Time Series Models for Business
EPBA Time Series Lecture 1

1 Introduction
1. Introduction
• A
time series
is a set of observations, denoted
by x
t
, each one being recorded at a specific time
t.
•
Discrete Time Series:
The set of times, T
0
, at
which observations are made is a discrete set,
T
{0 ±1 ±2
} N t
th t th
t
e.g., T
0
= {0, ±1, ±2, …}. Note that the set
contains a finite or countably infinite number of
elements.
•
Continuous Time Series:
The set of times, T0,
at which observations are made is an interval or
at which observations are made is an interval or
union of intervals of the real line, e.g., T
0
= {t: 0
≤
t
≤
1}.

A Formal Definition
A
time series model
[
1
]
for the observed data {x
t
}, is a
specification for the
joint distribution
of a sequence of
random variables {X
t
},
of which {x } is postulated to be a realization
of which {x
t
} is postulated to be a realization.
1
[
]
The term
time series
is often used to mean both the
data
and
the
process,
of which it is a realization.