BIOL 335 Study Guide - Final Guide: Spectral Density, Fourier Series, Shift Operator
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Practice problems (from fall 2010 nal exam: this question concerns the box jenkins forecasting method. In the following you may assume the observed time series has been pre-processed to appear stationary and with zero mean. This gure is monitored for each of two hundred days, and a statistician decides a good t to the series is the model. Given that the nal observation was 0. 738, use this model and the box jenkins forecasting procedure to predict the next three values of the series. For the ar(1) , we estimate zn +1 by 0 giving. = 0. 121. (5 marks) note that xn (l) 0 as l increases. (1 mark: (a) find the spectral density function of the following process, in which {zt} is white noise with mean zero and variance 2 : In general, for an ma(3) process the acvf is. ( k) k > 2 k = 0 k = 1 k = 2 k < 0.
