TIME SERIES ANALYSIS

PRACTICAL HOME ASSIGNMENT

- 50% of the final grade.
- to be handed in by June 22.
- submit electronically (max 6 pages)

ASSIGNMENT

a) find a time series of length between 200 and 2000

b) make a plot and consider if there is an evidence of
trend of seasonality

c) remove trend and seasonality if needed by the methods
discussed in the course

d) consider the residuals, think if they come from a white
noise model and try to speculate if they look stationary

e) use qq-plot to compare residuals with the normal distribution

f) make acf & pacf plots, can you propose at least one ARMA(p,q)
model based on these plots

g) choose the best AR(p) model using Yule-Walker estimation and
AIC criterion. Compare it with the best ARMA(p,q) model for
p=0,1, and q=1,2,3 using the AIC criteria (note: AIC is not equally
defined in two procedures)

h) choose one "optimal" model and estimate is parameters. If it seems
appropriate from acf plots fit GARCH model to the data.

i) simulate sequence of the same length as the residuals from
the estimated model and repeat steps f) & g)

j) using the model in h), assumption of Gaussianity and command
"predict" construct 90% prediction interval for the next 5 values
of the residual stochastic noise sequence. Finally use (invert) the
transformations in c) to make a 95% prediction interval for the next
value of the original time series

k) plot raw and smoothed peridodogram of the data, right after you
remove the trend in step c). Do you see any seasonality in the data,
and can you suggest possible period?