This paper studies the behaviour of Bitcoin returns at different sample frequencies. We consider high frequency returns starting from tick-by-tick price changes traded at the Bitstamp and Coinbase exchanges. We find evidence of a smooth intra-daily seasonality pattern, and an abnormal trade- and...

Structural change affects the estimation of economic signals, like the underlying growth rate or the seasonally adjusted series. An important issue, which has attracted a great deal of attention also in the seasonal adjustment literature, is its detection by an expert procedure. The general to...

This article presents a robust augmented Kalman filter that extends the data-cleaning filter (Masreliez and Martin, 1977) to the general state space model featuring nonstationary and regression effects. The robust filter shrinks the observations towards their one-step-ahead prediction based on...

This paper is concerned with the estimation of euro area potential output growth and its decomposition according to the sources of growth. The growth accounting exercise is based on a multivariate structural time series model which combines the decomposition of total output according to the...

The Beveridge-Nelson decomposition defines the trend component in terms of the eventual forecast function, as the value the series would take if it were on its long-run path. The paper in-troduces the multistep Beveridge-Nelson decomposition, which arises when the forecast function is obtained...

We apply a recently proposed Bayesian model selection technique, known as stochastic model specification search, for characterising the nature of the trend in macroeconomic time series. We illustrate that the methodology can be quite successfully applied to discriminate between stochastic and...

Structural change affects the estimation of economic signals, like the underlying growth rate or the seasonally adjusted series. An important issue, which has at- tracted a great deal of attention also in the seasonal adjustment literature, is its detection by an expert procedure. The...

The paper deals with the estimation of monthly indicators of economic activity for the Euro area and its largest member countries that possess the following attributes: relevance, representativeness and timeliness. Relevance is obtained by referring our monthly indicators to gross domestic...

EuroMInd-D is a density estimate of monthly gross domestic product (GDP) constructed according to a bottom-up approach, pooling the density estimates of eleven GDP components, by output and expenditure type. The components density estimates are obtained from a medium-size dynamic factor model of...

The paper derives an algorithm for computing leave-k-out diagnostics for the detection of patches of outliers for stationary and non-stationary state space models with regression effects. The algorithm is based on a reverse run of the Kalman filter on the smoothing errors and is both efficient...