Extraction of Common Signal from Series with Different Frequency

The extraction of a common signal from a group of time series is generally obtained using variables recorded with the same frequency or transformed to have the same frequency (monthly, quarterly, etc.). The statistical literature has not paid a great deal of attention to this topic. In this paper we extend an approach based on the use of dummy variables to the well known trend plus cycle model, in a multivariate context, using both quarterly and monthly data. This procedure is applied to the Italian economy, using the variables suggested by an Italian Institution (ISAE) to provide a national dating.Business cycle; State-space; Time Series; Trend; Turning Points

Classifying the Markets Volatility with ARMA Distance Measures

The financial time series are often characterized by similar volatility structures. The selection of series having a similar behavior could be important for the analysis of the transmission mechanisms of volatility and to forecast the time series, using the series with more similar structure. In this paper a metrics is developed in order to measure the distance between two GARCH models, extending well known results developed for the ARMA models. The statistic used to calculate it follows known distributions, so that it can be adopted as a test procedure. These tools can be used to develope an agglomerative algorithm in order to detect clusters of homogeneous series.GARCH models, clusters, agglomerative algorithm

Dating the Italian Business Cycle: A Comparison of Procedures

The problem of dating the business cycle has recently received many contributions, with a lot of proposed statistical methodologies, parametric and non parametric. Despite of this, only a few countries produce an official dating of the business cycle. In this work we try to apply some procedures for an automatic dating of the Italian business cycle in the last thirty years, checking differences among various methodologies and with the ISAE chronology. To this end parametric as well as non parametric methods are employed. The analysis is carried out both aggregating results from single time series and directly in a multivariate framework. The different methods are also evaluated with respect to their ability to timely track turning points. KEYWORDS: signal extraction, turning points, parametric methods, nonparametric methodssignal extraction, turning points, parametric methods, nonparametric methods

Signal Extraction in Continuous Time and the Generalized Hodrick- Prescott Filter

A widely used filter to extract a signal in a time series, in particular in the business cycle analysis, is the Hodrick-Prescott filter. The model that underlies the filter considers the data series as the sum of two unobserved component (signal and non signal) and a smoothing parameter which for quarterly series is set to a specified value. This paper proposes a generalization of the Hodrick-Prescott filter to a continuous time support, using the well-established relationship between cubic splines and state-space models. The spline formulation of the filter leads to a state space model with several practical advantages: first, the smoothing parameter can be either pre-specified or estimated as the other parameters in the model; second, the unobserved components can be modelled by the addition of particular ARIMA structures; lastly the model is capable of working in the presence of missing values or for irregular surveys. Monte Carlo experiments support these considerations.smoothing parameter, cubic spline, state-space model, irregular surveys.

Asset allocation using flexible dynamic correlation models with regime switching

The asset allocation decision is often considered as a trade-off between maximizing the expected return of a portfolio and minimizing the portfolio risk. The riskiness is evaluated in terms of variance of the portfolio return, so that it is fundamental to consider correctly the variance of its components and their correlations. The evidence of the heteroskedastic behavior of the returns and the time-varying relationships among the portfolio components have recently shifted attention to the multivariate GARCH models with time varying correlation. In this work we insert a particular Markov Switching dynamics in some Dynamic Correlation models to consider the abrupt changes in correlations affecting the assets in different ways. This class of models is very general and provides several specifications, constraining some coefficients. The models are applied to solve a sectorial asset allocation problem and are compared with alternative models

Clustering heteroskedastic time series by model-based procedures

Financial time series are often characterized by similar volatility structures, often represented by GARCH processes. The detection of clusters of series displaying similar behavior could be important to understand the differences in the estimated processes, without having to study and compare the estimated parameters across all the series. This is particularly relevant dealing with many series, as in financial applications. The volatility of a time series can be characterized in terms of the underlying GARCH process. Using Wald tests and the AR metrics to measure the distance between GARCH processes, it is possible to develop a clustering algorithm, which can provide three classifications (with increasing degree of deepness) based on the heteroskedastic patterns of the time series. The number of clusters is detected automatically and it is not fixed a priori or a posteriori. The procedure is evaluated by simulations and applied to the sector indexes of the Italian marke

Recognizing and forecasting the sign of financial local trends using hidden Markov models

The problem of forecasting financial time series has received great attention in the past, from both Econometrics and Pattern Recognition researchers. In this context, most of the efforts were spent to represent and model the volatility of the financial indicators in long time series. In this paper a different problem is faced, the prediction of increases and decreases in short (local) financial trends. This problem, poorly considered by the researchers, needs specific models, able to capture the movement in the short time and the asymmetries between increase and decrease periods. The methodology presented in this paper explicitly considers both aspects, encoding the financial returns in binary values (representing the signs of the returns), which are subsequently modelled using two separate Hidden Markov models, one for increases and one for decreases, respectively. The approach has been tested with different experiments with the Dow Jones index and other shares of the same market of different risk, with encouraging results

the Multi-State Markov Switching Model

In many real phenomena the behaviour of a certain variable, subjected to different regimes, depends on the state of other variables or the same variable observed in other subjects, so the knowledge of the state of the latter could be important to forecast the state of the former. In this paper a particular multivariate Markov Switching model is developed to represent this case. The transition probabilities of this model are characterized by the dependence on the regime of the other variables. The estimation of the transition probabilities provides useful informations for the researcher to forecast the regime of the variables analyzed. Theoretical background and an application are shown.regime-switching, multivariate time series, transition probabilities

MODELLING THE DISCRETE AND INFREQUENT OFFICIAL INTEREST RATE CHANGE IN THE UK

This paper is an empirical analysis of the manner in which official interest rates are determined by the Bank of England. We use a nonlinear framework that allow for the separate study of factors affecting the magnitude of positive and negative interest rate changes as well as their probabilities. Using this approach, new kinds of monetary shocks are defined and used to evaluate their impact on the UK economy. Among them, unanticipated negative interest rate changes are especially important. The model generalizes previous approaches in the literature and provides a rich methodology to understand central banks’ decisions and their consequences.

Modelling the discrete and infrequent official interest rate change in the UK

This paper is an empirical analysis of the manner in which official interest rates are determined by the Bank of England. We use a nonlinear framework that allow for the separate study of factors affecting the magnitude of positive and negative interest rate changes as well as their probabilities. Using this approach, new kinds of monetary shocks are defined and used to evaluate their impact on the UK economy. Among them, unanticipated negative interest rate changes are especially important. The model generalizes previous approaches in the literature and provides a rich methodology to understand central banks' decisions and their consequences