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 = ZtZt1;
b) Xt = Zt cos(ct) + Zt1 sin(ct);
c) Xt = a + bZt + cZt2.
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 HoltWinters procedures, provide your output and
compare the obtained results; which model seems to be better?
c) provide residual diagnostics for the additive and multiplicative
HoltWinters procedures (time series plot, acf plot, the runs and
Bartels test, QQ plot and the SW test);
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 Spring '09
 YuliaGel
 Forecasting, Standard Deviation, Unemployment, zt, multiplicative HoltWinters procedures, 488800 463900 440000 453800 451600 453400

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