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Homework 2

# Homework 2 - Homework 2 STAT 443 Spring 2009 1 Let Zt be a...

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Homework 2 STAT 443 Spring 2009 1. Let Zt be a sequence of independent normal random variables with zero mean and common finite standard deviation s. Let a, b and c be constants. Which, if any, of the following processes are weakly stationary? Justify your answer. a) Xt = ZtZt-1; b) Xt = Zt cos(ct) + Zt-1 sin(ct); c) Xt = a + bZt + cZt-2. 2. DESCRIPTIVE ABSTRACT: Monthly number of unemployed persons in Australia. Feb 1978 - Aug 1995. YOUR TASK: To forecast unemployment rate for the first eight months of 1995, i.e. from January to August 1995. You should a) provide an exploratory analysis of the data, i.e. time series and acf plots, and discuss any findings; b) apply the Holt smoothing procedure and additive and multiplicative Holt-Winters procedures, provide your output and compare the obtained results; which model seems to be better? c) provide residual diagnostics for the additive and multiplicative Holt-Winters procedures (time series plot, acf plot, the runs and Bartels test, QQ plot and the SW test);

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Homework 2 - Homework 2 STAT 443 Spring 2009 1 Let Zt be a...

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