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Unformatted text preview: s not achieved. t5 distribution replicates heavy tails of residuals quite well (based on the histogram), therefore we may use quantiles of this distribution for obtaining prediction intervals: Xt +h ± tα/2,5 · s.e.(Rt ), where Xt +h – point forecast; Rt – estimated residuals. In R, tα/2,5 can be obtained by: > alpha <- 0.05 > qt(alpha/2, df=5) [1] -2.570582 Compare with normal distribution: > qnorm(alpha/2, 0, 1) [1] -1.959964 GARCH model for DAX time series Other approaches: Q-Q plot Instead of using the histogram superimposing, the model distribution for residuals may be selected using Q-Q plot. However, in R some extra coding is required to compare the quantiles from observed data with those from hypothesized distribution if the latter is not normal. The function qqnorm is only for normal Q-Q plots. GARCH model for DAX time series Other approaches: bootstrap Alternatively, we may bootstrap the residuals (sample with replacement many times) and obtain the quantiles f...
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This note was uploaded on 08/04/2013 for the course ECON 201 taught by Professor Vandewaal during the Spring '09 term at Waterloo.

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