使用SAS VARMAX过程进行多重时间序列建模

需积分: 11 114 浏览量更新于2024-07-18 收藏 22.73MB PDF 举报

"《Multiple Time Series Modeling Using the SAS VARMAX Procedure》是由Anders Milhøj撰写的一本关于使用SAS VARMAX过程进行多元时间序列建模的专业书籍，旨在教导具有至少一门时间序列建模课程背景的经济学家如何利用SAS进行时间序列分析。书中强调了在现代计算能力的支持下，模型参数的估计变得迅速，使得传统的Box-Jenkins分析流程在很多情况下已过时。现在，通过自动滞后识别方法可以轻松拟合分布式滞后模型，甚至对于二元和多元模型，PROC VARMAX也能自动进行建模。书中还涉及Granger因果关系测试、反馈、均衡、协整和误差校正等主题。此外，考虑到参数化的不稳定性，书中也介绍了Bayesian方法在VARMAX过程中的应用，以及由于GARCH模型的普及，波动性建模已成为时间序列建模的标准部分，PROC VARMAX支持单变量和多变量GARCH模型，特别适用于关注风险的金融分析。本书通过实例教学，无论是初学者还是熟悉高级理论时间序列模型的读者，都能找到使用PROC VARMAX的有效途径。" 本书详细阐述了以下关键知识点： 1. **SAS VARMAX过程**：SAS的VARMAX（Vector Autoregressive Moving Average with eXogenous regressors）过程是用于拟合多元时间序列模型的工具，它能够处理自回归移动平均模型，包括外生变量。 2. **自动化滞后识别**：与传统的Box-Jenkins方法相比，VARMAX过程通过自动滞后识别方法简化了模型选择过程，可以快速比较不同模型的拟合度。 3. **Granger因果关系测试**：VARMAX过程支持Granger因果关系分析，可用于检验时间序列之间是否存在因果关系。 4. **反馈与均衡**：书中讨论了模型中的反馈机制和系统内的均衡状态，这对于理解和预测经济系统的行为至关重要。 5. **协整与误差校正**：协整概念用于处理非平稳时间序列之间的长期关系，而误差校正模型则能捕捉到这些序列之间的短期动态调整。 6. **Bayesian方法**：在多元建模中，由于参数化可能不稳定，书中有介绍如何利用Bayesian方法来稳定模型参数。 7. **GARCH模型**：VARMAX过程支持广义自回归条件异方差（GARCH）模型，这是金融领域常用的风险评估工具，可以捕捉到数据的波动性。 8. **金融分析应用**：书中特别提到了VARMAX和GARCH模型在金融分析中的应用，特别是在风险管理和市场波动性评估方面。 9. **实例教学**：全书采用实例驱动的教学方式，让读者能够从实践中学习如何使用PROC VARMAX进行复杂的时间序列分析。这本书对于那些希望掌握SAS软件进行高效、精准时间序列分析的统计学家、经济学家和数据分析工作者来说，是一本非常实用的参考指南。通过深入学习，读者将能够利用SAS VARMAX过程解决实际问题，无论是在学术研究还是在业务决策中。

Acknowledgment

I would like to thank Xilong Chen, Principal Research Statistician Developer with SAS Institute, for reviewing

early and final manuscripts for technical content and offering advice that helped improve this book

Chapter 1: Introduction

Introduction ................................................................................................................. 1

Ordinary Regression Models........................................................................................ 1

Regression Models in Time Series Analysis ................................................................ 2

Time Series Models ..................................................................................................... 3

Which Time Series Features to Model ....................................................................................... 4

Parameterized Models for Time Series...................................................................................... 4

Introduction

This chapter outlines the intentions of this book. First, it briefly describes the special problems that emerge

when time series data has to be analyzed by means of regression models, as compared with applications of

regression models in simpler situations. Explained next are the extra features that are necessary for performing

regressions analysis on multivariate time series.

Ordinary Regression Models

The subject of regression models is included in most introductory statistical courses. The basic formulation

using just a single right-hand side variable is as follows:

αβ ε

i ii

yx=+ +

Here is a simple example using this regression model with teenagers’ heights as the right side variable and the

weight as the left side variable. This data is clearly not a time series data set, but a cross-sectional data set.

Program 1.1 shows the SAS code for this analysis for the well-known data set CLASS in the SASHELP library.

The model specifies that the weight is considered as a linear function of the height. This relationship is not

exact, and the observed differences between the observed weight and the weight as predicted by the regression

line form the errors ε

Program 1.1: A Simple Application of PROC REG for Cross-Sectional Data

PROC REG DATA=SASHELP.CLASS;

MODEL WEIGHT=HEIGHT;

RUN;

The resulting regression is then presented as a table that shows the estimated parameter values, their standard

deviations, and results of the t-tests. Also, various plots are presented by PROC REG, using the SAS Output

Delivery System (ODS) GRAPHICS facilities. An example is the regression plot in Figure 1.1, which is useful

when only a single right side variable is used.

2 Multiple Time Series Modeling Using the SAS VARMAX Procedure

Figure 1.1: Regression Plot for Cross-Sectional Data Generated by Program 1.1

This analysis relies on many statistical assumptions in order to ensure that the estimation method is efficient and

that the printed standard deviations and p-values are correct. Moreover, the relationship between the two

variables must be linear. In this situation, the x-variable, which is the height of the teenager, is assumed to be

fixed in advance so that the assumption of exogeneity is met.

These assumptions are formulated for the residuals ε

. In short, the error terms must be independent and

identically distributed. Also, they are often assumed to have a Gaussian distribution. In the example in Program

1.1, these assumptions are met; at least, it is not clear that they are violated. In the context of this book, the most

important assumption is independence. The further assumption E[ε|X] = 0 (which is, of course, dubious in this

example) is irrelevant if the model by assumption describes only the conditional distribution of the y’s, given

the x’s.

A clear dependence will be present if the data set could include twins; otherwise, human beings are individuals.

The data set consists of teenagers. One might think that gender, race, or age could influence the relationship

between height and weight. If this information is available, it can be tested; age and gender are in fact variables

in the data set. If such effects are of some importance for the estimated relationship, they could lead to

dependence among the residuals—for example, that most of the girls have weights below the regression line,

while the observed weights for most of the boys are above the line. However, this effect is difficult to establish

with such a small data set.

For non–time series, correlation among the observations is usually not a serious problem. Most often, it is

simply a problem of a missing variable, like gender in this example, which could be easily solved by adding a

variable to the model.

Regression Models in Time Series Analysis

The most important problem when regression models are applied in time series analysis is that the residuals are

usually far from independent. The analysis in Program 1.2 gives an example. The code is attempting to explain

the log-transformed level of a price index (the variable LP) for more than 150 years in Denmark using the log-

transformed wage index, LW, as the right side variable. Both series are log-transformed.

Chapter 1: Introduction 3

Program 1.2: A Simple Application of PROC REG for Time Series Data

PROC REG DATA=SASMTS.WAGEPRICE;

MODEL LP=LW;

RUN;

The regression plot (Figure 1.2) clearly shows that something is wrong, because the observations seem to vary

systematically around the line, not randomly as in the previous example, Figure 1.1. It seems that the

observations move along a curve that “flutters” around the regression line. Wages and prices usually increase

over time, so the observations are nearly ordered by years from the left to the right. The twisting around the

regression line shows that the prices for many consecutive years could be high compared to the wages. But in

periods of many consecutive years, prices could be smaller when compared to the wages.

In statistical terms, this finding tells you that the residuals are highly autocorrelated.

Figure 1.2: Regression Plot for Time Series Data Generated by Program 1.2

Economically, the model makes sense, and the dependencies among error terms that are close in time are easily

understood. However, the whole idea of taking the level of the wages as input to a model for the level of the

prices is doubtful. Why not vice versa? Economically, one could argue that prices affect wages when workers

want to be compensated for an increasing price level. On the other hand, higher wages to some extent will

increase the price level because the production of goods becomes more expensive. This situation calls for a two-

dimensional model whereby both the wage and the price are used as left side variables. Moreover, the mutual

dependence is not necessarily immediate but could include lags. Such models form the basis for this book.

Time Series Models

A formal definition of time series is that it is a sequence of observations x

, x

, .., x

. The observations, the x’s,

can be one-dimensional, leading to a one-dimensional time series. The x’s can also consist of observations for

many variables, leading to a multidimensional series, which is the main feature of this book. Models for one-

dimensional series are the subject of another SAS book (Brocklebank and Dickey, 2003). Therefore, univariate

time series models are addressed in this book only as a part of the models for multidimensional time series.

剩余209页未读，继续阅读

sinat_41581062

粉丝: 21
资源: 174

使用SAS VARMAX过程进行多重时间序列建模

Proc sql beyond the basic using sas

Time-Series Prediction using GMDH in MATLAB: MATLAB 实现 GMDH for Time-Series Modeling and Prediction-matlab开发

Practical-time-series-analysis-master-time-series-data-processing-visualization-and-modeling-using-Python.pdf.pdf

Decision Tree Modeling Using SAS Course Notes

GluonTS – 概率时间序列建模(Probabilistic Time Series Modeling)

Advanced Predictive Modeling Using Sas EM51 Course Notes 2004

2019 Multilevel Modeling using R.pdf

Using Base SAS® and SAS® Enterprise Miner™ to Develop Customer Retention Modeling

Liquid-Solid Phase Change Modeling Using Fluent.pdf

Multiphysics Modeling Using COMSOL v.4-02.pdf

最新资源