Prof. Dr. W. Zucchini 1. ¨Ubungsblatt TIME SERIES ANALYSIS ...

Prof. Dr. W. Zucchini
1. Übungsblatt
TIME SERIES ANALYSIS Wintersemester 2010/2011
Question1: Classical Dcomposition
The following figure shows the development of the monetary base in Japan from
Jan. 1970 to Nov. 1999 (given in Bil. Yen)
a) Describe the main components of the time series in terms of classical decomposition.
b) In classical decomposition the components of a time series can be either
additive or multiplicative. What structure is present in this series? Which
conclusion do you draw from this?
c) The log transformation is closely related to the Box-Cox transformations.
– Describe how one goes about applying the Box-Cox transformations.
– What is the purpose and the aim of such transformations in general?
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Question 2: Filters
a) Explain the terms simple moving average, weighted moving average and
centered filter.
b) A simple moving average is given by
D t =
a∑
i=−a
Describe how a influences the filtering?
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2a + 1 x t+i
c) Explain the terms linearity, additivity und commutativity in the context of
filters.
Aufgabe 3: R
a) Read the dataset tui (Shares and trading volume of the TUI AG from
01/03/2000 to 05/14/2002) using read.table() with the option header=T.
The data is given as a matrix: The first column ("open") contains the
opening values, the second and third columns give the daily highs and lows,
respectively ("high" "low"). The fourth column contains the closing values
("close"). The trading volume ("volume") is given in the fifth column.
– Consider the closing values (tui[,4]). Plot the values and filter the
given time series using simple moving averages with (a = 2, 12 and
37). Add the filtered values to the figure using the lines() command.
b) The dataset yen from question 1 is stored as yen.dat . Read the data with
scan() and plot the time series.
– Transform the data if necessary and choose an appropriate filter in
order to obtain the trend T t . Create a plot of the estimated trend and
of the component (S t + e t )!
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