1,721,182 research outputs found
Predictability, real time estimation, and the formulation of unobserved components models
No full textThe formulation of unobserved components models raises some relevant interpretative issues, owing to the existence of alternative observationally equivalent specifications, differing for the timing of the disturbances and their covariance matrix. We illustrate them with reference to unobserved components models with ARMA(m, m) reduced form, performing the decomposition of the series into an ARMA(m, q) signal, q <= m, and a noise component. We provide a characterization of the set of covariance structures that are observationally equivalent, when the models are formulated both in the future and the contemporaneous forms. Hence, we show that, while the point predictions and the contemporaneous real time estimates are invariant to the specification of the disturbances covariance matrix, the reliability cannot be identified, except for special cases requiring q < m - 1
Another look at dependence: the most predictable aspects of time series
No full textSerial dependence and predictability are two sides of the same coin. The literature has considered alternative measures of these two fundamental concepts. In this article, we aim to distill the most predictable aspect of a univariate time series, that is, the one for which predictability is optimized. Our target measure is the mutual information between the past and future of a random process, a broad measure of predictability that takes into account all future forecast horizons, rather than focusing on the one-step-ahead prediction error mean square error. The most predictable aspect is defined as the measurable transformation of the series that maximizes the mutual information between past and future. This transformation arises from the linear combination of a set of basis functions localized at the quantiles of the unconditional distribution of the process. The mutual information is estimated as a function of the sample partial autocorrelations, using a semiparametric method that estimates an infinite sum by a regularized finite sum. The second most predictable aspect can also be defined, subject to suitable orthogonality restrictions. Finally, we illustrate the use of the most predictable aspect for testing the null hypothesis of no predictability and for point and interval prediction of the original time series
Estimating the Output Gap with High-Dimensional Time Series
No full textThe output gap measures the deviation of observed output from its potential, thereby defining imbalances in the real economy that affect utilization of resources and price inflation. A novel estimator of the output gap is proposed. It is based on a dynamic factor model that extracts from a high-dimensional set of time series the common component of a stationary transformation of the individual series. The latter results from the application of a nonlinear gap filter, such that for each of the individual time series the gap filter removes from the current value the historical local maximum, which in turn defines the potential. The smooth generalized principal components are extracted and the resulting common components are aggregated into a global output gap measure. An application is presented dealing with the U.S. industrial sector, where the proposed measure is constructed using the disaggregated market and industry groups time series. An evaluation of its external validity is conducted in comparison to alternative measures
Characterising asymmetries in business cycles using smooth transition structural time series models
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Low-Pass Filter Design using Locally Weighted Polynomial Regression and Discrete Prolate Spheroidal Sequences
Full text linkThe paper concerns the design of nonparametric low-pass filters that have the property of reproducing a polynomial of a given degree. Two approaches are considered. The first is locally weighted polynomial regression (LWPR), which leads to linear filters depending on three parameters: the bandwidth, the order of the fitting polynomial, and the kernel. We find a remarkable linear (hyperbolic) relationship between the cutoff period (frequency) and the bandwidth, conditional on the choices of the order and the kernel, upon which we build the design of a low-pass filter.
The second hinges on a generalization of the maximum concentration approach, leading to filters related to discrete prolate spheroidal sequences (DPSS). In particular, we propose a new class of lowpass filters that maximize the concentration over a specified frequency range, subject to polynomial reproducing constraints. The design of generalized DPSS filters depends on three parameters: the
bandwidth, the polynomial order, and the concentration frequency. We discuss the properties of the corresponding filters in relation to the LWPR filters, and illustrate their use for the design of low-pass filters by investigating how the three parameters are related to the cutoff frequency
Missing data in time series: a note on the equivalence of the dummy variable and the skipping approaches
No full textThe Multistep Beveridge-Nelson decomposition
No full textThe 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 article introduces the multistep Beveridge–Nelson decomposition, which arises when the forecast function is obtained by the direct autoregressive approach, which optimizes the predictive ability of the AR model at forecast horizons greater than one. We compare our proposal with the standard Beveridge–Nelson decomposition, for which the forecast function is obtained by iterating the one-step-ahead predictions via the chain rule. We illustrate that the multistep Beveridge–Nelson trend is more efficient than the standard one in the presence of model misspecification, and we subsequently assess the predictive validity of the extracted transitory component with respect to future growth
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