Use the Past to Predict the Future • A. Applications • Trend Analysis • linear trend • quadratic trend • exponential trend • ARIMA Models • autoregressive models • moving average models • autoregressive moving average models

  6. Use Assumptions To Cope With Constraints • A. Applications • 1. Limited number of observations: simple exponential smoothing • assume the model: (p, d, q) = (0, 1, 1) • 2. No or insufficient identifying exogenous variables: interpreting VAR impulse response functions • assume the error structure is dominated by one pure error or the other, e.g assume b1 = 0, then e1 = edcapu

  7. Standard VAR (lecture 17) • dcapu(t) = (a1 + b1 a2)/(1- b1 b2) +[ (g11+ b1 g21)/(1- b1 b2)] dcapu(t-1) + [ (g12+ b1 g22)/(1- b1 b2)] dffr(t-1) + [(d1+ b1 d2 )/(1- b1 b2)] x(t) + (edcapu(t) + b1 edffr(t))/(1- b1 b2) • But if we assume b1 =0, • thendcapu(t) = a1 +g11 dcapu(t-1) + g12 dffr(t-1) + d1 x(t) + edcapu(t) +

  8. Use Assumptions To Cope With Constraints • A. Applications • 3. No or insufficient identifying exogenous variables: simultaneous equations • assume the error structure is dominated by one error or the other, tracing out the other curve

  9. Simultaneity • There are two relations that show the dependence of price on quantity and vice versa • demand: p = a - b*q +c*y + ep • supply: q= d + e*p + f*w + eq

  10. Shift in demand with increased income, may trace out i.e. identify or reveal the supply curve price supply demand quantity

  11. Review • 2. Ideas That Are Transcending

  12. Reduce the unexplained sum of squares to increase the significance of results • A. Applications • 1. 2-way ANOVA: using randomized block design • example: minutes of rock music listened to on the radio by teenagers Lecture 1 Notes, 240 C • we are interested in the variation from day to day • to get better results, we control for variation across teenager

  13. Reduce the unexplained sum of squares to increase the significance of results • A. Applications • 2. Distributed lag models: model dependence of y(t) on a distributed lag of x(t) and • model the residual using ARMA

  14. Lab 7 240 C

  15. Reduce the unexplained sum of squares to increase the significance of results • A. Applications • 3. Intervention Models: model known changes (policy, legal etc.) by using dummy variables, e.g. a step function or pulse function

  16. Lab 8 240 C

  17. Model with no Intervention Variable

  18. Add seasonal difference of differenced step function

  19. Review • 2002 Final • Ideas that are transcending • Economic Models of Time Series • Symbolic Summary

  20. Time Series Models • Predicting the long run: trend models • Predicting short run: ARIMA models • Can combine trend and arima • Differenced series • Non-stationary time series models • Andrew Harvey “structural models using updating and the Kalman filter • Artificial neural networks

  21. The Magic of Box and Jenkins • Past patterns of time series behavior can be captured by weighted averages of current and lagged white noise: ARIMA models • Modifications (add-ons) to this structure • Distributed lag models • Intervention models • Exponential smoothing • ARCH-GARCH

  22. Economic Models of Time Series • Total return to Standard and Poors 500

  23. Model One: Random Walks • Last time we characterized the logarithm of total returns to the Standard and Poors 500 as trend plus a random walk. • Ln S&P 500(t) = trend + random walk = a + b*t + RW(t)

  24. 9 8 7 6 5 4 0 100 200 300 400 500 Lecture 3, 240 C: Trace of ln S&P 500(t) Logarithm of Total Returns to Standard & Poors 500 LNSP500 TIME

  25. The First Difference of ln S&P 500(t) • D ln S&P 500(t)=ln S&P 500(t) - ln S&P 500(t-1) • D ln S&P 500(t) = a + b*t + RW(t) - {a + b*(t-1) + RW(t-1)} • D ln S&P 500(t) = b + D RW(t) = b + WN(t) • Note that differencing ln S&P 500(t) where both components, trend and the random walk were evolutionary, results in two components, a constant and white noise, that are stationary.

  26. Trace of ln S&P 500(t) – ln S&P(t-1)

  27. Histogram of ln S&P 500(t) – ln S&P(t-1)

  28. Cointegration Example • The Law of One Price • Dark Northern Spring wheat • Rotterdam import price, CIF, has a unit root • Gulf export price, fob, has a unit root • Freight rate ambiguous, has a unit root at 1% level, not at the 5% • Ln PR(t)/ln[PG(t) + F(t)] = diff(t) • Know cointegrating equation: • 1* ln PR(t) – 1* ln[PG(t) + F(t)] = diff(t) • So do a unit root test on diff, which should be stationary; check with Johansen test

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