Jürgen Wolters

Introduction to Modern Time Series Analysis

This book presents modern developments in time series econometrics that are applied to macroeconomic and financial time series. It attempts to bridge the gap between methods and realistic applications. This book contains the most important approaches to analyse time series which may be stationary or nonstationary. Modelling and forecasting univariate time series is the starting point. For multiple stationary time series Granger causality tests and vector autoregressive models are presented. For real applied work the modelling of nonstationary uni- or multivariate time series is most important. Therefore, unit root and cointegration analysis as well as vector error correction models play a central part. Modelling volatilities of financial time series with autoregressive conditional heteroskedastic models is also treated.

Autoregressive Conditional Heteroscedasticity

All models discussed so far use the conditional expectation to describe the mean development of one or more time series. The optimal forecast, in the sense that the variance of the forecast errors will be minimised, is given by the conditional mean of the underlying model. Here, it is assumed that the residuals are not only uncorrelated but also homoscedastic, i.e. that the unexplained fluctuations have no dependencies in the second moments. However, BENOIT MANDELBROT (1963) already showed that financial market data have more outliers than would be compatible with the (usually assumed) normal distribution and that there are ‘volatility clusters’: small (large) shocks are again followed by small (large) shocks. This may lead to ‘leptokurtic distributions‘, which – as compared to a normal distribution – exhibit more mass at the centre and at the tails of the distribution. This results in ‘excess kurtosis’, i.e. the values of the kurtosis are above three.

A money demand system for German M3

A small macroeconomic model is constructed starting from a German money demand relation for M3 based on quarterly, seasonally unadjusted data for the period from 1976 to 1996. In contrast to previous studies we build a vector error correction model for M3, GNP, an inflation rate and an interest rate spread variable to represent opportunity costs of holding money. Furthermore, import price inflation is added as an exogenous variable. The model is used to analyze the relation between money growth and inflation by means of an impulse response analysis.

Money demand in Europe

H. Lutkepohl, J. Wolters: Preface.- Methodological Studies: D.F. Hendry, G.E. Mizon: Exogeneity, Causality, and Co-breaking in Economic Policy Analysis of a Small Econometric Model of Money in the UK.- N.R. Ericsson: Empirical Modeling of Money Demand.- Single Country Studies: A. Ripatti: Stability of the Demand for M1 and Harmonized M3 in Finland.- O. Eitrheim: The Demand for Broad Money in Norway, 1969-1993.- M. Scharnagl: The Stability of German Money Demand: Not Just a Myth.- H. Lutkepohl, J. Wolters: A Money Demand System for German M3.- J.L. Vega: Money Demand Stability: Evidence from Spain.- N.R. Ericsson, D.F. Hendry, K.M. Prestwich: Friedman and Schwartz (1982) Revisited: Assessing Annual and Phase-Average Models of Money Demand in the United Kingdom.- N.R. Ericsson, S. Sharma: Broad Money Demand and Financial Liberalization in Greece.- M. Peytrignet, C. Stahel: Stability of Money Demand in Switzerland: A Comparison of the M2 and M3 Cases.- Multi-Country Studies: K. Juselius: Changing Monetary Transmission Mechanisms within the EU.- G. Fagan, J. Henry: Long Run Money Demand in the EU: Evidence for Area-Wide Aggregates.- M.M.G. Fase, C.C.A. Winder: Wealth and the Demand for Money in the European Union.

Uncovered Interest Rate Parity and the Expectations Hypothesis of the Term Structure: Empirical Results for the US and Europe

If interest rates are considered to be integrated of order one (I(1)) uncovered interest rate parity (UIP) implies that domestic and foreign nominal interest rates should be integrated with cointegrating vector (1,-1). On the other hand, if the expectations hypothesis of the term structure (EHT) is true another equilibrium condition can be derived, namely that domestic short- and long- term interest rates should cointegrate with the vector (1,-1). Thus UIP and EHT imply that three cointegrating vectors should exist in the four dimensional system of short- and long-run domestic and foreign interest rates. These hypotheses are tested with monthly observations of short- and long-term European and US interest rates for the period 1994(1) to 2001(12). It is found that only one cointegrating relation exists between these four interest rates. It is a linear combination between the spread in Euroland and the spread in the US. A vector error correction model for the spreads gives further insights into the dynamic relations between the interest rates in the US and Euroland.

Are Real Interest Rates Stable?, An International Comparison

The question whether real interest rates are stable, has, with the exception of a very few papers, not been tackled so far. In empirical investigations, one has traditionally assumed that nominal and real interest rates are stationary. This was the basis for applying traditional econometric methods. In the last few years, however, quite a lot of empirical papers have found that nominal interest rates for various countries are not stationary but contain a unit root.1) If this finding is correct, it can have implications for the stochastic structure of real interest rates and for the econometric methodology which one should apply. But also from a theoretical point of view, it is important to know the time series behaviour of real interest rates. In general, the theoretical approaches at least implicitly assume stationary real interest rates.

Money and Prices in Germany

In this contribution the linkages between money growth and inflation are investigated. Two vector error correction models are estimated one with data before and the other one with data including the German monetary union (GMU), which took place on 1 July 1990. The models contain the variables money, prices, output, and interest rate. We found one cointegrating relation, which can be interpreted as a long-run money demand equation. Including the GMU this relation remains stable if the structural break is captured by dummy variables. Although the dynamic structure of the two vector error correction models is nearly not influenced by the GMU the linkages between money growth and inflation are sensitive whether international price movements are included or not.

Nonstationary Panel Data

In Chapter 4 we introduced an approach to analyse vectors of stationary time series, while Chapter 6 was devoted to the nonstationary case. With yth we denote the ith component at time t, t = 1, …, T. In typical time series applications the dimension of the vector is small (for instance equal to 3 in Examples 4.4. or 6.8), while the time dimension is rather large (T > 100). In a panel situation the number of components or units, denoted by N, is large as well, i = 1, …, N. There may be N price indices, N exchange rates or generally N countries or units. The unrestricted VAR(p) model from equation (4.1) allows each component to depend on its own lagged values and on the past of all other components. Hence, (4.1) includes p•N2 + N parameters when modelling time series from N units, a number growing fast with the dimension N. Already with N = 10 there would be hundreds of parameters to estimate. Therefore, the VAR approach is not applicable unless the cross-sectional dimension is rather small.

Zur Ökonometrischen Modellierung Kurz- und Langfristiger Abhängigkeiten; Dargestellt am Beispiel der Zinsstruktur

Fur die empirische Wirtschaftsforschung spielt die dynamische Spezifikation okonometrischer Hypothesen eine sehr wichtige Rolle. Viele der Kontroversen uber die Wirksamkeit wirtschaftspolitischer Masnahmen sind Folgen unangemessener empirischer Erfassungen des kurz- und langfristigen Verhaltens der Wirtschaftssubjekte.

Ökonometrische Modelle bei zeitreihendaten versus multivariate Zeitreihenmodelle—Eine Übersicht

This paper surveys the typical econometric and time series approaches. Contrary to the widely held view that these approaches have little in common, it is argued that strong dependencies exist between both methods and that for sound empirical research one should use an integration of these two methodologies.