Lecture_4_Regression_Part_1

# Lecture_4_Regression_Part_1 - 1 Lecture 4 (Part 1)...

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Lecture 4 (Part 1) Regression and Forecasting Read: (WK Ch 4, 5; other books) EC 413/513 Economic Forecast and Analysis (Professor Lee) 1

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Topics: Regression for Forecasting Trend and Seasonality Regression for Demand Analysis More on Regression Analysis 1. Modeling & Forecasting Trend Using Regression Linear TREND Consider a regression with a time trend Y t = a + b × t + e t t=1,2,. ., T Or, in general, Y t = a + bX t + e t t=1,2,. ., T Y t = Dependent Variable X t or t = Independent Variable a = constant or intercept b = slope coefficient = marginal effect = How much Y will increase, on average, when X increases by one unit (= Y/ X) Get back to Y t = a + b × t + e t t=1,2,. ., T Then, = average increase of Y t per year. Why? 2
Note: If we use YEAR instead of t, the estimate of the slope coefficient (b) remains the same. Y t = a + b YEAR + e t t=1,2,. ., T Example ; Regression results t = 115.8 + 8.6 × t or t = -17041.2 + 8.6 × YEAR (note: YEAR = t + 1995) Thus, the average increase per year is 8.6. Forecasting Trend 6 = 115.8 + 8.6 × 6 = 167.40 or 2001 = -17041.2 + 8.6 × 2001 = 167.40 7 = 115.8 + 8.6 × 7 = ? Y t t time YEAR 123 1 1 1996 134 2 2 1997 143 3 3 1998 150 4 4 1999 158 5 5 2000 Y t t time YEAR t 123 1 1 1996 115.8 + 8.6 × 1 = 124.4 134 2 2 1997 115.8 + 8.6 × 2 = 133.0 143 3 3 1998 115.8 + 8.6 × 3 = 141.6 150 4 4 1999 115.8 + 8.6 × 4 = 150.2 158 5 5 2000 115.8 + 8.6 × 5 = 158.8 - 6 6 2001 ? - 7 7 2002 ? 3

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TREND in LOG What if? log( Y t ) = a + b × t + e t t=1,2,. ., T What does the estimate of b imply? = ? log( t ) = 4.765 + 0.061 × t (or log( t ) = -117.65 + 0.061 × YEAR ) 0.061 = Forecasts From Logged model log( 6 ) = 4.765 + 0.061 × 6 = 5.131 6 = e 5.131 = 169.18 why? log(y) = x y = e x Ex) log( 7 ) = ? and 7 = ? Note: We often use log-linear model when Y increases exponentially. Y t t YEAR log(Y t ) 123 1 1996 134 2 1997 143 3 1998 150 4 1999 158 5 2000 - 6 2001 ? - 7 2002 ? 4
Monthly Data (quarterly data, daily data, weekly data…) t = 5.847 - 0.035 × t Thus, the average decrease per month is 0.035 log( t ) = 1.766 – 0.006 × t →Τ he average decrease in growth rates per month is 0.6%. Quadratic TREND Y t = a + b 1 × t + b 2 × t 2 + e t t=1,2,. ., T If b 2 > 0, U-shaped. If b 2 < 0, inverse U-shaped. Calculating Growth Rates r t = × 100 % = × 100 % This is the standard definition of the (arithmetic) growth rates. Y t Month t 5.81 Jan-05 1 5.80 Feb-05 2 5.73 Mar-05 3 5.67 Apr-05 4 5.70 May-05 5 5

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But, consider the average growth rates. Is it right? Calculating Geometric Growth The basic equation for geometric growth is Y t = Y 0 (1+r) t Y 2 = Y 0 (1+r) 2 75 = 100(1+r) 2 (75/100) = (1+r) 2 (0.75) 1/2 = (1+r) r = - 1 = 0.866 – 1 = -0.134 or -13.4% From this calculation, we can obtain a CONSTANT growth rate r. In finance, people often use the following formula.
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## This note was uploaded on 02/29/2012 for the course EC 513 taught by Professor Staff during the Fall '08 term at Alabama.

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Lecture_4_Regression_Part_1 - 1 Lecture 4 (Part 1)...

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