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Lecture Notes in Statistics 119
Edited by P. Bickel, P. Diggle, S. Fienberg, K. Krickeberg,
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Masanao Aoki
Arthur M. Havenner
Editors
Applications of Computer Aided
Time Series Modeling
, Springer
Masanao Aoki
Department of Economics
University of California, Los Angeles
Los Angeles, CA 90024
Arthur M. Havenner
Department of Agricultural Economics
University of California, Davis
Davis, CA 95616
CIP data available.
Printed on acid-free paper.
01997 Springer-Verlag New York, Inc.
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9 876 5 432 I
ISBN-13: 978-0-387-94751-8 e-ISBN-13: 978-1-4612-2252-1
DOl: 10.1007/978-1-4612-2252-1
Preface
This book consists of three parts: Part One is composed of two introductory
chapters. The first chapter provides an instrumental varible interpretation of
the state space time series algorithm originally proposed by Aoki (1983), and
gives an introductory account for incorporating exogenous signals in state space
models. The second chapter, by Havenner, gives practical guidance in apply
ing this algorithm by one of the most experienced practitioners of the method.
Havenner begins by summarizing six reasons state space methods are advanta
geous, and then walks the reader through construction and evaluation of a state
space model for four monthly macroeconomic series: industrial production in
dex, consumer price index, six month commercial paper rate, and money stock
(Ml). To single out one of the several important insights in modeling that he
shares with the reader, he discusses in Section 2ii the effects of sampling er
rors and model misspecification on successful modeling efforts. He argues that
model misspecification is an important amplifier of the effects of sampling error
that may cause symplectic matrices to have complex unit roots, a theoretical
impossibility. Correct model specifications increase efficiency of estimators and
often eliminate this finite sample problem. This is an important insight into
the positive realness of covariance matrices; positivity has been emphasized by
system engineers to the exclusion of other methods of reducing sampling error
and alleviating what is simply a finite sample problem.
The second and third parts collect papers that describe specific applications.
Part Two collects papers on linear models, and Part Three presents recurrent
neural networks as useful nonlinear models. Applications in agriculture, macroe
conomics, financial economics, and engineering are featured. More specifically,
the chapter by Berwald and Havenner provides a good illustration of the poten
tial of state space modeling in agricultural applications. They model soybean
complex spot and futures prices (six-dimensional observation vectors). These
series are volatile and difficult to model. They use both in-sample and out
of-sample forecasts to evaluate the model they estimate. Egan and Havenner
compare state space, VA R, and futures markets of sequentially produced types
of cattle. Arndt and Foster model monthly U. S. spot wheat prices in nine geo
graphically separate markets. Their results tend to support the hypothesis that
spot wheat markets are inefficient. Fiorito calculates impulse response functions
from the estimated model for the U. S. labor markets. This chapter is a good
illustration of how one might use the estimated models for policy analysis by
calculating impulse responses of the economy to various exogenous shocks.
State space modeling of time series with exogenous signals has been sketched
out in Chapter One. The applications reported in the next three papers all in
corporate exogenous signals as parts of their models. Dorfman compares several
exchange rate models reported in the literature. His study points to the use
fulness of some macroeconomic variables as exogenous signals in forecasting
exchange rates. Ostemark examines the effects of Japanese stock markets on
Finnish derivatives by building state space models of the series. DiRusio has an
example of an exchange rate as an exogenous signal in his model.
vi
Mendelssohn and Schwing tackle the very difficult problem of building time
series models of climactic changes with both trend and seasonal components.
Because of these components, they use an alternative method for building time
series models due to Akaike, Kitagawa, and Gersch.
Part Three consists of two contributions on neural networks. State space
time series models are linear models and may not work well with time series
in which nonlinear effects are significant. For example, financial time series
often contain significant nonlinear components. The chapter by Rhee reports
on forecasting stock indices with recurrent neural networks, and the chapter by
Saxen is a theoretical background piece that connects simple recurrent neural
networks with familiar ARMA models.
Masanao Aoki
August 1996
Los Angeles, California
Table of Contents
Preface v
PART I
INTRODUCTION TO STATE SPACE MODELING
1. The SSATS algorithm and subspace methods 3
Masanao Aold
2. A guide to state space modeling of multiple time series 15
Arthur M. Havenner
PART II
APPLICATIONS OF STATE SPACE ALGORITHM
1. Evaluating state space forecasts of soybean complex prices 75
Derek Berwald and Arthur M. Havenner
2. A state space model of monthly US wheat prices 91
Channing Arndt and Kenneth Foster
3. Managing the heard: price forecasts for california cattle production 107
Lorraine Egan and Arthur Havenner
4. Labor market and cyclical fluctuations 121
Riccardo Fiorito
5. Modeling cointegrated processes by a vector-valued state space algorithm 141
Ralf Ostermark
6. A method for identification of combined deterministic stochastic systems 181
David Di Ruscio
7. Competing exchange rate models 237
Jeffrey H. Dorfman
8. Application of state-space models to ocean climate varibility in the northeast 255
pacific ocean
Roy Mendelssohn and Franklin B. Schwing
PARTll
APPLICATIONS OF NEURAL NETWORKS
1. On the equivalence between ARMA models and simple recurrent neural net-
works 281
Henrik Saxen
2. Forecasting stock market indicies with recurrent neural networks 291
Maxwell J. Rhee
Part I
Introduction to State Space Modeling
The SSATSI Algorithm and Subspace Methods
Masanao Aoki
Department of Economics
University of California
Los Angeles, California 90095-1477
Keywords: Instrumental Variables, State Space Modeling, Subspace Method.
Abstract
This chapter summarizes the development of the State Space Aoki Time Series algo
rithm since its inception in 1983 as an instrumental variables method, and relates it
to subspace methods popular in the engineering literature from the viewpoint of or
thogonal projections. Except for the numerical method used to calculate orthogonal
projections these two classes of methods are conceptually equivalent.2
1 Background
As evidenced in the literatures on statistics, macroeconomic time series, economet
rics, and control and systems, the "art" of time series modeling is practiced in many
disciplines with slightly.different emphases which are dictated by intended applica
tions. For vector-valued time series, state space modeling algorithms seem superior
to the ARMA modeling approaches. In the former category of modeling procedures
we have the Aoki algorithm, originally announced in 1983 and modified subsequently
in Aoki (1987, 1990) and in Havenner and Aoki (1988), and subspace methods which
are popular in the control and systems literature.3
We observe some degree of duplication of effort in some parts of the engineering
literature of what has been available in the instrumental variables version of the Aoki
algorithm. More specifically, it appears that improvements and modifications of the
original Aoki algorithm which were carried out by Aoki and others since 1987 appear
lState Space Aoki TIme Series
2March 1996. The author benefited from seeing an unpUblished manuscript by G. Picci and T.
Katayama (1996a. b). The author also thanks A. Havenner for helpful discussion.
3See Viberg (1994) or van derVeen et aI. (1993) for surveys of the subspace methods.
