Temporal aggregaton of univariate linear time series models

In this paper we feature state-of-the-art econometric methodology of temporal aggregation for univariate linear time series, namely ARIMA-GARCH models. We present a unified overview of temporal aggregation techniques for this broad class of processes and we explain in detail, although intuitively, the technical machinery behind the results. An empirical application with Belgian public deficit data illustrates the main issues.Temporal aggregation; ARIMA, GARCH, seasonality

What do we know about comparing aggregate and disaggregate forecasts?

This paper compares the performance of "aggregate" and "disaggregate" predictors in forecasting contemporaneously aggregated vector ARMA processes. An aggregate predictor is built by forecasting directly the aggregate process, as it results from contemporaneous aggregation of the data generating vector process. A disaggregate predictor is obtained by aggregating univariate forecasts for the individual components of the data generating vector process. The necessary and sufficient condition for the equality of mean squared errors associated with the two competing methods is provided in the bivariate VMA(1) case. Furthermore, it is argued that the condition of equality of predictors as stated in Lütkepohl (1984b, 1987, 2004) is only sufficient (not necessary) for the equality of mean squared errors. Finally, it is shown that the equality of forecasting accuracy for the two predictors can be achieved using specific assumptions on the parameters of the VMA(1) structure. Monte Carlo simulations are in line with the analytical results. An empirical application that involves the problem of forecasting the Italian monetary aggregate M1 in the pre-EMU period is presented to illustrate the main findings.contemporaneous aggregation, forecasting

Aggregation of exponential smoothing processes with an application to portfolio risk evaluation

In this paper we propose a unified framework to analyse contemporaneous and temporal aggregation of exponential smoothing (EWMA) models. Focusing on a vector IMA(1,1) model, we obtain a closed form representation for the parameters of the contemporaneously and temporally aggregated process as a function of the parameters of the original one. In the framework of EWMA estimates of volatility, we present an application dealing with Value-at-Risk (VaR) prediction at different sampling frequencies for an equally weighted portfolio composed of multiple indices. We apply the aggregation results by inferring the decay factor in the portfolio volatility equation from the estimated vector IMA(1,1) model of squared returns. Empirical results show that VaR predictions delivered using this suggested approach are at least as accurate as those obtained by applying the standard univariate RiskMetrics TM methodology.contemporaneous and temporal aggregation, EWMA, volatility, Value-at-Risk

Temporal aggregation of univariate and multivariate time series models: A survey

We present a unified and up-to-date overview of temporal aggregation techniques for univariate and multivariate time series models explaining in detail how these techniques are employed. Some empirical applications illustrate the main issues.Temporal aggregation, ARIMA, Seasonality, GARCH, Vector ARMA, Spurious causality, Multivariate GARCH

A Regression Discontinuity Design for Ordinal Running Variables: Evaluating Central Bank Purchases of Corporate Bonds

Regression discontinuity (RD) is a widely used quasi-experimental design for causal inference. In the standard RD, the assignment to treatment is determined by a continuous pretreatment variable (i.e., running variable) falling above or below a pre-fixed threshold. In the case of the corporate sector purchase programme (CSPP) of the European Central Bank, which involves large-scale purchases of securities issued by corporations in the euro area, such a threshold can be defined in terms of an ordinal running variable. This feature poses challenges to RD estimation due to the lack of a meaningful measure of distance. To evaluate such program, this paper proposes an RD approach for ordinal running variables under the local randomization framework. The proposal first estimates an ordered probit model for the ordinal running variable. The estimated probability of being assigned to treatment is then adopted as a latent continuous running variable and used to identify a covariate-balanced subsample around the threshold. Assuming local unconfoundedness of the treatment in the subsample, an estimate of the effect of the program is obtained by employing a weighted estimator of the average treatment effect. Two weighting estimators---overlap weights and ATT weights---as well as their augmented versions are considered. We apply the method to evaluate the causal effect of the CSPP and find a statistically significant and negative effect on corporate bond spreads at issuance.Comment: Also available as Temi di discussione (Economic working papers) 1213, Bank of Italy, Economic Research and International Relations Are

The effects of financial and real wealth on consumption: new evidence from OECD countries

In this paper we present new estimates of the effect of households’ financial and real wealth on consumption. The analysis makes reference to eleven OECD countries and takes into account quarterly data from 1997 to 2008. Unlike most of the previous literature on European countries, we measure financial wealth using quarterly harmonized data on households’ financial assets and liabilities, which have been gleaned from the flow of funds. For comparison, we also employ national share price indices as a proxy for financial wealth. We rely on 1) standard static panel and 2) single-country level autoregressive distributed lag estimations. Furthermore, we implement a recent econometric approach that allows for more flexible assumptions in the non-stationary panel framework under consideration. Our results show that both net financial wealth and real wealth have a positive effect on consumption. Overall, the influence of net financial assets is stronger than that of real assets.consumption, household financial and real wealth, wealth effects, panel cointegration.

Seasonal adjustment of bank deposits and loans

This paper illustrates the seasonal adjustment procedure for bank deposits and loans, focusing on the policy for the revision of seasonally adjusted data. Seasonal adjustment is semi-automatic when the commonly used software package, TRAMO-SEATS, is used to produce seasonally adjusted series. With reference to the frequency of seasonally adjusted data revisions, three alternative methods (current adjustment, concurrent adjustment, partial concurrent adjustment) are tested according to a quantitative criterion. A simulation study measures the speed of convergence of the estimates, obtained with these three updating methods, to reach a “final" estimate to be used as a benchmark. The results favour the use of the partial concurrent adjustment method, that suggests identifying the ARIMA model and the effects of the deterministic components once a year, and updating the corresponding coefficients once a month.destagionalizzazione, partial concurrent adjustment

Testing fiscal sustainability in Poland: a Bayesian analysis of cointegration

Fiscal sustainability is a central topic for most of the transition economies of Eastern Europe. This paper focuses on a particular country: Poland. The main purpose is to investigate, empirically, whether the post-transition fiscal policy is consistent with the intertemporal budget constraint, used as a formal theorical framework. To test debt stabilization, the empirical analysis is made in two steps, in which different inferential approaches are adopted. In the first step we perform the preliminary unit roots analysis and the selection of the cointegration rank using parametric and bootstrap procedures. In the second step we apply Bayesian inference to the estimation of the cointegrating vector and of the adjustment parameters. In this way, we experiment the usefulness of Bayesian inference in precisely assessing the magnitude of the cointegrating vector. Moreover, we show to what extent the likehood of the data is important in revising the available prior information, relying on numerical integration techniques.Bayesian inference, fiscal sustainability, cointegration, bootstrap