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In this paper, we propose a novel model to analyze serially correlated two-dimensional functional data observed sparsely and irregularly on a domain which may not be a rectangle. Our approach employs a mixed effects model that specifies the principal component functions as bivariate splines on triangles and the principal component scores as random effects which follow an auto-regressive model. We apply the thin-plate penalty for regularizing the bivariate function estimation and develop an effective EM algorithm along with Kalman filter and smoother for calculating the penalized likelihood estimates of the parameters. Our approach was applied on simulated datasets and on Texas monthly average temperature data from January year 1915 to December year 2014. Supplementary materials accompanying this paper appear online. [ABSTRACT FROM AUTHOR]

We developed an enhanced Kalman‐based approach to quantify abrupt changes and significant non‐linearity in vertical land motion (VLM) along the coast of Chile and the Antarctic Peninsula using a combination of multi‐mission satellite altimetry (ALT), tide gauge (TG), and GPS data starting from the early 1990s. The data reveal the spatial variability of co‐seismic and post‐seismic subsidence at TGs along the Chilean subduction zone in response to the Mw8.8 Maule 2010, Mw8.1 Iquique 2014, and Mw8.3 Illapel 2015 earthquakes that are not retrievable from the interpolation of sparse GPS observations across space and time. In the Antarctic Peninsula, where continuous GPS data do not commence until ∼1998, the approach provides new insight into the ∼2002 change in VLM at the TGs of +5.3 ± 2.2 mm/yr (Palmer) and +3.5 ± 2.8 mm/yr (Vernadsky) due to the onset of ice‐mass loss following the Larsen‐B Ice Shelf breakup. We used these data to constrain viscoelastic Earth model parameters for the northern Antarctic Peninsula, obtaining a preferred lithosphere thickness of 115 km and upper mantle viscosity of 0.9 × 1018 Pa s. Our estimates of regionally‐correlated ALT systematic errors are small, typically between ∼±0.5–2.5 mm/yr over single‐mission time scales. These are consistent with competing orbit differences and the relative errors apparent in ALT crossovers. This study demonstrates that, with careful tuning, the ALT‐TG technique can provide improved temporal and spatial sampling of VLM, yielding new constraints on geodynamic models and assisting sea‐level change studies in otherwise data sparse regions and periods. Plain Language Summary: The difference in sea‐level records from satellite altimeters and coastal tide gauges can reveal the Earth surface's vertical land motion (VLM) and potential errors in either system. Time‐varying changes in the VLM can occur because of phenomena such as earthquakes or glacier melt which changes the mass load on the crust. We developed a flexible data combination framework to use records from multi‐mission altimeters (ALTs), tide gauges (TGs), and GPS sites to allow the estimation of substantial non‐linear VLM that complements the previous estimates which can be sparse in the 1990s especially. We considered the study period since the launch time of TOPEX mission in ∼1992. We used our new approach to investigate the earthquake‐induced deformation at TG locations along the near‐coast subduction zone in Chile that could not be inferred from temporally and spatially sparse GPS records. We also provide insights into the rapid change in VLM at coastal TGs in the Antarctic Peninsula after the Larsen‐B Ice Shelf breakup in ∼2002, where the existing knowledge dates to ∼1998 from only one GPS at Palmer station. These significant insights into present‐day deformation help to fill the knowledge gap from GPS‐inferred records and improve VLM sampling across space and time. More generally, this new approach may assist resolve complex VLM for sea‐level studies globally and could add new constraints to inverse geophysical modeling, especially where GPS data are sparse in space and/or time. Key Points: We developed an advanced Kalman approach to estimate highly non‐linear vertical land motion using altimeter, tide gauge and GPS data, while simultaneously capturing significant mission‐specific systematic errorsWe derived new estimates of pre‐seismic velocity, co‐seismic jumps, and post‐seismic velocity at tide gauges in Chile that add additional constraints on the solid‐Earth response to major earthquakes in the regionWe observed the onset of rapid uplift at tide gauges in the Antarctic Peninsula caused by the 2002 breakup of the Larsen‐B Ice Shelf, filling a historical knowledge gap from GPS records and further constraining modeled viscoelastic deformation [ABSTRACT FROM AUTHOR]

This paper derives the limit of the Kalman filter and smoother as the inverse of the process noise covariance tends to zero (the zero informational limit) in the case that there is direct feedthrough (of full column rank) of the process noise input to the measurements. Two forms of the filter in the limit are derived with the second being a standard Kalman filter without unknown inputs. The latter form is used to derive necessary and sufficient conditions for convergence and stability of the filter. These consist of a controllability condition and a minimum phase condition. The filter and smoother are applied to an automotive example to estimate an unknown road profile. The example illustrates the usefulness of the stability and convergence conditions to inform the choice of a suitable set of sensors. [ABSTRACT FROM AUTHOR]

Healthcare processes comprise multiple stages in practice. Also, few researchers have addressed Phase I monitoring of healthcare outcomes. Hence, the purpose of the proposed method is Phase I monitoring by two risk adjusted control charts in multistage healthcare processes. The proposed control charts are based on the Bernoulli state space model and consider other categorical covariates in addition to patient's risk. To estimate the model parameters, an expectation-maximization algorithm is applied in a Kalman filter and smoother framework. The performance of the proposed monitoring schemes is compared in two and three stages. The simulation results show that the standardized likelihood ratio test method has competitive performance relative to Hotelling's chart under different step shifts and drift. Also, Hotelling's chart is superior to the standardized likelihood ratio test method in for outlier patients. Finally, a real case is utilized to show the applicability of the proposed risk adjusted charts. [ABSTRACT FROM AUTHOR]

Spatial–temporal Gaussian process regression is a popular method for spatial–temporal data modeling. Its state-of-art implementation is based on the state-space model realization of the spatial–temporal Gaussian process and its corresponding Kalman filter and smoother, and has computational complexity O (N M 3) , where N and M are the number of time instants and spatial input locations, respectively, and thus can only be applied to data with large N but relatively small M. In this paper, our primary goal is to show that by exploring the Kronecker structure of the state-space model realization of the spatial–temporal Gaussian process, it is possible to further reduce the computational complexity to O (M 3 + N M 2) and thus the proposed implementation can be applied to data with large N and moderately large M. The proposed implementation is illustrated over applications in weather data prediction and spatially-distributed system identification. Our secondary goal is to design a kernel for both the Colorado precipitation data and the GHCN temperature data, such that while having more efficient implementation, better prediction performance can also be achieved than the state-of-art result. [ABSTRACT FROM AUTHOR]

This article proposes a new framework to estimate and analyse structural fiscal balances of the UK, by combining the state-space modelling with the Bayesian DSGE modelling. In this way, trends and cycles of aggregate variables can be extracted from data consistently with the macroeconomic theory. A setting of an integrated random walk for the underlying stochastic trends fits the data best. An expansion in government spending can increase nominal fiscal revenue to a certain degree, but the effect is not persistent due to two kinds of crowd-out effects: it crowds out domestic investment; and it pushes up the price of domestic goods and simultaneously crowds out the foreign demand. The shocks to the nominal interest rate, foreign output and the government spending are the three major contributors to the variation of the fiscal revenue cycle. [ABSTRACT FROM AUTHOR]

ABSTRACT The paper presents a comparative real-time analysis of alternative indirect estimates relative to monthly euro area employment. In the experiment quarterly employment is temporally disaggregated using monthly unemployment as related series. The strategies under comparison make use of the contribution of sectoral data of the euro area and its six larger member states. The comparison is carried out among univariate temporal disaggregations of the Chow and Lin type and multivariate structural time series models of small and medium size. Specifications in logarithms are also systematically assessed. All multivariate set-ups, up to 49 series modelled simultaneously, are estimated via the EM algorithm. Main conclusions are that mean revision errors of disaggregated estimates are overall small, a gain is obtained when the model strategy takes into account the information by both sector and member state and that larger multivariate set-ups perform very well, with several advantages with respect to simpler models.Copyright © 2014 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Multivariate temporal disaggregation deals with the historical reconstruction and nowcasting of economic variables subject to temporal and contemporaneous aggregation constraints. The problem involves a system of time series that are related not only by a dynamic model but also by accounting constraints. The paper introduces two fundamental (and realistic) models that implement the multivariate best linear unbiased estimation approach that has potential application to the temporal disaggregation of the national accounts series. The multivariate regression model with random walk disturbances is most suitable to deal with the chained linked volumes (as the nature of the national accounts time series suggests); however, in this case the accounting constraints are not binding and the discrepancy has to be modeled by either a trend-stationary or an integrated process. The tiny, compared with other driving disturbances, size of the discrepancy prevents maximum-likelihood estimation to be carried out, and the parameters have to be estimated separately. The multivariate disaggregation with integrated random walk disturbances is suitable for the national accounts aggregates expressed at current prices, in which case the accounting constraints are binding. [ABSTRACT FROM AUTHOR]

In this paper, we propose a robust Kalman filter and smoother for the errors-in-variables (EIV) state space models subject to observation noise with outliers. We introduce the EIV problem with outliers and then present the minimum covariance determinant (MCD) estimator which is a highly robust estimator in terms of protecting the estimate from the outliers. Then, we propose the randomized algorithm to find the MCD estimate. However, the uniform sampling method has a high computational cost and may lead to biased estimates, therefore we apply the sub-sampling method. A Monte Carlo simulation result shows the efficiency of the proposed algorithm. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society [ABSTRACT FROM AUTHOR]

Continuous monitoring of the evolution of the economy is fundamental for the decisions of public and private decision makers. The paper proposes EUROMIND, which is a new monthly indicator of the euro area economic conditions, based on tracking real gross domestic product monthly, relying on information provided in the Eurostat Euro-IND database. EUROMIND has several original economic and statistical features. First, it considers both the output and the expenditure sides of the economy, as it provides a monthly estimate of the value added of the six branches of economic activity and of the main gross domestic product components by type of expenditure (final consumption, gross capital formation and net exports), and combines the estimates with optimal weights reflecting their relative precision. Second, the indicator is based on information at both the monthly and the quarterly level, modelled with a dynamic factor specification cast in state space form. Third, since estimation of the multivariate dynamic factor model with mixed frequency data can be numerically complex, computational efficiency is achieved by implementing univariate filtering and smoothing procedures. Finally, special attention is paid to chain linking and its implications, via a multistep procedure that exploits the additivity of the volume measures expressed at the prices of the previous year. [ABSTRACT FROM AUTHOR]

The article explores and illustrates some of the typical trade-offs which arise in designing filters for the measurement of trends and cycles in economic time series, focusing, in particular, on the fundamental trade-off between the reliability of the estimates and the magnitude of the revisions as new observations become available. This assessment is available through a novel model based approach, according to which an important class of highpass and bandpass filters, encompassing the Hodrick-Prescott (HP) filter, are adapted to the particular time series under investigation. Via a suitable decomposition of the innovation process, it is shown that any linear time series with ARIMA representation can be broken down into orthogonal trend and cycle components, for which the class of filters is optimal. The main results then follow from Wiener-Kolmogorov (WK) signal extraction theory, whereas exact finite sample inferences are provided by the Kalman filter and smoother for the relevant state space representation of the decomposition. [ABSTRACT FROM AUTHOR]

The paper advocates the use of state space methods to deal with the problem of temporal disaggregation by dynamic regression models, which encompass the most popular techniques for the distribution of economic flow variables, such as Chow–Lin, Fernández and Litterman. The state space methodology offers the generality that is required to address a variety of inferential issues that have not been dealt with previously. The paper contributes to the available literature in three ways: (i) it concentrates on the exact initialization of the different models, showing that this issue is of fundamental importance for the properties of the maximum likelihood estimates and for deriving encompassing autoregressive distributed lag models that nest exactly the traditional disaggregation models; (ii) it points out the role of diagnostics and revisions histories in judging the quality of the disaggregated estimates and (iii) it provides a thorough treatment of the Litterman model, explaining the difficulties commonly encountered in practice when estimating this model. [ABSTRACT FROM AUTHOR]

The price elasticity of raw milk supply in Japan is estimated over time by a structural time-series model in state space form, and the changes in elasticity are tested by the diagnosing test of de John and Penzer in 1998. The supply function is modeled with a local linear trend and a strictly exogenous autoregressive distributed lag price. The seasonality in the data is adjusted by a structural time-series model. In the 1970–1997 period, there were major dairy policy changes in Japan: a production adjustment, related penalties, and two-tier pricing. Hokkaido is the region that mainly provides the supply of raw milk for milk products, while Tofuken is the region that mainly produces drinking milk. The estimated price elasticity in Hokkaido became stable after imposition of the production adjustment. On the other hand, price elasticity in Tofuken became stable after the inflation of the mid-1970s. Price elasticity is estimated to be more inelastic as well as more likely to converge in inelasticity in Hokkaido than in Tofuken. We discuss the relationship between changes in dairy policy and changes in price elasticity. [ABSTRACT FROM AUTHOR]

Abstract. The paper derives an algorithm for computing leave-k-out diagnostics for the detection of patches of outliers for stationary and nonstationary 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 and easy to implement. The US index of industrial production for textiles is used to illustrate the application of the algorithm. [ABSTRACT FROM AUTHOR]

When paired comparisons are made sequentially over time as for example in chess competitions, it is natural to assume that the underlying abilities do change with time. Previous approaches are based on fixed updating schemes where the increments and decrements are fixed functions of the underlying abilities The parameters that determine the functions have to be specified a priori and are based on rational reasoning. We suggest an alternative scheme for keeping track with the underlying abilities Our approach is based on two components a response model that specifies the connection between the observations and the underlying abilities and a transition model that specifies the variation of abilities over time The response model is a very general paired comparison model allowing for ties and ordered responses The transition model incorporates random walk models and local linear trend models Taken together, these two components form a non-Gaussian state-space model Based on recent results, recursive posterior mode estimation algorithms are given and the relation to previous approaches is worked out The performance of the method is illustrated by simulation results and an application to soccer data of the German Bundesliga. [ABSTRACT FROM AUTHOR]