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Introduction to ARIMA

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 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

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

Together, the model can be described as ARIMA (p, d, q), or

)( =

)(

ΒΦ

where

)

-(1=

∇

plus

ΒΒΦ

-...--1=)(

φφ

and

ΒΘ

-...--1=(B)

θθ

1 Time Series Techniques for Economists.

剩余27页未读，继续阅读

NotImplementedError: statsmodels.tsa.arima_model.ARMA and statsmodels.tsa.arima_model.ARIMA have been removed in favor of statsmodels.tsa.arima.model.ARIMA (note the . between arima and model) and statsmodels.tsa.SARIMAX.

这个错误提示是因为 `statsmodels` 库在新版（0.12.0）中更新了 ARIMA 模型的实现方式，将原来的 `statsmodels.tsa.arima_model.ARMA` 和 `statsmodels.tsa.arima_model.ARIMA` 移除，改为使用 `statsmodels.tsa....

ARIMA-GARCH的python代码

In this code, you first fit an ARIMA model to your data using the `ARIMA` function from the `statsmodels.tsa.arima_model` module. The `order` parameter specifies the order of the AR, I, and MA ...

arima模型参考文献

New introduction to multiple time series analysis. Berlin: Springer. 5. Wei, W. W. S. (2006). Time series analysis: univariate and multivariate methods (2nd ed.). Boston: Pearson Education. 希望对...

Traceback (most recent call last): File "F:\pythonproject\ARIMA-GRACH\3.py", line 26, in <module> arima_model = ARIMA(train_data, order=(10, 1, 0)) File "E:\anaconda\lib\site-packages\statsmodels\tsa\arima_model.py", line 45, in init super().init(*args, **kwargs) File "E:\anaconda\lib\site-packages\statsmodels\tsa\arima_model.py", line 29, in init raise NotImplementedError(ARIMA_DEPRECATION_ERROR) NotImplementedError: statsmodels.tsa.arima_model.ARMA and statsmodels.tsa.arima_model.ARIMA have been removed in favor of statsmodels.tsa.arima.model.ARIMA (note the . between arima and model) and statsmodels.tsa.SARIMAX. statsmodels.tsa.arima.model.ARIMA makes use of the statespace framework and is both well tested and maintained. It also offers alternative specialized parameter estimators.

这个错误是因为你使用了一个已经被弃用的 statsmodels.tsa.arima_model.ARIMA 模型，应该使用新的 statsmodels.tsa.arima.model.ARIMA 模型。你需要更新你的代码来使用新的模型。具体来说，你需要从 statsmodels....

from statsmodels.tsa.arima_model import ARIMA 中如何插卡arima模型的summary

在使用ARIMA模型进行时间序列分析时，可以通过以下代码获取模型的summary： ``` # 假设已经拟合好了ARIMA模型并存储在变量model中 from statsmodels.tsa.arima_model import ARIMA # 获取ARIMA模型的summary model...

arima_model = sm.tsa.ARIMA(train_data, order=(8, 1, 0)).fit() arima_result = arima_model.fit(disp=False) print(arima_result.summary())检查并修改

这段代码有点问题，因为你用 `arima_model.fit()` 已经进行了拟合，所以不需要再用 `arima_result = arima_model.fit()` 进行一次拟合。可以直接使用 `arima_model.summary()` 来查看 ARIMA 模型的拟合结果。修改...

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