Part II – TIME SERIES ANALYSIS
C1 Introduction to TSA
"If we could first know where we are, then
whither we are tending, we could then decide
what to do and how to do it."
Abraham Lincoln, 1809-1865
© Angel A. Juan & Carles Serrat - UPC 2007/2008
2.1.1: Motivation

An essential aspect of managing any organization is
planning for the future. The long-run success of an
organization is closely related to how well management is
able to anticipate the future and develop appropriate
strategies.

The purpose of this part is to introduce several methods
which make use of existent historical data to produce
forecasts (predictions).

Historical data form a time series, i.e.: a set of observations
on a variable measured at successive points in time or over
successive periods of time.

Examples: daily temperature measurements, weekly sales
figures, monthly stock market prices, quarterly profits,
yearly power-consumption data, etc,

Two main goals of time series analysis:
1.
Identifying the nature of the phenomenon represented by the
sequence of observations, and
2.
Forecasting (predicting future values of the time series
variable)
2.1.2: Classification of Forecasting Methods

Forecasting methods can be classified as quantitative or qualitative.

Quantitative forecasting methods can be used when:

1.
Past information about the variable being forecast is available,
2.
The information can be quantified, and
3.
It can be assumed that the pattern of the past will continue into the
future
In such cases, a forecast can be developed using a time series
method or a causal method:



Time series methods: The historical data are restricted to past values of
the variable. The objective is to discover a pattern in the historical data
and then extrapolate the pattern into the future. Ex.: trend analysis,
classical decomposition, moving averages, exponential smoothing,
ARIMA.
Causal forecasting methods: Based on the assumption that the variable
we are forecasting has a cause-effect relationship with one or more
other variables (e.g.: the sales volume can be influenced by advertising
expenditures). Ex.: regression analysis.
Qualitative methods generally involve the use of expert judgment to
develop forecasts.
Time Series
Methods
Causal
Forecasting
Methods
2.1.3: General Aspects of Time Series

In TSA it is assumed that the data consist of a
systematic pattern (usually a set of identifiable
components) and random noise (error) which
usually makes the pattern difficult to identify.

Most TSA techniques involve some form of
filtering out noise in order to make the pattern
more salient.


Time series patterns can be usually described
in terms of two basic classes of components:

Trend: Represents a general systematic
component that changes over time and does
not repeat.

Seasonality: It repeats itself in systematic
intervals over time.
Those two general classes of time series
components may coexist in real-life data.
In this example, the amplitude of the
seasonal changes remains
approximately constant. This pattern
is called additive seasonality.
In this example, the amplitude of the
seasonal changes increases with
the overall trend. This pattern is
called multiplicative seasonality.
seasonality
2.1.4: Plotting a Time Series (Minitab)

File: RIVERC.MTW

Stat > Time Series > Time Series
Plot…
• C1 Hour: lists the time of day
(in military format) of each
measurement.
• C2 Temp: gives the temperature
measurement in ºC.
The plot indicates a periodical pattern
beginning with temperatures at 2 p.m. around
42 degrees, which rise for the next 8 hours
and then fall until they reach a low of about 37
degrees at 7 a.m. This suggests that your time
series model might include a seasonal
component.
45,0
42,5
Temp
The river data are fairly well-behaved, as evidenced
by the time series plot. If you were to draw a
horizontal line at the mean of the series, you would
see that the data oscillate with the same cyclical
pattern. A time series like this, whose mean and
variance do not change with time, is called
stationary. Conversely, a time series that appears to
wander and does not systematically fluctuate around
a single value is called nonstationary.
Time Series Plot of Temp
40,0
37,5
35,0
1400 2200
700
1600
100
1000 1900
Hour
400
1300
2200
700
2.1.5: Classification of Time Series Methods

Simple forecasting and smoothing methods:

Based on the idea that reliable forecasts can be achieved by modeling
patterns in the data that are usually visible in a time series plot.

Your choice of method should be based upon whether the patterns are
static (constant in time) or dynamic (changes in time), the nature of the
trend and seasonal components, and how far ahead that you wish to
forecast.


Simple
Forecasting
Methods
Smoothing
Methods
Generally easy and quick to apply.
ARIMA methods:

Also make use of patterns in the data, but these patterns may not be
easily visible in a plot of the data.

Instead, ARIMA modeling uses differencing and the autocorrelation
and partial autocorrelation functions to help identify an acceptable
model.

ARIMA stands for Autoregressive Integrated Moving Average, which
represent the filtering steps taken in constructing the ARIMA model
until only random noise remains.

Fitting a model is an iterative approach that may not lend itself to
application speed and volume.
ARIMA
Methods
References for Time Series Analysis

Anderson, D.; Sweeney, D.; Williams, T. (2004): Statistics
for Business and Economics. South-Western College Pub.

Berk, K.; Carey, P. (2003): Data Analysis with Microsoft
Excel. Duxbury Press.

Hanke, J.; Wichern, D. (2004): Business Forecasting.
Prentice Hall.

McKenzie, J.; Goldman, R. (1998): The Student Edition of
MINITAB for Windows. Addison Wesley Longman.

Mendenhall, W.; Sincich, T. (2003): A Second Course in
Statistics: Regression Analysis. Prentice Hall.

StatSoft (2007): Electronic Statistics Textbook. Available
at http://www.statsoft.com/textbook/stathome.html