This document discusses time series analysis. It defines a time series as a set of numerical values of some variable obtained at regular intervals over time. The objectives of time series analysis are to understand the behavior of variables over time and evaluate changes. There are four main components of a time series: trend, which is a long-term movement; cycles, which are medium-term fluctuations; seasonality, which are short-term and regular fluctuations; and irregularity, which are unpredictable short-term changes. Time series can be decomposed using either a multiplicative or additive model to isolate the effects of each component.

1. TIME SERIES
PREPARED BY:JAMSHID RAQI
TIME SERIES

2. Content:
 Introduction
 Objectives of Times Series
 Components of Times Series
 Important of Times Series
 Types of Times Series
 Application of Times Series

3. What is a Time Series?
A time series is a set of numerical values of some variable
obtained at regular period over time. These numerical values are
usually tabulated or graphed to understand the behavior of the
variable.
Year Export
2000 2
2001 3
2002 6
2003 4
2004 10
2005 10
2006 15
0
2
4
6
8
10
12
14
16
1999 2000 2001 2002 2003 2004 2005 2006 2007
export

4. Objectives of Time Series:
 In time series analyses, it is assumes that the
various factors which have already influenced the
patterns of change in the value of the variable
under study will continue to do so almost in the
same manner in future also.
 The review and evaluation of progress in any
phenomenon are made based on time series
data. For example evaluation of the policy of
controlling inflation and price rise is done based
on various price indices that are based on the
analysis of time series.

5. Time Series Patterns
In time series its assumed that the data consist of a pattern along
with random fluctuations. This may be expressed in the following
form:
= +
Actual Value of
the variable at
time t
Mean Value of the
variable at time t
Random deviation
from mean value of
the variable at time t

6. Components of Time Series:
The time series data contain four components:
Trend, Cyclicality, Seasonality, and Irregularity. Not all
time series have all these components. Figure 1.2
shows the effects of these time series components
over a period of time.

7.  Trend: Some times a time series displays a steady
tendency of either upward or downward
movement in the average value of the forecast y
over time. Such a tendency is called a trend.
When observations are plotted against time, a
straight line describes the increase or decrease in
the time series over a period of time.
 Cycles: upward and downward movements in
the variable value about the trend time over a
time period are called cycles. A business cycle
may vary in length, usually more than a year but
less than 5 to 7 years.

8.  Seasonal: It is a special case of a cycle
component of time series in which fluctuations are
repeated usually within a year (Egg. Daily, weakly,
monthly, quarterly) with a high degree of
regularity. For example, average sales for a retail
store may increase greatly during festival
seasons.
 Irregular: Variations are rapid charges or bleeps
in the data caused by short term unanticipated
and non recurring factors. Irregular fluctuations
can happen as often as day to day.

9. Time Series Decomposition Models
The Analysis of Time Series Consist of two major steps:
 Identifying the various factors or influences which
produce the variations in the time series.
 Isolating, analyzing and measuring the effect of
these factors independently holding other things
constant.
There are two main Model Time Series:
 Multiplicative Model
 Addictive Model

10. Multiplicative Model :
The actual values of a time series, Y can be found by multiplying
its four components at a particular time period. The effect of four
components on the time series is interdependent. The
multiplicative time series model is defined as:
Y=T*C*S*I ………….. Multiplicative Model
Addictive Model:
In this Model it is assumed that the effect of various components
on a time series can be estimated by adding these components.
The addictive time series model is defined as:
Y=T+C+S+I …………. Addictive Model

11. .