HW09_sol - 1 HOMEWORK 13 - SOLUTIONS Problem 1 Part A The...

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Unformatted text preview: 1 HOMEWORK 13 - SOLUTIONS Problem 1 Part A The time series, autocorrelation and partial autocorrelation are plotted: 50 45 40 35 30 25 20 15 10 5 1 310 300 290 280 270 260 250 240 230 Index IBM Time Series Plot of IBM 13 12 11 10 9 8 7 6 5 4 3 2 1 1.0 0.8 0.6 0.4 0.2 0.0-0.2-0.4-0.6-0.8-1.0 Lag Autocorrelation Autocorrelation Function for IBM (with 5% significance limits for the autocorrelations) 13 12 11 10 9 8 7 6 5 4 3 2 1 1.0 0.8 0.6 0.4 0.2 0.0-0.2-0.4-0.6-0.8-1.0 Lag Partial Autocorrelation Partial Autocorrelation Function for IBM (with 5% significance limits for the partial autocorrelations) 2 Autocorrelation Function: IBM Lag ACF T LBQ 1 0.873917 6.30 42.05 2 0.758678 3.44 74.38 3 0.658609 2.48 99.23 4 0.543362 1.84 116.50 5 0.439703 1.40 128.06 6 0.343897 1.06 135.27 7 0.283718 0.85 140.30 8 0.223898 0.66 143.50 9 0.157671 0.46 145.12 10 0.127413 0.37 146.21 11 0.119147 0.35 147.18 12 0.077878 0.23 147.60 13 0.065736 0.19 147.91 Partial Autocorrelation Function: IBM Lag PACF T 1 0.873917 6.30 2 -0.021386 -0.15 3 0.000414 0.00 4 -0.120172 -0.87 5 -0.025614 -0.18 6 -0.042191 -0.30 7 0.092009 0.66 8 -0.043171 -0.31 9 -0.066716 -0.48 10 0.077330 0.56 11 0.073955 0.53 12 -0.141448 -1.02 13 0.086754 0.63 The autocorrelations are significant from lag 1 through lag 3 and decrease with time (all positive). The partial autocorrelation has a significant positive value at lag 1 with the remaining partial autocorrelations appearing insignificant. This suggests an AR(1) model (the autocorrelation and partial autocorrelation appear similar to those from figure 9-2A) with a constant: t t t Y Y 1 1 Part B The data is non-stationary. An analysis of the data suggests a positive linear trend (Price = 251 + 0.644 * Period, R-square = 0.382, regression is significant). In addition the sample autocorrelations do not decay rapidly....
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HW09_sol - 1 HOMEWORK 13 - SOLUTIONS Problem 1 Part A The...

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