Seasonality, Forecast Extensions and Business Cycle Uncertainty

Seasonality is one of the most important features of economic time series. The possibility to abstract from seasonality for the assessment of economic conditions is a widely debated issue. In this paper we propose a strategy for assessing the role of seasonal adjustment on business cycle measurement. In particular, we provide a method for quantifying the contribution to the unreliability of the estimated cycles extracted by popular filters, such as Baxter and King and Hodrick-Prescott. The main conclusion is that the contribution is larger around the turning points of the series and at the extremes of the sample period; moreover, it much more sizeable for highpass filters, like the Hodrick-Prescott filter, which retain to a great extent the high frequency fluctuations in a time series, the latter being the ones that are more affected by seasonal adjustment. If a bandpass component is considered, the effect has reduced size. Finally, we discuss the role of forecast extensions and the prediction of the cycle. For the time series of industrial production considered in the illustration, it is not possible to provide a reliable estimate of the cycle at the end of the sample.Linear filters; Unobserved Components; Seasonal Adjustment; Reliability.

Predicting Betas: Two new methods

Betas play a central role in modern finance. The estimation of betas from historical data and their extrapolation into the future is of considerable practical interest. We propose two new methods: the first is a direct generalization of the method in Blume (1975), and the second is based on Procrustes rotation in phase space. We compare their performance with various competitors and draw some conclusions.systematic risk, beta coefficients, risk prediction, Procustes rotation

Statistical Software for State Space Methods

In this paper we review the state space approach to time series analysis and establish the notation that is adopted in this special volume of the Journal of Statistical Software. We first provide some background on the history of state space methods for the analysis of time series. This is followed by a concise overview of linear Gaussian state space analysis including the modelling framework and appropriate estimation methods. We discuss the important class of unobserved component models which incorporate a trend, a seasonal, a cycle, and fixed explanatory and intervention variables for the univariate and multivariate analysis of time series. We continue the discussion by presenting methods for the computation of different estimates for the unobserved state vector: filtering, prediction, and smoothing. Estimation approaches for the other parameters in the model are also considered. Next, we discuss how the estimation procedures can be used for constructing confidence intervals, detecting outlier observations and structural breaks, and testing model assumptions of residual independence, homoscedasticity, and normality. We then show how ARIMA and ARIMA components models fit in the state space framework to time series analysis. We also provide a basic introduction for non-Gaussian state space models. Finally, we present an overview of the software tools currently available for the analysis of time series with state space methods as they are discussed in the other contributions to this special volume.

Structural Time Series Models and the Kalman Filter: a concise review

The continued increase in availability of economic data in recent years and, more impor- tantly, the possibility to construct larger frequency time series, have fostered the use (and development) of statistical and econometric techniques to treat them more accurately. This paper presents an exposition of structural time series models by which a time series can be decomposed as the sum of a trend, seasonal and irregular components. In addition to a detailled analysis of univariate speci?cations we also address the SUTSE multivariate case and the issue of cointegration. Finally, the recursive estimation and smoothing by means of the Kalman ?lter algorithm is described taking into account its di¤erent stages, from initialisation to parameter?s estimation. JEL codes: C10, C22, C32

Forecasting and Signal Extraction with Misspecified Models

The paper illustrates and compares estimation methods alternative to maximum likelihood, among which multistep estimation and leave-one-out cross-validation, for the purposes of signal extraction, and in particular the separation of the trend from the cycle in economic time series, and long-range forecasting, in the presence of a misspecified, but simply parameterised model. Our workhorse models are two popular unobserved components models, namely the local level and the local linear model. The paper introduces a metric for assessing the accuracy of the unobserved components estimates and concludes that cross- validation is not a suitable estimation criterion for the purpose considered, whereas multistep estimation can be valuable. Finally, we propose a local likelihood estimator in the frequency domain that provides a simple and alternative way of making operative the notion of emphasising the long-run properties of a time series.Business cycles, Unobserved components models, Cross- validation, Smoothing, Hodrick-Prescott filter, Multistep estimation.