Linköping university
Time series analysis, 732A21
Computer lab 1: Time series decomposition
Learning objectives
The main objective of this computer lab is to make the student acquainted with standard
methods for time series decomposition.
After completing the lab the student shall be able to:
(i)
Use Minitab or other statistical software to decompose time series of data into
trend and seasonal and irregular components;
(ii)
Explain the terms seasonally adjusted and detrended series;
(iii)
Undertake a time series decomposition using moving averages;
(iv)
Undertake a time series decomposition by regressing the response on seasonal
dummies.
Assignment 1: Decomposing a time series of monthly
temperature records
The Excel file ‘CentralEngland.xls’ contains monthly mean Central England Temperature
records in degrees C, 1659-2007. (This is the world’s longest temperature series!) Copy
the dataset to Minitab and undertake a time series decomposition. Make a graph of: (i) the
seasonally adjusted (deseasonalized) time series of data, and (ii) the seasonal
components. Has the seasonal pattern been stable over the entire study period? Can you
discern a recent trend in the seasonally adjusted series? Is there, in the present
application, any significant difference between the seasonally adjusted series obtained
with additive and multiplicative models, respectively?
Assignment 2: Decomposing a time series of car registrations
using moving averages
The Excel file ‘carsmonthly.xls’ contains monthly data on car registrations in Sweden.
Copy the dataset to Minitab and use a suitable centered moving average function to
remove (or suppress) the seasonal pattern in the car registration data. How long shall the
seasonal period be? Extract the residuals from the moving average smoothing and
decompose them into seasonal components and irregular variation.
Use Minitab to directly decompose the car registration series into trend and seasonal and
irregular components. Compare and comment the seasonal components obtained with this
method and the method based on smoothing using moving averages.
Linköping university
Time series analysis, 732A21
Assignment 3: Time series decomposition and regression on
seasonal dummies
The excel file ‘Rhine.xls’ contains monthly flow-weighted concentrations of total
nitrogen in the Rhine River.
Copy the dataset to Minitab and use the function patterned data to define dummy
variables for each month (Jan – Dec). A dummy variable for Jan is 1 for each January
observation and otherwise zero.
Use ordinary least squares regression to regress the total nitrogen concentration on time
and all but one of the seasonal dummies. (What would happen if you tried to use
dummies for all the twelve months?). Make a simple bar diagram which illustrates the
regression coefficients for the seasonal dummies.
Then use Minitab’s additive model for time series decomposition and make a graph of the
extracted seasonal components. Explain how the seasonal components obtained by
regression on seasonal dummies are related to the seasonal components obtained with a
standard additive time series decomposition.
To hand in
This course has individual written lab reporting. Write a concise report that shows that
you have done the assignments and reflected over the results obtained.
Deadline for reporting is normally one week after the lab has been made available on the
course website.