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

Granger Causality and the Sampling of Economic Processes

This paper provides a discussion of the developments in econometric modelling that are designed to deal with the problem of spurious Granger causality relationships that can arise from temporal aggregation.We outline the distortional e ects of using discrete time models that explicitly depend on the unit of time and outline a remedy of constructing timeinvariant discrete time models via a structural continuous time model.In an application to testing for money-income causality, we demonstrate the importance of incorporating exact temporal aggregation restrictions on the discrete time data.We do this by conducting causality tests in discrete time models that: (a) impose the temporal aggregation restrictions exactly; (b) impose the temporal aggregation restrictions approximately; and (c) do not impose these restrictions at all.sampling;aggregation;models

The Distortionary Effects Of Temporal Aggregation On Granger Causality

Economists often have to use temporally aggregated data in causality tests. A number of theoretical studies have pointed out that temporal aggregation has distorting effects on causal inference. This paper provides a quantitative assessment of the magnitude of the distortions created by temporal aggregation by plugging in theoretical cross covariances into the limiting values of least squares estimates. Some Monte Carlo results and an application are provided to assess the impact in small samples. It is observed that in general the most distorting causal inferences are likely at low levels of temporal aggregation. At high levels of aggregation, causal information concentrates in contemporaneous correlations. At present, a data-based approach is not available to establish the direction of causality between contemporaneously correlated variables.

Temporal Aggregation and Risk-Return Relation

The function form of a linear intertemporal relation between risk and return is suggested by Merton’s (1973) analytical work for instantaneous returns, whereas empirical studies have examined the nature of this relation using temporally aggregated data, i.e., daily, monthly, quarterly, or even yearly returns. Our paper carefully examines the temporal aggregation effect on the validity of the linear specification of the risk-return relation at discrete horizons,and on its implications on the reliablility of the resulting inference about the risk-return relation based on different observation intervals. Surprisingly, we show that, based on the standard Heston’s (1993) dynamics, the linear relation between risk and return will not be distorted by the temporal aggregation at all. Neither will the sign of this relation be flipped by the temporal aggregation, even at the yearly horizon. This finding excludes the temporal aggregation issue as a potential source for the conflicting empirical evidence about the risk-return relation in the earlier studies.

Temporal Aggregation and Ordinary Least Squares Estimation of Cointegrating Regressions

The paper derives the asymptotic distribution of the ordinary least squares estimator of cointegrating vectors with temporally aggregated time series. It is shown, that temporal aggregation reduces the bias and variance of the estimator for average sampling (temporal aggregation of flow series) and does not affect the limiting distribution for systematic sampling (temporal aggregation of stock series). A Monte Carlo experiment shows the consistency of the finite sample results with the asymptotic theory.

On the relationship between inflation persistence and temporal aggregation

This paper examines the impact of temporal aggregation on alternative definitions of inflation persistence. Using the CPI and the core PCE deflator of the US, our results show that temporal aggregation from the monthly to the quarterly to the annual frequency induces persistence in the inflation series.

Temporal Aggregation, Causality Distortions, and a Sign Rule

Temporally aggregated data is a bane for Granger causality tests. The same set of variables may lead to contradictory causality inferences at different levels of temporal aggregation. Obtaining temporally disaggregated data series is impractical in many situations. Since cointegration is invariant to temporal aggregation and implies Granger causality this paper proposes a sign rule to establish the direction of causality. Temporal aggregation leads to a distortion of the sign of the adjustment coefficients of an error correction model. The sign rule works better with highly temporally aggregated data. The practitioners, therefore, may revert to using annual data for Granger causality testing instead of looking for quarterly, monthly or weekly data. The method is illustrated through three applications.Granger causality test, cointegration, error correction model, adjustment coefficient, sign rule

Temporal aggregation of multivariate GARCH processes

This paper derives results for the temporal aggregation of multivariate GARCH processes in the general vector specification. It is shown that the class of weak multivariate GARCH processes is closed under temporal aggregation. Fourth moment characteristics turn out to be crucial for the low frequency dynamics for both stock and flow variables. The framework used in this paper can easily be extended to investigate joint temporal and contemporaneous aggregation. Discussing causality in volatility, I find that there is not much room for spurious instantaneous causality in multivariate GARCH processes, but that spurious Granger causality will be more common however numerically insignificant. Forecasting volatility, it is generally advisable to aggregate forecasts of the disaggregate series rather than forecasting the aggregated series directly, and unlike for VARMA processes the advantage does not diminish for large forecast horizons. Finally, results are derived for the distribution of multivariate realized volatility if the high frequency process follows multivariate GARCH. A numerical example illustrates some of the resultsmultivariate GARCH, temporal aggregation, causality in volatility, forecasting volatility, realized volatility

Temporal Aggregation Effects on the Construction of Portfolios of Stocks or Mutual Funds through Optimization Techniques - Some Empirical and Monte Carlo Results

In this paper we test the effects of temporal aggregation (disaggregation) on the efficiency of portfolio construction using the mean variance optimization approach. Using Monte Carlo techniques and empirical data from the Athens Stocks Exchange we confirm that the use of temporally aggregated data effects very seriously the efficiency of the constructed portfolio. Especially as the degree of temporal aggregation increases the application of optimization techniques could lead to different results regarding the percentage of stocks participation, the weights and finally the total portfolio performance.Portfolio Optimization, Stocks; Temporal Aggregation; Stochastic Simulation, The Banking Sector of the Athens Stocks Exchange

Temporal aggregation of an ESTAR process

Nonlinear models of deviations from PPP have recently provided an important, theoretically well motivated, contribution to the PPP puzzle. Most of these studies use temporally aggregated data to empirically estimate the nonlinear models. As noted by Taylor (2001), if the true DGP is nonlinear, the temporally aggregated data could exhibit misleading properties regarding the adjustment speeds. We examine the effects of different levels of temporal aggregation on estimates of ESTAR models of real exchange rates.