Tuesday, Aug 5: 8:30 AM - 10:20 AM
4085
Contributed Papers
Music City Center
Room: CC-201B
Main Sponsor
Business and Economic Statistics Section
Presentations
The decomposition of time series into their fundamental components is a key problem in many disciplines. Singular Spectrum Analysis (SSA) is a nonparametric method for time series modeling and forecasting. By applying Singular Value Decomposition (SVD) to the trajectory matrix-or equivalently, by diagonalizing the second-moment matrix-SSA extracts quasi-orthogonal components that maximize variability. These components provide natural estimates of the underlying trend, cycles, and noise in the original time series. However, standard SSA does not explicitly associate these components with specific oscillation frequencies.
We introduce a novel extension of SSA that simultaneously achieves frequency identification and variance diagonalization. As a byproduct, our approach also yields a consistent estimator of the spectral density. We illustrate the performance of the method through simulations and apply it to various real-world datasets including paleoclimate temperature records and Gross Domestic Product data from multiple countries. In the latter application, we disentangle common from idiosyncratic fluctuations per frequency in international business cycles.
Keywords
signal extraction
time series
singular spectrum analysis
cycles
frequency identification
eigenvalues
Overparameterization poses a significant challenge for standard vector autoregressive (VAR) models, particularly in high-dimensional time series, as it restricts the number of variables and lags that can be effectively incorporated. To address this, we introduce partial envelope models designed for efficient dimension reduction in multivariate time series. Our approach provides a parsimonious framework by selectively focusing on key lag variables, leading to substantial efficiency gains in coefficient estimation compared to standard VAR models. By concentrating on a subset of relevant lags, our models enhance estimation efficiency while maintaining predictive accuracy. We demonstrate these efficiency improvements through simulated experiments and a real-data analysis, highlighting the advantages of our proposed partial envelope methodology.
Keywords
VAR
Dimension reduction
Envelopes
Threshold autoregressive (TAR) models are widely used in nonlinear time series analysis, where the autoregressive structure changes according to threshold variables. While previous studies have proposed methods for estimating threshold values, they generally assume that the threshold variable and autoregressive order are known. This study focuses on general scenarios where the threshold variable could be a linear combination of multiple lag variables and aims to address: (1) estimation of the threshold variable by finding the optimal linear combination coefficients, (2) determination of the autoregressive order, and (3) estimation of threshold values and determination of suitable regime number. For efficient computations, we adopt Bayesian optimization to determine threshold structures, which involves a re-parameterization transforming the parameter estimation problem into a model selection problem implemented via a greedy algorithm (Chan et al., 2017). The proposed methodology applies to univariate and multivariate time series and achieves an accurate threshold structure determination resulting in efficient forecasts, validated via simulation studies and applications.
Keywords
Bayesian optimization
High-dimensional AIC
Threshold autoregression
Co-Author(s)
Pei-Ching Ho, National Tsing Hua University
Lai-Heng Sim, National Tsing Hua University
First Author
Nan-Jung Hsu, Institute of Statistics and Data Science, National Tsing Hua University
Presenting Author
Nan-Jung Hsu, Institute of Statistics and Data Science, National Tsing Hua University
Expected shortfall is defined as the truncated mean of a random variable that falls below a specified quantile level. This statistic is widely recognized as an important risk measure. Motivated by the empirical observation of clustering patterns in financial risks, we consider a joint autoregressive model for both conditional quantile and expected shortfall in this manuscript. Existing estimation methods for such models typically rely on minimizing a nonlinear and nonconvex joint loss function, which is challenging to solve and often yields inefficient estimators. We employ a weighted two-step estimation approach to estimate the proposed models. Our proposed estimator has greater efficiency compared to those obtained by existing methods both theoretically and numerically, for a general class of location-scale family time series. Our empirical results on stock market data indicate that the proposed models effectively capture the clustering patterns and leverage effects on the conditional expected shortfall.
Keywords
Expected Shortfall
Time Series
Financial Risk Management
Neyman Orthogonality
Quantile Regression
We develop tests for the correct specification of the conditional distribution in multivariate GARCH models based on empirical processes. We transform the multivariate data into univariate data based on the marginal and conditional cumulative distribution functions specified by the null model. The test statistics considered are based on empirical processes of the transformed data in the presence of estimated parameters. The limiting distributions of the proposed test statistics are model dependent and are not free from the underlying nuisance parameters, making the tests difficult to implement. To address this, we develop a novel bootstrap procedure which is shown to be asymptotically valid irrespective of the presence of nuisance parameters. This approach utilises a particular scalable iterated bootstrap method and is simple to implement as the associated test statistics have simple closed form expressions. A simulation study demonstrates that the new tests perform well in finite samples. A real data example illustrates the testing procedure.
Keywords
Bootstrap
Multivariate GARCH
Specification test
The Ornstein-Uhlenbeck process is widely used in financial engineering to describe the dynamics of interest rates, currency exchange rates, and asset price volatilities. Influential observations may significantly affect the validity of inferential procedures and conclusions drawn from them. Identifying atypical data is, therefore, an essential step in any statistical analysis. The local influence approach is a set of methods designed to detect the effect of small perturbations of the model or data on the inference. In this work, we derive local influence methods for stochastic interest rate models typically used to model and predict interest or exchange rates. In particular, we develop and implement local influence diagnostic techniques based on likelihood displacement. We primarily discuss the Vasicek model with perturbation of the variance and the response. Additionally, we propose a statistic to test the hypothesis of constant volatility based on the Gradient test. Finally, we illustrate the methodology using the monthly exchange rate between the US dollar and the Swiss franc over a period exceeding 20 years and assess the performance through a simulation study.
Keywords
Ornstein-Uhlenbeck processes
Local influence diagnostics
Stochastic interest rate models
Likelihood inference
Gradient test