Andrea Silvestrini

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, although intuitively, the technical machinery behind the results. Some empirical applications illustrate the main issues.

Forecasting aggregate demand: Analytical comparison of top-down and bottom-up approaches in a multivariate exponential smoothing framework

Forecasting aggregate demand is a crucial matter in all industrial sectors. In this paper, we provide the analytical prediction properties of top-down (TD) and bottom-up (BU) approaches when forecasting aggregate demand, using multivariate exponential smoothing as demand planning framework. We extend and generalize the results obtained by Widiarta, Viswanathan and Piplani (2009) by employing an unrestricted multivariate framework allowing for interdependency between the variables. Moreover, we establish the necessary and sufficient condition for the equality of mean squared errors (MSEs) of the two approaches. We show that the condition for the equality of MSEs also holds even when the moving average parameters of the individual components are not identical. In addition, we show that the relative forecasting accuracy of TD and BU depends on the parametric structure of the underlying framework. Simulation results confirm our theoretical findings. Indeed, the ranking of TD and BU forecasts is led by the parametric structure of the underlying data generation process, regardless of possible misspecification issues.

The Italian financial cycle: 1861–2011

In this paper we investigate the main features of the Italian financial cycle, extracted by means of a structural trend-cycle decomposition of the credit-to-GDP ratio, using annual observations from 1861 to 2011. In order to draw conclusions based on solid historical data, we provide a thorough reconstruction of the key balance-sheet time series of Italian banks, considering all the main assets and liabilities over the last 150 years. We come to three main conclusions. First, while there was a close correlation between loans and deposits (relative to GDP) until the mid-1970s, over the last 30 years this link has become more tenuous, and the volume of loans has increased in relation to deposits. The banks have covered this “funding gap�? mainly by issuing new debt securities. Second, the Italian financial cycle has a much longer duration than traditional business cycles. Third, taking into account the deviation of the credit-to-GDP ratio from its trend, an acceleration of credit preceded a banking crisis in 8 out of the 12 episodes listed by Reinhart and Rogoff (2009). A Logit regression confirms a positive association between the probability of a banking crisis and a previous acceleration of the credit-to-GDP gap. However, there were also periods - such as the early 1970s - in which the growth of the credit-to-GDP ratio was not followed by a banking crisis.

Random Switching Exponential Smoothing and Inventory Forecasting

Exponential smoothing models represent an important prediction tool both in business and in macroeconomics. This paper provides the analytical forecasting properties of the random coefficient exponential smoothing model in the “multiple source of error” framework. The random coefficient state-space representation allows for switching between simple exponential smoothing and local linear trend. Therefore it enables controlling, in a flexible manner, the random changing dynamic behavior of the time series. The paper establishes the algebraic mapping between the state-space parameters and the implied reduced form ARIMA parameters. In addition, it shows that the parametric mapping allows overcoming the difficulties that are likely to emerge in estimating directly the random coefficient state-space model. Finally, it presents an empirical application comparing the forecast accuracy of the suggested model vis-a-vis other benchmark models, both in the ARIMA and in the exponential smoothing class. Using time series relative to wholesalers inventories in the USA, the out-of-sample results show that the reduced form of the random coefficient exponential smoothing model tends to be superior to its competitors.

Temporal aggregation of cyclical models with business cycle applications

This paper focuses on temporal aggregation of the cyclical component model as introduced by Harvey (1989). More specifically, it provides the properties of the aggregate process for any generic period of aggregation. As a consequence, the exact link between aggregate and disaggregate parameters can be easily derived. The cyclical model is important due to its relevance in the analysis of business cycle. Given this, two empirical applications are presented in order to compare the estimated parameters of the quarterly models for German and US gross domestic products with those of the corresponding models aggregated to annual frequency.

Marginalization and aggregation of exponential smoothing models in forecasting portfolio volatility

This paper examines exponentially weighted moving average models for predicting volatility and assessing risk in portfolios. It proposes a method that identifies the decay factors of the marginal volatility models for portfolio’s individual components, without imposing the same smoothing constant across all assets. To illustrate how the method can be applied, the paper provides an example dealing with Value-at-Risk calculation, prediction and backtesting evaluation of an equally weighted portfolio composed of CDS banking indices, which are useful market indicators for credit risk.