A Moment-Based Notion of Time Dependence for Functional Time Series

Salish, Nazarii; Gleim, Alexander

doi:10.2139/ssrn.3032500

Cited by 3 publications

(3 citation statements)

References 34 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We consider two sources of uncertainty: truncation errors in the principal component decomposition and forecast errors in the projected principal component scores. Since principal component scores are regarded as surrogates of the original functional time series, these principal component scores capture the temporal dependence structure inherited in the original functional time series (see also Salish & Gleim, 2015; Paparoditis, 2018; Shang, 2018). By adequately bootstrapping the forecast principal component scores, we can generate a set of bootstrapped , conditional on the estimated mean function and estimated functional principal components from the observed Z in (3).…”

Section: Forecasting Methodsmentioning

confidence: 99%

Forecasting age distribution of death counts: an application to annuity pricing

Shang

Haberman

2019

Ann. actuar. sci.

View full text Add to dashboard Cite

We consider a compositional data analysis approach to forecasting the age distribution of death counts. Using the age-specific period life-table death counts in Australia obtained from the Human Mortality Database, the compositional data analysis approach produces more accurate one-to 20-step-ahead point and interval forecasts than Lee-Carter method, Hyndman-Ullah method, and two naïve random walk methods. The improved forecast accuracy of period life-table death counts is of great interest to demographers for estimating survival probabilities and life expectancy, and to actuaries for determining temporary annuity prices for various ages and maturities. Although we focus on temporary annuity prices, we consider long-term contracts which make the annuity almost lifetime, in particular when the age at entry is sufficiently high.

show abstract

Section: Forecasting Methodsmentioning

confidence: 99%

Forecasting age distribution of death counts: an application to annuity pricing

Shang

Haberman

2019

Ann. actuar. sci.

View full text Add to dashboard Cite

show abstract

“…When it comes to FPC analysis, many results on the convergence of the sample FPCs to their population counterparts are available in the literature. Results of this type are developed for independent observations (see Dauxois et al 1982), linear process (see Bosq 2000), weakly dependent data (see Hörmann and Kokoszka 2010), and data with long-range dependence (see Salish and Gleim 2019). However, as we have seen in the previous section, if the factors in model ( 1) are weakly correlated with the idiosyncratic error, the covariance function of Y t is time-dependent (see Assumption 2(d) and equation ( 4)), which makes the analysis different from those of the above references.…”

Section: Estimation Of the Primitivesmentioning

confidence: 99%

Approximate Factor Models for Functional Time Series

Otto¹,

Salish²

2022

Preprint

Self Cite

View full text Add to dashboard Cite

A functional dynamic factor model for time-dependent functional data is proposed. We decompose a functional time series into a predictive low-dimensional common component consisting of a finite number of factors and an infinite-dimensional idiosyncratic component that has no predictive power. The conditions under which all model parameters, including the number of factors, become identifiable are discussed. Our identification results lead to a simple-to-use two-stage estimation procedure based on functional principal components. As part of our estimation procedure, we solve the separation problem between the common and idiosyncratic functional components. In particular, we obtain a consistent information criterion that provides joint estimates of the number of factors and dynamic lags of the common component. Finally, we illustrate the applicability of our method in a simulation study and to the problem of modeling and predicting yield curves. In an out-of-sample experiment, we demonstrate that our model performs well compared to the widely used term structure Nelson-Siegel model for yield curves.

show abstract

“…seen a rise of literature addressing modelling and forecasting of functional time series (see e.g., Bosq, 2000, Hyndman and Shang, 2009, Hörmann and Kokoszka, 2010, Hörmann and Kokoszka, 2012, and Salish and Gleim, 2019. The majority of the existing contributions in the forecasting of functional time series have been tailored to one-dimensional manifolds rather than surfaces.…”

mentioning

confidence: 99%

Forecasting Environmental Data: An example to ground-level ozone concentration surfaces

Gleim¹,

Salish²

2022

Preprint

Self Cite

View full text Add to dashboard Cite

Environmental problems are receiving increasing attention in socioeconomic and health studies. This in turn fosters advances in recording and data collection of many related real-life processes. Available tools for data processing are often found too restrictive as they do not account for the rich nature of such data sets. In this paper, we propose a new statistical perspective on forecasting spatial environmental data collected sequentially over time. We treat this data set as a surface (functional) time series with a possibly complicated geographical domain. By employing novel techniques from functional data analysis we develop a new forecasting methodology. Our approach consists of two steps. In the first step, time series of surfaces are reconstructed from measurements sampled over some spatial domain using a finite element spline smoother. In the second step, we adapt the dynamic functional factor model to forecast a surface time series. The advantage of this approach is that we can account for and explore simultaneously spatial as well as temporal dependencies in the data. A forecasting study of ground-level ozone concentration over the geographical domain of Germany demonstrates the practical value of this new perspective, where we compare our approach with standard functional benchmark models.1. Introduction. Studies on the prediction of environmental data sampled across time and over geographical areas/regions have received wide attention across many fields. Examples of such studies include air quality control (see, e.g.,

show abstract

A Moment-Based Notion of Time Dependence for Functional Time Series

Cited by 3 publications

References 34 publications

Forecasting age distribution of death counts: an application to annuity pricing

Forecasting age distribution of death counts: an application to annuity pricing

Approximate Factor Models for Functional Time Series

Forecasting Environmental Data: An example to ground-level ozone concentration surfaces

Contact Info

Product

Resources

About