arXiv subjects

Philipp Otto

Publications and source records attributed to Philipp Otto.

At least 37 records · Page 2Linked to original sources

arXiv2023

Statistical monitoring of European cross-border physical electricity flows using novel temporal edge network processes

Conventional modelling of networks evolving in time focuses on capturing variations in the network structure. However, the network might be static from the origin or experience only deterministic, regulated changes in its structure, providing either a physical infrastructure or a specified connection arrangement for some other processes. Thus, to detect change in its exploitation, we need to focus on the processes happening on the network. In this work, we present the concept of monitoring random Temporal Edge Network (TEN) processes that take place on the edges of a graph having a fixed structure. Our framework is based on the Generalized Network Autoregressive statistical models with time-dependent exogenous variables (GNARX models) and Cumulative Sum (CUSUM) control charts. To demonstrate its effective detection of various types of change, we conduct a simulation study and monitor the real-world data of cross-border physical electricity flows in Europe.

stat.AP↗

arXiv2023

Dynamic Spatiotemporal ARCH Models: Small and Large Sample Results

This paper explores the estimation of a dynamic spatiotemporal autoregressive conditional heteroscedasticity (ARCH) model. The log-volatility term in this model can depend on (i) the spatial lag of the log-squared outcome variable, (ii) the time-lag of the log-squared outcome variable, (iii) the spatiotemporal lag of the log-squared outcome variable, (iv) exogenous variables, and (v) the unobserved heterogeneity across regions and time, i.e., the regional and time fixed effects. We examine the small and large sample properties of two quasi-maximum likelihood estimators and a generalized method of moments estimator for this model. We first summarize the theoretical properties of these estimators and then compare their finite sample properties through Monte Carlo simulations.

stat.ME↗

arXiv2023

A Markov-switching spatio-temporal ARCH model

Stock market indices are volatile by nature, and sudden shocks are known to affect volatility patterns. The autoregressive conditional heteroskedasticity (ARCH) and generalized ARCH (GARCH) models neglect structural breaks triggered by sudden shocks that may lead to an overestimation of persistence, causing an upward bias in the estimates. Different regime-switching models that have abrupt regime-switching governed by a Markov chain were developed to model volatility in financial time series data. Volatility modelling was also extended to spatially interconnected time series, resulting in spatial variants of ARCH models. This inspired us to propose a Markov switching framework of the spatio-temporal log-ARCH model. In this article, we discuss the Markov-switching extension of the model, the estimation procedure and the smooth inferences of the regimes. The Monte-Carlo simulation studies show that the maximum likelihood estimation method for our proposed model has good finite sample properties. The proposed model was applied to 28 stock indices data that were presumably affected by the 2015-2016 Chinese stock market crash. The results showed that our model is a better fit compared to that of the one-regime counterpart. Furthermore, the smoothed inference of the data indicated the approximate periods where structural breaks occurred. This model can capture structural breaks that simultaneously occur in nearby locations.

stat.ME↗

arXiv2023

Spatial autoregressive fractionally integrated moving average model

In this paper, we introduce the concept of fractional integration for spatial autoregressive models. We show that the range of the dependence can be spatially extended or diminished by introducing a further fractional integration parameter to spatial autoregressive moving average models (SARMA). This new model is called the spatial autoregressive fractionally integrated moving average model, briefly sp-ARFIMA. We show the relation to time-series ARFIMA models and also to (higher-order) spatial autoregressive models. Moreover, an estimation procedure based on the maximum-likelihood principle is introduced and analysed in a series of simulation studies. Eventually, the use of the model is illustrated by an empirical example of atmospheric fine particles, so-called aerosol optical thickness, which is important in weather, climate and environmental science.

stat.ME↗

arXiv2023

Spatiotemporal modelling of PM$_{2.5}$ concentrations in Lombardy (Italy) -- A comparative study

This study presents a comparative analysis of three predictive models with an increasing degree of flexibility: hidden dynamic geostatistical models (HDGM), generalised additive mixed models (GAMM), and the random forest spatiotemporal kriging models (RFSTK). These models are evaluated for their effectiveness in predicting PM$_{2.5}$ concentrations in Lombardy (North Italy) from 2016 to 2020. Despite differing methodologies, all models demonstrate proficient capture of spatiotemporal patterns within air pollution data with similar out-of-sample performance. Furthermore, the study delves into station-specific analyses, revealing variable model performance contingent on localised conditions. Model interpretation, facilitated by parametric coefficient analysis and partial dependence plots, unveils consistent associations between predictor variables and PM$_{2.5}$ concentrations. Despite nuanced variations in modelling spatiotemporal correlations, all models effectively accounted for the underlying dependence. In summary, this study underscores the efficacy of conventional techniques in modelling correlated spatiotemporal data, concurrently highlighting the complementary potential of Machine Learning and classical statistical approaches.

stat.AP↗

arXiv2023

Spatial and Spatiotemporal Volatility Models: A Review

Spatial and spatiotemporal volatility models are a class of models designed to capture spatial dependence in the volatility of spatial and spatiotemporal data. Spatial dependence in the volatility may arise due to spatial spillovers among locations; that is, if two locations are in close proximity, they can exhibit similar volatilities. In this paper, we aim to provide a comprehensive review of the recent literature on spatial and spatiotemporal volatility models. We first briefly review time series volatility models and their multivariate extensions to motivate their spatial and spatiotemporal counterparts. We then review various spatial and spatiotemporal volatility specifications proposed in the literature along with their underlying motivations and estimation strategies. Through this analysis, we effectively compare all models and provide practical recommendations for their appropriate usage. We highlight possible extensions and conclude by outlining directions for future research.

econ.EM↗

arXiv2023

Statistical process monitoring of artificial neural networks

The rapid advancement of models based on artificial intelligence demands innovative monitoring techniques which can operate in real time with low computational costs. In machine learning, especially if we consider artificial neural networks (ANNs), the models are often trained in a supervised manner. Consequently, the learned relationship between the input and the output must remain valid during the model's deployment. If this stationarity assumption holds, we can conclude that the ANN provides accurate predictions. Otherwise, the retraining or rebuilding of the model is required. We propose considering the latent feature representation of the data (called "embedding") generated by the ANN to determine the time when the data stream starts being nonstationary. In particular, we monitor embeddings by applying multivariate control charts based on the data depth calculation and normalized ranks. The performance of the introduced method is compared with benchmark approaches for various ANN architectures and different underlying data formats.

stat.ME↗

arXiv2023

Network log-ARCH models for forecasting stock market volatility

This paper presents a novel dynamic network autoregressive conditional heteroscedasticity (ARCH) model based on spatiotemporal ARCH models to forecast volatility in the US stock market. To improve the forecasting accuracy, the model integrates temporally lagged volatility information and information from adjacent nodes, which may instantaneously spill across the entire network. The model is also suitable for high-dimensional cases where multivariate ARCH models are typically no longer applicable. We adopt the theoretical foundations from spatiotemporal statistics and transfer the dynamic ARCH model for processes to networks. This new approach is compared with independent univariate log-ARCH models. We could quantify the improvements due to the instantaneous network ARCH effects, which are studied for the first time in this paper. The edges are determined based on various distance and correlation measures between the time series. The performances of the alternative networks' definitions are compared in terms of out-of-sample accuracy. Furthermore, we consider ensemble forecasts based on different network definitions.

stat.AP↗

arXiv2022

A Dynamic Spatiotemporal Stochastic Volatility Model with an Application to Environmental Risks

This article introduces a dynamic spatiotemporal stochastic volatility (SV) model with explicit terms for the spatial, temporal, and spatiotemporal spillover effects. Moreover, the model includes time-invariant site-specific constant log-volatility terms. Thus, this formulation allows to distinguish between spatial and temporal interactions, while each location may have a different volatility level. We study the statistical properties of an outcome variable under this process and show that it introduces spatial dependence in the outcome variable. Further, we present a Bayesian estimation procedure based on the Markov Chain Monte Carlo (MCMC) approach using a suitable data transformation. After providing simulation evidence on the proposed Bayesian estimator's performance, we apply the model in a highly relevant field, namely environmental risk modeling. Even though there are only a few empirical studies on environmental risks, previous literature undoubtedly demonstrated the importance of climate variation studies. For example, for local air quality in Northern Italy in 2021, we show pronounced spatial and temporal spillovers and larger uncertainties/risks during the winter season compared to the summer season.

stat.ME↗

arXiv2022

Agrimonia: a dataset on livestock, meteorology and air quality in the Lombardy region, Italy

The air in the Lombardy region, Italy, is one of the most polluted in Europe because of limited air circulation and high emission levels. There is a large scientific consensus that the agricultural sector has a significant impact on air quality. To support studies quantifying the role of the agricultural and livestock sectors on the Lombardy air quality, this paper presents a harmonised dataset containing daily values of air quality, weather, emissions, livestock, and land and soil use in the years 2016 - 2021, for the Lombardy region. The pollutant data come from the European Environmental Agency and the Lombardy Regional Environment Protection Agency, weather and emissions data from the European Copernicus programme, livestock data from the Italian zootechnical registry, and land and soil use data from the CORINE Land Cover project. The resulting dataset is designed to be used as is by those using air quality data for research.

stat.AP↗

arXiv2022

Adaptive LASSO estimation for functional hidden dynamic geostatistical model

We propose a novel model selection algorithm based on a penalized maximum likelihood estimator (PMLE) for functional hidden dynamic geostatistical models (f-HDGM). These models employ a classic mixed-effect regression structure with embedded spatiotemporal dynamics to model georeferenced data observed in a functional domain. Thus, the parameters of interest are functions across this domain. The algorithm simultaneously selects the relevant spline basis functions and regressors that are used to model the fixed-effects relationship between the response variable and the covariates. In this way, it automatically shrinks to zero irrelevant parts of the functional coefficients or the entire effect of irrelevant regressors. The algorithm is based on iterative optimisation and uses an adaptive least absolute shrinkage and selector operator (LASSO) penalty function, wherein the weights are obtained by the unpenalised f-HDGM maximum-likelihood estimators. The computational burden of maximisation is drastically reduced by a local quadratic approximation of the likelihood. Through a Monte Carlo simulation study, we analysed the performance of the algorithm under different scenarios, including strong correlations among the regressors. We showed that the penalised estimator outperformed the unpenalised estimator in all the cases we considered. We applied the algorithm to a real case study in which the recording of the hourly nitrogen dioxide concentrations in the Lombardy region in Italy was modelled as a functional process with several weather and land cover covariates.

stat.ME↗

arXiv2022

Estimation of the Spatial Weighting Matrix for Spatiotemporal Data under the Presence of Structural Breaks

In this paper, we propose a two-step lasso estimation approach to estimate the full spatial weights matrix of spatiotemporal autoregressive models. In addition, we allow for an unknown number of structural breaks in the local means of each spatial locations. The proposed approach jointly estimates the spatial dependence, all structural breaks, and the local mean levels. In addition, it is easy to compute the suggested estimators, because of a convex objective function resulting from a slight simplification. Via simulation studies, we show the finite-sample performance of the estimators and provide a practical guidance, when the approach could be applied. Eventually, the invented method is illustrated by an empirical example of regional monthly real-estate prices in Berlin from 1995 to 2014. The spatial units are defined by the respective ZIP codes. In particular, we can estimate local mean levels and quantify the deviation of the observed prices from these levels due to spatial spill over effects.

stat.CO↗

arXiv2022

A Multivariate Spatial and Spatiotemporal ARCH Model

This paper introduces a multivariate spatiotemporal autoregressive conditional heteroscedasticity (ARCH) model based on a vec-representation. The model includes instantaneous spatial autoregressive spill-over effects in the conditional variance, as they are usually present in spatial econometric applications. Furthermore, spatial and temporal cross-variable effects are explicitly modelled. We transform the model to a multivariate spatiotemporal autoregressive model using a log-squared transformation and derive a consistent quasi-maximum-likelihood estimator (QMLE). For finite samples and different error distributions, the performance of the QMLE is analysed in a series of Monte-Carlo simulations. In addition, we illustrate the practical usage of the new model with a real-world example. We analyse the monthly real-estate price returns for three different property types in Berlin from 2002 to 2014. We find weak (instantaneous) spatial interactions, while the temporal autoregressive structure in the market risks is of higher importance. Interactions between the different property types only occur in the temporally lagged variables. Thus, we see mainly temporal volatility clusters and weak spatial volatility spill-overs.

stat.ME↗

arXiv2022

Dynamic Spatiotemporal ARCH Models

Geo-referenced data are characterized by an inherent spatial dependence due to the geographical proximity. In this paper, we introduce a dynamic spatiotemporal autoregressive conditional heteroscedasticity (ARCH) process to describe the effects of (i) the log-squared time-lagged outcome variable, i.e., the temporal effect, (ii) the spatial lag of the log-squared outcome variable, i.e., the spatial effect, and (iii) the spatial lag of the log-squared time-lagged outcome variable, i.e., the spatiotemporal effect, on the volatility of an outcome variable. Furthermore, our suggested process allows for the fixed effects over time and space to account for the unobserved heterogeneity. For this dynamic spatiotemporal ARCH model, we derive a generalized method of moments (GMM) estimator based on the linear and quadratic moment conditions of a specific transformation. We show the consistency and asymptotic normality of the GMM estimator, and determine the best set of moment functions. We investigate the finite-sample properties of the proposed GMM estimator in a series of Monte-Carlo simulations with different model specifications and error distributions. Our simulation results show that our suggested GMM estimator has good finite sample properties. In an empirical application, we use monthly log-returns of the average condominium prices of each postcode of Berlin from 1995 to 2015 (190 spatial units, 240 time points) to demonstrate the use of our suggested model. Our estimation results show that the temporal, spatial and spatiotemporal lags of the log-squared returns have statistically significant effects on the volatility of the log-returns.

stat.ME↗

arXiv2021

Generalized Spatial and Spatiotemporal ARCH Models

In time-series analyses, particularly for finance, generalized autoregressive conditional heteroscedasticity (GARCH) models are widely applied statistical tools for modelling volatility clusters (i.e., periods of increased or decreased risk). In contrast, it has not been considered to be of critical importance until now to model spatial dependence in the conditional second moments. Only a few models have been proposed for modelling local clusters of increased risks. In this paper, we introduce a novel spatial GARCH process in a unified spatial and spatiotemporal GARCH framework, which also covers all previously proposed spatial ARCH models, exponential spatial GARCH, and time-series GARCH models. In contrast to previous spatiotemporal and time series models, this spatial GARCH allows for instantaneous spill-overs across all spatial units. For this common modelling framework, estimators are derived based on a non-linear least-squares approach. Eventually, the use of the model is demonstrated by a Monte Carlo simulation study and by an empirical example that focuses on real estate prices from 1995 to 2014 across the ZIP-Code areas of Berlin. A spatial autoregressive model is applied to the data to illustrate how locally varying model uncertainties (e.g., due to latent regressors) can be captured by the spatial GARCH-type models.

stat.ME↗

arXiv2021

Online network monitoring

The application of network analysis has found great success in a wide variety of disciplines; however, the popularity of these approaches has revealed the difficulty in handling networks whose complexity scales rapidly. One of the main interests in network analysis is the online detection of anomalous behaviour. To overcome the curse of dimensionality, we introduce a network surveillance method bringing together network modelling and statistical process control. Our approach is to apply multivariate control charts based on exponential smoothing and cumulative sums in order to monitor networks determined by temporal exponential random graph models (TERGM). This allows us to account for temporal dependence, while simultaneously reducing the number of parameters to be monitored. The performance of the proposed charts is evaluated by calculating the average run length for both simulated and real data. To prove the appropriateness of the TERGM to describe network data, some measures of goodness of fit are inspected. We demonstrate the effectiveness of the proposed approach by an empirical application, monitoring daily flights in the United States to detect anomalous patterns.

stat.ME↗

arXiv2020

A Spatiotemporal Functional Model for Bike-Sharing Systems -- An Example based on the City of Helsinki

Understanding the usage patterns for bike-sharing systems is essential in terms of supporting and enhancing operational planning for such schemes. Studies have demonstrated how factors such as weather conditions influence the number of bikes that should be available at bike-sharing stations at certain times during the day. However, the influences of these factors usually vary over the course of a day, and if there is good temporal resolution, there could also be significant effects only for some hours/minutes (rush hours, the hours when shops are open, and so forth). Thus, in this paper, an analysis of Helsinki's bike-sharing data from 2017 is conducted that considers full temporal and spatial resolutions. Moreover, the data are available at a very high frequency. Hence, the station hire data is analysed in a spatiotemporal functional setting, where the number of bikes at a station is defined as a continuous function of the time of day. For this completely novel approach, we apply a functional spatiotemporal hierarchical model to investigate the effect of environmental factors and the magnitude of the spatial and temporal dependence. Challenges in computational complexity are faced using a bootstrapping approach. The results show the necessity of splitting the bike-sharing stations into two clusters based on the similarity of their spatiotemporal functional observations in order to model the station hire data of Helsinki's bike-sharing system effectively. The estimated functional influences of the proposed factors are different for the two clusters. Moreover, the estimated parameters reveal high random effects in the data that are not explained by the mean of the process. In this random-effects model, the temporal autoregressive parameter dominates the spatial dependence.

stat.AP↗

arXiv2020

Statistical learning for change point and anomaly detection in graphs

Complex systems which can be represented in the form of static and dynamic graphs arise in different fields, e.g. communication, engineering and industry. One of the interesting problems in analysing dynamic network structures is to monitor changes in their development. Statistical learning, which encompasses both methods based on artificial intelligence and traditional statistics, can be used to progress in this research area. However, the majority of approaches apply only one or the other framework. In this paper, we discuss the possibility of bringing together both disciplines in order to create enhanced network monitoring procedures focussing on the example of combining statistical process control and deep learning algorithms. Together with the presentation of change point and anomaly detection in network data, we propose to monitor the response times of ambulance services, applying jointly the control chart for quantile function values and a graph convolutional network.

cs.LG↗