Svend Hylleberg

The Japanese consumption function

Abstract A theory of seasonal cointegration and integration is discussed in Hylleberg, Engle, Granger, and Yoo (1990) and tests for seasonal unit roots are also developed. To estimate and test for seasonal cointegration at each frequency, a two-step procedure similar to the one suggested by Engle and Granger (1987) is investigated in this paper. Using Japanese dataon consumption and income, evidence in favour of seasonal cointegration at frequency 1 4 is found. An economic interpretation of this cointegrating relation is presented using the notion of a slightly impatient borrowing-constrained utility-maximizing consumer. While the test statistics for noncointegration occurring at the frequency 1 2 of a cycle have the same distribution as the test statistic obtained for the zero frequency case by Engle and Granger (1987) and Engle and Yoo (1987), the distribution of the test statistics for noncointegration at the frequency 1 4 (and 3 4 ) is derived based on the asymptotic distribution theory for testing a pair of complex roots on the unit circle [Ahtola and Tiao (1987), Chan and Wei (1988)]. The critical values and evidence on the power of the test are obtained through Monte Carlo simulations.

Cointegration and Error Correction Mechanisms

Starting from a multivariate Wold representation for N variables that are integrated of order 1, this paper shows that, given that the N variables have r cointegrating vectors, there is an equivalence between five alternative representations of the multivariate model: the autoregressive representation; the error-correction representation; the interim multiplier representation; the Bewley (1979) representation; and the common trend representation. Proof of the theorem uses a result based on the Smith-McMillan lemma for polynomial matrices. The paper concludes by commenting on the different representations. Copyright 1989 by Royal Economic Society.

Seasonality in Macroeconomic Time Series

Recently, the seasonal characteristics of macroeconomic time series have drawn a lot of attention. It has been argued that the seasonal component of many macroeconomic time series constitutes a major part of the series measured as a proportion of the variance. In addition it has been found that the seasonal component of most macroeconomic time series is constant and best “explained” by seasonal dummies. Specifically it is often found that a Christmas boom is followed by a beginning of the year trough.Based on quarterly and monthly macroeconomic time series from a large number of countries this paper shows that many macroeconomic time series have seasonal components that are changing over time. Furthermore, the Christmas boom and especially the 1st quarter trough is not found nearly as often as one might expect.

Tests for seasonal unit roots general to specific or specific to general

Abstract In this paper the small sample properties of tests for seasonal unit roots in quarterly time series are evaluated and compared. The basic difference between the two tests is that the test proposed by Hylleberg, Engle, Granger, and Yoo (1990), the HEGY test, adopts the general to specific strategy and tests the null of a unit root, while the test proposed by Canova and Hansen (1993), the CH test, adopts the specific to general principle and tests the null of a stationary process around a deterministic seasonal pattern. The main result of the Monte Carlo experiments is that the two tests complement each other.

Spurious deterministic seasonality

It is sometimes assumed that the R2 of a regression of a first-order differenced time series on seasonal dummy variables reflects the amount of seasonal fluctuations that can be explained by deterministic variation in the series. In this paper we show that neglecting the presence of seasonal unit roots may yield spuriously high values of this coefficient.

A note on the distribution of the least squares estimator of a random walk with drift

Abstract It is shown that the application of the result that the Dickey-Fuller ‘ T ’ obtained from a regression with an intercept is asymptotically normal if the DGP is a random walk with drift may be of little use in small samples unless the drift is enormous. In fact the Dickey-Fuller distribution may give a better approximation in many case.

Seasonal Integration and the Evolving Seasonals Model

In this paper it is argued that describing seasonal patterns as an evolving seasonals model in which the coefficients attached to seasonal trigonometric terms follow simple autoregressive processes can be very useful when one is faced with the task of extending well known results obtained for non-seasonal time series to the seasonal case. Such a perspective gains its utility from the fact that this evolving seasonal Model (ESM) can be decomposed into quantities that are non-seasonal and the behaviour of these variables can be examined with standard techniques. It emerges that this strategy will deliver methods currently in use for the analysis of seasonal series, and is also flexible enough to suggest some new alternatives.

A note on the distribution of the least squares estimator of a random walk with drift: Some analytical evidence

Abstract In this paper we define the notion of a local drift in a unit root process. The theory provides a bridge between the apparent diverging asymptotic theories that apply when a drift is either present or absent in an integrated time-series. Our asymptotic results help to explain the Monte Carlo results of Hylleberg and Mizon ( Economics Letters , 1989, 29, 225–230) and Schmidt ( Advances in Econometrics , 1988, 8, 161–200).

Seasonality in Economic Models

Seasonality has been a major research area in economics for several decades. The paper asses the recent development in the literature on the treatment of seasonality in economics, and divides it into three interrelated groups. The first group, the Pure Noise Model, consists of methods based on the view that seasonality is noise contaminating the data or more correctly contaminating the information of interest for the economists. The second group, the Time Series Models, treats seasonality as a more integrated part of the modeling strategy, with the choice of model being data driven. The third group, Economic Models of Seasonality, introduces economic theory, i.e. optimizing behavior into the modeling of seasonality.

Common Periodic Correlation Features and the Interaction of Stocks and Flows in Daily Airport Data

We propose the multivariate representation of univariate and bivariate (possibly nonstationary) periodic models as a benchmark for the imposition of common periodic correlation (CPC) feature restrictions to obtain parameter parsimony. CPCs are short-run common dynamic features that co-vary across the different days of the week and possibly also across weeks and that can be common across different time series. We also show how periodic models can be used to describe interesting dynamic links in the interaction between stock and flow variables. We apply the proposed modeling framework to a dataset of daily arrivals and departures in airport transit data.