CONVERTING TIME SERIES DATA FOR INFORMATION

SYSTEMS INTEGRATION

Li Peng

Software School, Hunan University, Changsha, Hunan, China

Keywords: Integration of heterogeneous data source, data conversion, time-series, calendar.

Abstract: Most enterprises have an autonomous and heterogeneous information system. The same data may be

diversely represented in different information systems. The core of solutions for integrating heterogeneous

data sources is data conversion. One of the major issues of data conversion is how to convert data that

contains temporal information. In this paper I propose a method to effectively convert time-series data

appearing in enterprises. The concept of calendar is integrated into the proposed method. The method is

based on a generalized representing form for data. The converting operations and processes are defined and

presented.

1 INTRODUCTION

Most enterprises have an autonomous and

heterogeneous information system. The same data

may be diversely represented in different

information systems. A typical example is time-

series data which arises very often in applications

like scheduling, manufacturing and process control.

A temporal data “15.4.2005” may be an integer “52”

in another application. The cause of the

inconsistency is that enterprises use various calendar

systems in their applications. The temporal values of

time-series data are determined by the used calendar

system.

The core of solutions for integrating information

systems is data conversion. In this paper, I mainly

discuss how to convert time-series data. Since time-

series data is associated with calendar systems, this

work focuses on converting calendar systems. In

previous related work, the researchers have defined

some calendar operations to derive various user-

defined calendars (Lee, Elmasri and Won, 1996).

However, some complex conversions, for example,

restructuring hierarchical calendars and the

conversion between irregular calendars can not

achieved by using these operations.

In this paper, I propose a systematic method to

convert calendar systems. It contains required

processes and operations. The basis of the

converting method is a generalized representing

form for data, with which all the calendar systems

used in enterprises can be represented in a consistent

form.

This paper is organized as follows. Section 2

gives an overview of calendar systems used in

enterprises. Section 3 presents a generalized

representing form for data. Section 4 describes the

method for converting calendar systems. Section 5

concludes the paper with a summary of the

contributions of this research.

2 CALENDAR SYSTEMS USED

IN ENTERPRISES

A calendar is a temporal model. Each calendar has a

time domain which consists of a sequence of

temporal values. The calendar systems used in

enterprises can be classified in four essential types:

continuous calendar system, discrete calendar

system, complete calendar system and composite

calendar system (Dangelmaier & Ketterer, 1995).

Each type of calendar systems is described as

follows.

The continuous calendar system is modelled as

being isomorphic to the real numbers, with each real

number corresponding to an instant.

The discrete calendar system is modelled as

being isomorphic to the integers. An example of

discrete calendars is “days of January”.

289

Peng L. (2006).

CONVERTING TIME SERIES DATA FOR INFORMATION SYSTEMS INTEGRATION.

In Proceedings of the Eighth International Conference on Enterprise Information Systems - DISI, pages 289-292

DOI: 10.5220/0002491702890292

 SciTePress

(B)

day

(B)

day

date

(P)

(B)

month

(B)

year

(B)

day

wor

-day

(R)

(B)

month

(B)

year

The complete calendar system has no gap. There

are no events which can not be assigned in this

calendar. The Gregorian calendar is an example of

complete calendars.

The composite calendar system has gaps and

consists of a number of time domains. These time

domains can not overlap. The Business calendar, in

which all holidays and weekends have been

excluded, is an example of composite calendars.

A calendar system used in enterprises can be

either one of the four essential types or a

composition of them. For instance, the Gregorian

calendar is a complete discrete calendar.

3 A GENERALIZED

REPRESENTING FORM FOR

CALENDAR SYSTEMS

In many temporal data model, time-series data is

modelled as an attribute that is treated with similar

semantics as other attributes, but with some

extensions to handle characteristics of time-series.

Such an attribute is called a time-series attribute

(Lee, Elmasri & Won, 1996).

Since time-series attribute can have complex

data values and the data values are determined by

the associated calendar, following constructors are

defined to represent various calendar systems.

At first, a node with the token “B” is used to

represent a simple attribute. The domain of a time-

series attribute represented with the node “B” is

integers. In Figure 1, the node “B” represents a

simple attribute “day”.

Figure 1: The note “B” represents a simple time-series

attribute

The constructor “P” represents a complete

calendar. The domain of a complete calendar

represented with the constructor “P” is the Cartesian

product of the domains of its components. For

example, the Gregorian calendar is described with

the complex attribute “date”, and “date” can be

described with component attributes “year”,

“month” and “day”. If dom (year) = 2005, dom

(month) =1, and dom (day) = {1, 2, …, 31}, the

domain of the attribute “date” would be the

Cartesian product dom (date) = {(2005, 1, 1), (2005,

1, 2), …, (2005, 1, 31)}. The structure in Figure 2

can be expressed as: date = P: (year, month, day).

Figure 2: The constructor “P” represents a complete

calendar system

The constructor “R” represents a composite

calendar. The domain of a composite calendar

represented with the constructor “R” is a subset of

the domain of its corresponding “P” constructor.

Here, the “R” constructor and the corresponding “P”

constructor are described with the identical

component attributes. A Business calendar can be

represented with “R” constructor. In this calendar all

holidays and weekends have been excluded. For

example, if the domain of its corresponding

complete calendar dom (date) = {(2005, 1, 1), (2005,

1, 2), …, (2005, 1, 31)}, the domain of the Business

calendar would be {(2005, 1, 3), (2005, 1, 4), (2005,

1, 5), (2005, 1, 6), (2005, 1, 7), (2005, 1, 10), …,

(2005, 1, 31)}. The structure in Figure 3 can be

expressed as: work-day = R:(year, month, day).

Figure 3: The constructor “R” represents a composite

calendar system.

A calendar is a human abstraction of the physical

time space, and the physical time space is considered

as a hierarchy of totally ordered sets of time

intervals (Lee, Elmasri, Won, 1996). Here I define a

ICEIS 2006 - DATABASES AND INFORMATION SYSTEMS INTEGRATION

290

(B)

day

Figure 4: The constructor “H” represents the hierarchical

structure of a calendar

calenda

(H)

(B)

month

(B)

year

“H” constructor to describe the hierarchies of

calendar systems. In a hierarchy, the time intervals

at each level are described by using a time unit.

Since the time intervals of each level are partitioned

according to the relationship between the time unit

at this level and the time units at the higher levels,

the domain of each level would be a set of Cartesian

products (except the highest level). As an example,

the hierarchical domain of the Gregorian calendar is

given in Figure 5 and Figure 4 shows the

hierarchical structure. The structure can be also

expressed as: calendar = H:(year, month, day).

The generalized representing form can be

described by a tuple ﹤ constructors, domains of

component attributes, constraints ﹥ , where

constructors are defined above, constraints limit the

values of attributes. For example, a constraint in the

Gregorian calendar is: if month = 2, then dom (day)

= {1, 2, …, 28}.

4 CONVERTING CALENDAR

SYSTEMS

Converting calendar systems mainly involves

following issues: converting a complete calendar to

another complete calendar, converting a complete

calendar to a composite calendar, and converting a

composite calendar to another composite calendar.

In this section, the converting processes are

presented in detail.

4.1 Converting a Complete

Calendar to Another Complete

Calendar

If the time units used in the source calendar and the

time units used in the destination calendar are not

identical, the hierarchical structure of the source

calendar would be restructured. At first, one or both

of calendars need to be converted to a calendar(s)

with the greatest common time unit. An example is

converting P:(year, month, day) to P:( year, week,

day). Since the time units used in the two calendars

are not identical, the hierarchical structure of

P:(year, month, day) will be restructured. The

corresponding hierarchical structure of P:(year,

month, day) is H:(year, month, day) and that of P:(

year, week, day) is H:(year, week, day). The

restructuring process is presented below:

Step1: Here, the common time unit is “day”. It is

the lowest level of the both hierarchies. The domain

of the lowest level (a set of Cartesian products) of

the source hierarchy is transformed to a set of

integers. For example, {(2005, 1, 1), (2005, 1, 2), …,

(2005, 12, 31)} → {1, 2, …, 365}.

Step2: According to the relationship between the

time unit at the lowest level and the time unit at the

higher level, the integers are partitioned and

assigned to the time unit at the higher level. For

example, {1, 2, …, 365} → {(1, 6), (1, 7), (2, 1), (2,

2), …, (53, 6)}.

Step3: Step2 will be recursively executed to

build the whole hierarchical structure of destination

calendar.

4.2 Converting a Complete

Calendar to a Composite

Calendar

If the time units used in the source calendar and in

the destination calendar are not identical, the

hierarchical structure of the source calendar would

be first restructured. Then, an operation exclude is

used to exclude time intervals from the source

calendar. In addition, an operation union is used to

combine time intervals. The operations are defined

below:

exclude (I, C): Exclude the time interval I from

the calendar C.

union (I

, I

): Combine time intervals I

and I

For example, exclude (union (holidays,

weekends), P:(year, month, day)) → R:(year, month,

day).

CONVERTING TIME SERIES DATA FOR INFORMATION SYSTEMS INTEGRATION

291

4.3 Converting a Composite

Calendar to Another Composite

Calendar

To avoid loss of data in the conversion, the

corresponding complete calendar for the source

calendar will be utilized. This complete calendar

will be converted to the corresponding complete

calendar for the destination calendar. According to

the structure of the destination calendar, the time

intervals will be excluded from the complete

destination calendar by using the operation exclude.

An example is converting R:(year, month, day)

to R:(year, week, day). The converting process is

illustrated below:

Step1: The hierarchical structure of the source

calendar H:(year, month, day) will be converted to

H:(year, week, day).

Step2: The operation exclude is used to exclude

time intervals from the destination calendar

(complete).

exclude (union (holidays, weekends), P:(year,

week, day)) → R:(year, week, day).

5 CONCLUSION

In this paper, I proposed a systematic method that

enables effectively converting time-series data

appearing in enterprises. Time-series data is

modelled as an attribute that is associated with a

calendar. Therefore, this work focuses on converting

calendar systems. I presented a generalized

representing form, with which various complex

structures of calendar systems can be represented in

a consistent form. The converting processes and

operations are based on the representing form. The

conversion between different calendars is presented

in detail.

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2005

(2005, 1) (2005, 12)…

(2005, 1, 1), …, (2005, 1, 31), …, (2005, 12, 1), …, (2005, 12, 31)

ure 5: The hierarchical

omain of the Gre

orian calenda

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