Robert M. Kunst

On the Role of Seasonal Intercepts in Seasonal Cointegration

In the paper we consider the role of seasonal intercepts in seasonal cointegration analysis. For the nonseasonal unit root, such intercepts can generate a stochastic trend with a drift common to all observations. For the seasonal unit roots, however, we show that unrestricted seasonal intercepts generate trends that are different across the seasons. Since such seasonal trends may not appear in economic data, we propose a modified empirical method to test for seasonal cointegration. This method is illustrated on German consumption and income data.

A forecasting comparison of some var techniques

Abstract Higher dimensional multivariate time series models suffer from the problem of over-parametrisation which impairs their forecasting performance. Starting from such unrestricted vector autoregressive models the paper discusses two ways to cope with this difficulty. The first approach reduces the number of free parameters by applying a subset modelling strategy. The second approach takes a Bayesian point of view by formulating ‘priors’ which are then combined with sample information, but leaving the original specification unaltered. Using Austrian quarterly macroeconomic time series a comparative study is undertaken by running alternative forecasting exercises. Both methods improve out-of-sample forecasting performance substantially at the cost of some bias in ex-post simulations. Comparing the ex-ante predictions of the two approaches, the former does better at short horizons whereas the latter gains as the forecast horizon lengthens.

Fractionally Integrated Models with ARCH Errors: With an Application to the Swiss One-Month Euromarket Interest Rate

We introduce ARFIMA-ARCH models, which simultaneously incorporate fractional differencing and conditional heteroskedasticity. We develop the likelihood function and we use it to construct the bias-corrected maximum (modified profile) likelihood estimator. Finite-sample properties of the estimation procedure are explored by Monte Carlo simulation. Backus and Zin (1993) have motivated the existence of fractional integration in interest rates by the persistence of the short rate and the variability of the long end of the yield curve. An empirical investigation of a daily one-month Swiss Euromarket interest rate finds a difference parameter of 0.72. This indicates non-stationary behavior. In contrast to first-order integrated models, the long-run cumulative response of shocks to the series is zero.

Seasonal Cointegration in Macroeconomic Systems: Case Studies for Small and Large European Countries

Stochastic seasonality in vector autoregressions draws attention to seasonal cointegrating vectors. Based upon the assumption of stochastic seasonality, seasonal cointegration is found in a six-dimensional vector autogregression of quarterly macroeconomic series which were not seasonally adjusted. The same experiment is performed on parallel data from four European economies: Austria, Finland, Germany, and the United Kingdom. Univariate and multivariate statistical evidence supports stochastic seasonality in Finland and Germany, whereas deterministic cycles dominate in Austria and the United Kingdom. Eventual correspondences of seasonal structures across countries are also analyzed. Copyright 1993 by MIT Press.

Seasonal cointegration, common seasonals, and forecasting seasonal series

Seasonal cointegration generalizes the idea of cointegration to processes with unit roots at frequencies different from 0. Here, “common seasonals,” also a dual notion of common trends, is adopted for the seasonal case. The features are demonstrated in exemplary models for German and U.K. data. An evaluation of the predictive value of accounting for seasonal cointegration shows that seasonal cointegration may be difficult to exploit to improve predictive accuracy even in cases where seasonal non-cointegration is clearly rejected on statistical grounds. The findings from the real-world examples are corroborated by Monte Carlo simulation.

TESTING FOR CYCLICAL NON‐STATIONARITY IN AUTOREGRESSIVE PROCESSES

This paper deals with the distributions evolving from the likelihood‐ratio test for the factor 1 −Bn in the lag polynomial Φ(B) under the basic assumption that the data series is generated by the autoregressive model Φ(B)Xt = et where {et} denotes Gaussian white noise. A characterization of the statistic and its asymptotic properties is given. Asymptotic and finite‐sample significance points are tabulated. The test procedure is illustrated by an economics example.

The impact of seasonal constants on forecasting seasonally cointegrated time series

In this paper we focus on the effect of (i) deleting, (ii) restricting or (iii) not restricting seasonal intercept terms on forecasting sets of seasonally cointegrated macroeconomic time series for Austria, Germany and the UK. A first empirical result is that the number of cointegrating vectors as well as the relevant estimated parameter values vary across the three models. A second result is that the quality of out-of-sample forecasts critically depends on the way seasonal constants are treated. In most cases, predictive performance can be improved by restricting the effects of seasonal constants. However, we find that the relative advantages and disadvantages of each of the three methods vary across the data sets and may depend on sample-specific features.

Decisions On Seasonal Unit Roots

Decisions on the presence of seasonal unit roots in economic time series are commonly taken on the basis of statistical hypothesis tests. Some of these tests have absence of unit roots as the null hypothesis, while others use unit roots as their null. Following a suggestion by Hylleberg (1995) to combine such tests in order to reach a clearer conclusion, we evaluate the merits of such test combinations on the basis of a Bayesian decision setup. We find that the potential gains over a pure application of the most common test due to Hylleberg et al. (1990) can be small.

Modelling exchange rates: long-run dependence versus conditional heteroscedasticity

Indications for two different features not captured by low-order linear time-series models can be found in day-to-day changes of exchange rates: long memory and conditional heteroscedasticity. These characteristics have inspired the development of ARFIMA and GARCH models. By means of Monte Carlo simulation, it is demonstrated that either of the two features stands a non-negligible chance of being detected spuriously in the presence of the other. A table of explicit empirical small-sample quantiles for identification of long-memory structures in the presence of GARCH effects is included.

Analysis of Austrian Stocks: Testing for Stability and Randomness

This paper is concerned with subjecting two popular assumptions about the behavior of stock market prices to empirical tests: first, the random walk hypothesis developed by Bachelier (1900), Osborne (1959), and Mandelbrot (1963); second, the stable distributions hypothesis by Mandelbrot (1963) and Fama (1965). For this purpose, ten time series from the Vienna Stock Exchange were used. The first hypothesis was tested using both non-parametric and parametric methods. To obtain evidence with regard to the seond hypothesis, a graphical procedure and statistical estimation on the basis of the empirical characteristic function were applied. On analysis of our data, it turned out that, at least for the time period under consideration (1985–1990), severe doubts are cast on the above assumptions.