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Introduction to ARIMA
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Introduction to ARIMA Introduction to ARIMA
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Authors:
Martin Klint Hansen
Morten Christoffersen
Introduction to
ARIMA
in SAS 9.1.2
Description: IT-Department
Time series analysis for SAS 9.1.2, used for calculating forecasts, Ver. 010106
Macros: Range-mean plot and Mean Absolute Percentage Error (MAPE)
NOTICE:
In order to use the macros the following files must be placed in the right
folder on the respective computer. The macros have the following file
names: RM.SAS, and MAPE.SAS.
These are located on the X-drive at the ASB: X:\SAS\MACRO (can also
be accessed from your home PC with the WS_FTP client). However, the
correct placement is the C-drive in the SAS macro folder:
C:\Program Files\SAS\SAS 9.1\core\sasmacro\
Typographic conventions
Here, the following symbols have a special meaning:
[] - denotes an option, i.e. it can be filled in if desired.
| - denotes alternatives
<> - denotes a variable which must be entered by the user.
Note that it is not necessary to key <>, and that the variable can be
specified according to the user’s preference.
References:
Mills, Terence C. Time series techniques for economists
Cambridge University Press, Cambridge 1990.
Box, George E.P, Timeseries analysis: Forecasting and Control
Jenkins, Gwilym M. Holden-Day, San Francisco 1976.
Madsen, Henning Forecast Economic Time Series - An Introduction
Internal teaching material H No 156
IFI, The Aarhus School of Business, 1992.
CONTENTS
1 INTRODUCTION..................................................................................................... 1
1.1 NATURE OF THE PROBLEM......................................................................................................... 1
2 SPECIFICATION................................................................................................. 2
2.1 BY-STATEMENT........................................................................................................................ 2
2.2 IDENTIFY-STATEMENT ............................................................................................................ 3
2.3 ESTIMATE-STATEMENT........................................................................................................... 4
2.4 FORECAST-STATEMENT......................................................................................................... 5
3 USE OF RELATED MACROS ............................................................................ 7
3.1 RANGE-MEAN PLOT .................................................................................................................. 7
3.2 MAPE ..................................................................................................................................... 8
4 GENERAL EXAMPLE......................................................................................... 8
1
1 INTRODUCTION
PROC ARIMA can be used with both univariate and multivariate time series and
transfer function models. This user’s guide focuses solely on its use within univariate
time series.
1.1 Nature of the problem
PROC ARIMA uses the Box-Jenkins
1
method for the identification, estimation and
forecasting of time series which are either stationary or which require differentiating
to become stationary. PROC ARIMA cannot be used to evaluate whether the
prerequisite of variance homogeneity has been fulfilled - this is done graphically by
means of the macro %RM. The forecasting ability can be evaluated via the macro
%MAPE. Any preliminary transformations/manipulations must be carried out before
calling PROC ARIMA.
With PROC ARIMA, it is assumed that the process is generated from a sequence of
white noise, together with one or more of the linear filters outlined in fig. 1.
Figure 1 Flow chart for ARIMA models
t
x
Together, the model can be described as ARIMA (p, d, q), or
)( =
w
)(
q
t
p
Β
Θ
ΒΦ
where
x
)
-(1=
x
=
w
t
d
t
d
t
Β
∇
plus
Β
ΒΒΦ
p
p1
p
-...--1=)(
φφ
1
and
Β
ΒΘ
q
q1
q
-...--1=(B)
θθ
1
1 Time Series Techniques for Economists.
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