The use of preliminary data in econometric forecasting: an application with the Bank of Italy Quarterly Model

This paper considers forecasting by econometric and time series models using preliminary (or provisional) data. The standard practice is to ignore the distinction between provisional and final data. We call the forecasts that ignore such a distinction naive forecasts, which are generated as projections from a correctly specified model using the most recent estimates of the unobserved final figures. It is first shown that in dynamic models a multistepahead naive forecast can achieve a lower mean square error than a single-step-ahead one, intuitively because it is less affected by the measurement noise embedded in the preliminary observations. The best forecasts are obtained by combining, in an optimal way, the information provided by the model with the new information contained in the preliminary data. This can be done in the state space framework, as suggested in the literature. Here we consider two simple methods to combine, in general suboptimally, the two sources of information: modifying the forecast initial conditions via standard regressions and using intercept corrections. The issues are explored with reference to the Italian national accounts data and the Bank of Italy Quarterly Econometric Model (BIQM). A series of simulation experiments with the model show that these methods are quite effective in reducing the extra volatility of prediction due to the use of preliminary data.preliminary data, macroeconomic forecasting, Bank of Italy Quarterly Econometric Model

Tests of time-invariance

Quantiles provide a comprehensive description of the properties of a variable and tracking changes in quantiles over time using signal extraction methods can be informative. It is shown here how stationarity tests can be generalized to test the null hypothesis that a particular quantile is constant over time by using weighted indicators. Corresponding tests based on expectiles are also proposed; these might be expected to be more powerful for distributions that are not heavy-tailed. Tests for changing dispersion and asymmetry may be based on contrasts between particular quantiles or expectiles. We report Monte Carlo experiments investigating the effectiveness of the proposed tests and then move on to consider how to test for relative time invariance, based on residuals from fitting a time-varying level or trend. Empirical examples, using stock returns and U.S. inflation, provide an indication of the practical importance of the tests

STAR-GARCH Models for Stock Market Interactions in the Pacific Basin Region, Japan and US

We investigate the financial interactions between countries in the Pacific Basin region (Korea, Singapore, Malaysia, Hong Kong and Taiwan), Japan and US. The originality of the paper is the use of STAR-GARCH models, instead of standard correlation-cointegration techniques. For each country in the Pacific Basin region, we find statistically adequate STAR-GARCH models for the series of stock market daily returns, using Nikkei225 and S&P500 as alternative threshold variables. We provide evidence for the leading role of Japan in the period 1988-1990 (pre-Japanese crisis years), whereas our results suggest that the Pacific Basin region countries are more closely linked with the US during the period 1995-1999 (post- Japanese crisis years).STAR-GARCH models, stock market integration, Pacific-Basin capital markets, outliers

Testing for Stochastic Trends in Series with Structural Breaks

This paper considers the problem of testing for the presence of stochastic trends in multivariate time series with structural breaks. The breakpoints are assumed to be known. The testing framework is the multivariate Locally Best Invariant test and the common trend test of Nyblom and Harvey (2000). The asymptotic distributions of the test statistics are derived under a general specification of the deterministic component, which allows for structural breaks as a particular case. Asymptotic critical values are provided for the case of a single breakpoint. A modified statistic is then proposed, the asymptotic distribution of which is independent of the breakpoint location and belongs to the Cramér-von Mises family. This modification is particularly advantageous in the case of multiple breakpoints. It is also shown that the asymptotic distributions of the test statistics are unchanged when seasonal dummy variables and/or weakly dependent exogenous regressors are included. Finally, as an example, the tests are applied to UK macroeconomic data and to data on road casualties in Great Britain.cointegration, common trends, Cramér-von Mises distribution, locally best invariant test, structural breaks

Bootstrap LR tests of stationarity, common trends and cointegration

The paper considers likelihood ratio (LR) tests of stationarity, common trends and cointegration for multivariate time series. As the distribution of these tests is not known, a bootstrap version is proposed via a state space representation. The bootstrap samples are obtained from the Kalman filter innovations under the null hypothesis. Monte Carlo simulations for the Gaussian univariate random walk plus noise model show that the bootstrap LR test achieves higher power for medium-sized deviations from the null hypothesis than a locally optimal and one-sided LM test, that has a known asymptotic distribution. The power gains of the bootstrap LR test are significantly larger for testing the hypothesis of common trends and cointegration in multivariate time series, as the alternative asymptotic procedure -obtained as an extension of the LM test of stationarity- does not possess properties of optimality. Finally, it is showed that the (pseudo) LR tests maintain good size and power properties also for non-Gaussian series. As an empirical illustration, we find evidence of two common stochastic trends in the volatility of the US dollar exchange rate against european and asian/pacific currencies.Kalman filter, state-space models, unit roots

Stability of planets in triple star systems

Context: Numerous theoretical studies of the stellar dynamics of triple systems have been carried out, but fewer purely empirical studies that have addressed planetary orbits within these systems. Most of these empirical studies have been for coplanar orbits and with a limited number of orbital parameters. Aims: Our objective is to provide a more generalized empirical mapping of the regions of planetary stability in triples by considering both prograde and retrograde motion of planets and the outer star; investigating highly inclined orbits of the outer star; extending the parameters used to all relevant orbital elements of the triple's stars and expanding these elements and mass ratios to wider ranges that will accommodate recent and possibly future observational discoveries. Methods: Using N-body simulations, we integrated numerically the various four-body configurations over the parameter space, using a symplectic integrator designed specifically for the integration of hierarchical multiple stellar systems. The triples were then reduced to binaries and the integrations repeated to highlight the differences between these two types of system. Results: This established the regions of secular stability and resulted in 24 semi-empirical models describing the stability bounds for planets in each type of triple orbital configuration. The results were then compared with the observational extremes discovered to date to identify regions that may contain undiscovered planets.Comment: 12 pages, 8 figures, 14 tables. Accepted for publication in Astronomy & Astrophysic

Convergences of prices and rates of inflation

We consider how unit root and stationarity tests can be used to study the convergence properties of prices and rates of inflation. Special attention is paid to the issue of whether a mean should be extracted in carrying out unit root and stationarity tests and whether there is an advantage to adopting a new (Dickey-Fuller) unit root test based on deviations from the last observation. The asymptotic distribution of the new test statistic is given and Monte Carlo simulation experiments show that the test yields considerable power gains for highly persistent autoregressive processes with relatively large initial conditions, the case of primary interest for analysing convergence. We argue that the joint use of unit root and stationarity tests in levels and first differences allows the researcher to distinguish between series that are converging and series that have already converged, and we set out a strategy to establish whether convergence occurs in relative prices or just in rates of inflation. The tests are applied to the monthly series of the Consumer Price Index in the Italian regional capitals over the period 1970-2003. It is found that all pairwise contrasts of inflation rates have converged or are in the process of converging. Only 24% of price level contrasts appear to be converging, but a multivariate test provides strong evidence of overall convergence.Dickey-Fuller test, initial condition, law of one price, stationarity test

Testing against stochastic trend and seasonality in the presence of unattended breaks and unit roots

This paper considers the problem of testing against stochastic trend and seasonality in the presence of structural breaks and unit roots at frequencies other than those directly under test, which we term unattended breaks and unattended unit roots respectively. We show that under unattended breaks the true size of the Kwiatkowski et. al. (1992) [KPSS] test at frequency zero and the Canova and Hansen (1995) [CH] test at the seasonal frequencies fall well below the nominal level under the null with an associated, often very dramatic, loss of power under the alternative. We demonstrate that a simple modification of the statistics can recover the usual limiting distribution appropriate to the case where there are no breaks, provided unit roots do not exist at any of the unattended frequencies. Where unattended unit roots occur we show that the above statistics converge in probability to zero under the null. However, computing the KPSS and CH statistics after pre-filtering the data is simultaneously efficacious against both unattended breaks and unattended unit roots, in the sense that the statistics retain their usual pivotal limiting null distributions appropriate to the case where neither occurs. The case where breaks may potentially occur at all frequencies is also discussed. The practical relevance of the theoretical contribution of the paper is illustrated through a number of empirical examples.stationarity tests, structural breaks, pre-filtering, unattended unit roots