The Impact of Sampling Frequency and Volatility Estimators on Change-Point Tests

The paper evaluates the performance of several recently proposed change-point tests applied to conditional variance dynamics and conditional distributions of asset returns. These are CUSUM-type tests for beta-mixing processes and EDF-based tests for the residuals of such nonlinear dependent processes. Hence the tests apply to the class of ARCH and SV type processes as well as data-driven volatility estimators using high-frequency data. It is shown that some of the high-frequency volatility estimators substantially improve the power of the structural breaks tests especially for detecting changes in the tail of the conditional distribution. Similarly, certain types of filtering and transformation of the returns process can improve the power of CUSUM statistics. We also explore the impact of sampling frequency on each of the test statistics. Ce papier évalue la performance de plusieurs tests de changement structurel CUSUM et EDF pour la structure dynamique de la variance conditionelle et de la distribution conditionnelle. Nous étudions l'impact 1) de la fréquence des observations, 2) de l'utilisation des données de haute fréquence pour le calcul des variances conditionnelles et 3) de transformation des séries pour améliorer la puissance des tests.Change-point tests, CUSUM, Kolmogorov-Smirnov, GARCH, quadratic variation, power variation, high-frequency data, location-scale distribution family, tests de changement structurel, CUSUM, Kolmogov-Smirnov, GARCH, variation quadratique, 'power variation', données de haute fréquence

Detecting Multiple Breaks in Financial Market Volatility Dynamics

The paper evaluates the performance of several recently proposed tests for structural breaks in conditional variance dynamics of asset returns. The tests apply to the class of ARCH and SV type processes as well as data-driven volatility estimators using high-frequency data. In addition to testing for the presence of breaks, the statistics identify the number and location of multiple breaks. We study the size and power of the new test for detecting breaks in the second conditional variance under various realistic univariate heteroskedastic models, change-point hypotheses and sampling schemes. The paper concludes with an empirical analysis using data from the stock and FX markets for which we find multiple breaks associated with the Asian and Russian financial crises. These events resulted in changes in the dynamics of volatility of asset returns in the samples prior and post the breaks.change-point, break dates, ARCH, high-frequency data.

Political and Economic Uncertainty and Investment Behaviour in Pakistan

This study analyses the effect of political stability and macroeconomic uncertainty on aggregate investment behaviour in Pakistan over the period 1960–2015. The Auto-Regressive Distributed Lags (ARDL) methodology is applied to explore both the long-run equilibrium relationship and short-run behaviour of investment. The macroeconomic uncertainty variable is derived from real exchange rate and is computed by the best-fitted GARCH model. The results reveal robust effects of political stability and macroeconomic uncertainty on overall investment activity in Pakistan. The government nationalisation policy, GDP growth, user cost of capital, credit availability and degree of openness are found to be the other key determining factors for investment both in long- and short-run. However, the favourable impact of physical infrastructure on investment holds in long-run only, while its effect is adverse though insignificantly in short-run. The findings support the neoclassical flexible accelerator principle and are consistent with economic theory. The volume of available funds is the binding constraint for investment and the McKinnon-Shaw hypothesis is validated in the short-run. Keywords: Aggregate Investment, Irreversibility, Macroeconomic Uncertainty, Political Stability, GARCH, ARDL, Bound Testing Approach, Pakista

Transformer을 이용한 자기회귀 시계열의 구조적 변화점 탐지

학위논문(석사) -- 서울대학교대학원 : 자연과학대학 통계학과, 2023. 8. 이상열.In this paper, we discuss a method for detecting structural change point in autoregressive time series using transformer based deep learning model. Detecting structural changes can be achieved using the LSCUSUM test, which is one of the most popular methods for change point detection. A crucial aspect of constructing the LSCUSUM test is to adequately estimate the residuals, and choosing an appropriate model is of paramount importance. Given that many time series exhibit nonlinear characteristics, it becomes imperative to employ deep learning methods for capturing and effectively modeling these nonlinearities. Therefore, in this context, we utilize a transformer-based deep learning model that leverages the powerful self-attention mechanism. In the process, we compute empirical size and power about our method and apply to two real datasets.본 논문에서는 트랜스포머 기반 딥러닝 모델을 이용하여 자기회귀 시계열에서 구조적 변화 지점을 탐지하는 방법에 대해 논의한다. 변화 지점 감지를 위한 방법 중 하나인 LSCUSUM 검정을 사용하여 구조적 변화를 감지할 수 있는데, LSCUSUM 검정의 가장 중요한 측면은 잔차를 정확하게 추정하는 것이므로, 적절한 모델을 선택하는 것이 가장 중요하다. 많은 시계열이 비선형 특성을 나타내므로 이러한 비선형성을 포착하고 효과적으로 모형화하기 위해 딥 러닝 방법을 사용하는 것이 필수적이다. 따라서 우리는 self-attention 메커니즘을 활용하는 transformer 기반 딥 러닝 모델을 활용한다. 또한, 본 연구에서는 transformer 기반의 변화점 탐지 방법에 대한 크기와 검정력을 Monte Carlo simulation으로 계산하고, 두 실제 데이터 세트에 적용한다.Abstract i Chapter 1 Introduction 1 Chapter 2 Model Description 6 2.1 Transformer 6 2.2 Location and scale-based CUSUM test 8 Chapter 3 Simulation Study 11 3.1 Selecting Optimal Tuning Parameters 11 3.2 Monte Carlo Simulation 13 Chapter 4 Empirical Applications 15 Chapter 5 Conclusion and Discussion 17 국문초록 21석

A methodology for discriminant time series analysis applied to microclimate monitoring of fresco paintings

[EN] The famous Renaissance frescoes in Valencia¿s Cathedral (Spain) have been kept under confined temperature and relative humidity (RH) conditions for about 300 years, until the removal of the baroque vault covering them, carried out in 2006. In the interest of longer-term preservation and in order to maintain these frescoes in good condition, a unique monitoring system was implemented to record both air temperature and RH. Sensors were installed in different points at the vault of the apse, during the restoration process. The present study proposes a statistical methodology for analyzing a subset of RH data recorded in 2008 and 2010, from the sensors. This methodology is based on fitting different functions and models to the time series, in order to classify the sensors. The methodology proposed, computes classification variables and applies a discriminant technique to them. The classification variables correspond to estimates of parameters of the models and features such as mean and maximum, among others. These features are computed using values of the functions such as spectral density, sample autocorrelation (sample ACF), sample partial autocorrelation (sample PACF), and moving range (MR). The classification variables computed were structured as a matrix. Next, Sparse Partial Least Squares Discriminant Analysis (sPLS-DA) was applied in order to discriminate sensors according to their position in the vault. It was found that the classification of sensors derived from Seasonal ARIMA-TGARCH showed the best performance (i.e., lowest classification error rate). Based on these results, the methodology applied here can be useful for characterizing the differences in RH, measured at different positions in a historical building.This project received funding from the European Union's Horizon 2020 research and innovation programme under grant agreement No. 814624. Furthermore, the project was partially supported by Instituto Colombiano de Credito Educativo y Estudios Tecnicos en el Exterior (ICETEX) by means of Programa credito Pasaporte a la Ciencia ID 3595089, and also by Pontificia Universidad Javeriana Cali (Nit 860013720-1) through the Convenio de Capacitacion para Docentes O. J. 086/17.Ramírez, S.; Zarzo Castelló, M.; Perles, A.; García Diego, FJ. (2021). A methodology for discriminant time series analysis applied to microclimate monitoring of fresco paintings. Sensors. 21(2):1-28. https://doi.org/10.3390/s21020436S12821

Bootstrap score tests for fractional integration in heteroskedastic ARFIMA models, with an application to price dynamics in commodity spot and futures markets

Empirical evidence from time series methods which assume the usual I(0)/I(1) paradigm suggests that the efficient market hypothesis, stating that spot and futures prices of a commodity should co-integrate with a unit slope on futures prices, does not hold. However, these statistical methods are known to be unreliable if the data are fractionally integrated. Moreover, spot and futures price data tend to display clear patterns of time-varying volatility which also has the potential to invalidate the use of these methods. Using new tests constructed within a more general heteroskedastic fractionally integrated model we are able to find a body of evidence in support of the efficient market hypothesis for a number of commodities. Our new tests are wild bootstrap implementations of score-based tests for the order of integration of a fractionally integrated time series. These tests are designed to be robust to both conditional and unconditional heteroskedasticity of a quite general and unknown form in the shocks. We show that the asymptotic tests do not admit pivotal asymptotic null distributions in the presence of heteroskedasticity, but that the corresponding tests based on the wild bootstrap principle do. A Monte Carlo simulation study demonstrates that very significant improvements in finite sample behaviour can be obtained by the bootstrap vis-à-vis the corresponding asymptotic tests in both heteroskedastic and homoskedastic environments

Parameter Change Test for Time Series of Counts

학위논문 (박사)-- 서울대학교 대학원 자연과학대학 통계학과, 2017. 8. 이상열.In this thesis, we consider parameter change test for time series of counts. First we consider the problem of testing for parameter change in zero-inflated generalized Poisson (ZIGP) autoregressive models. We verify that the ZIGP process is stationary and ergodic and that the conditional maximum likelihood estimator (CMLE) is strongly consistent and asymptotically normal. Then, based on these results, we construct CMLE- and residual-based cumulative sum tests and show that their limiting null distributions are a function of independent Brownian bridges. Simulation results are provided for illustration and a real data analysis is performed on data of crimes in Australia. Second we consider bivariate Poisson integer-valued GARCH(1,1) models, constructed via a trivariate reduction method of independent Poisson variables. We verify that the CMLE of the model parameters is asymptotically normal. Then, based on these results, we construct CMLE- and residual-based CUSUM tests and derive that their limiting null distributions are a function of independent Brownian bridges. A simulation study are conducted for illustration. We analyze two daily data sets of car accidents that occurred in Sungdong and Seocho counties in Seoul, Korea. Finally, we consider the problem of testing for a parameter change in general nonlinear integer-valued time series models where the conditional distribution of current observations is assumed to follow a one-parameter exponential family. We consider score-, (standardized) residual-, and estimate-based CUSUM tests, and show that their limiting null distributions take the form of the functions of Brownian bridges. Based on the obtained results, we then conduct a comparison study of the performance of CUSUM tests, through the use of Monte Carlo simulations. Our findings demonstrate that the standardized residual-based CUSUM test largely outperforms the others.Abstract i List of Tables viii List of Figures x 1 Introduction 1 2 Literature Review 6 2.1 CUSUM test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.2 The Poisson AR models . . . . . . . . . . . . . . . . . . . . . . . . . 8 3 Parameter Change Test for Zero-Inflated Generalized Poisson Autoregressive Models 9 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 3.2 Zero-inflated generalized Poisson AR model . . . . . . . . . . . . . . 10 3.3 Change point test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 3.3.1 Estimates-based CUSUM test . . . . . . . . . . . . . . . . . . 15 3.3.2 Residual-based CUSUM test . . . . . . . . . . . . . . . . . . . 18 3.4 Simulation results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 3.5 Real data analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 3.5.1 Number of robbery with rearms in Inner Sydney . . . . . . . 21 3.5.2 Number of assault police in Inner Sydney . . . . . . . . . . . . 22 3.6 Concluding remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 3.7 Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 3.8 Supplementary Material . . . . . . . . . . . . . . . . . . . . . . . . . 27 4 Asymptotic Normality and Parameter Change Test for Bivariate Poisson INGARCH Models 55 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 4.2 Bivariate Poisson INGARCH model . . . . . . . . . . . . . . . . . . . 56 4.3 Change point test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 4.3.1 Estimate-based CUSUM test . . . . . . . . . . . . . . . . . . . 59 4.3.2 Residual-based CUSUM test . . . . . . . . . . . . . . . . . . . 60 4.4 Simulation results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 4.5 Real data analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 4.6 Concluding remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 4.7 Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 4.8 Supplementary Material . . . . . . . . . . . . . . . . . . . . . . . . . 69 5 Comparison Study on CUSUM Tests for General Nonlinear Integer-valued GARCH Models 86 5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 5.2 Models and likelihood inferences . . . . . . . . . . . . . . . . . . . . 87 5.2.1 Basic set-up and asymptotics . . . . . . . . . . . . . . . . . . 87 5.2.2 INGARCH(1,1) models . . . . . . . . . . . . . . . . . . . . . . 90 5.3 Change point test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92 5.3.1 Score vector-based CUSUM test . . . . . . . . . . . . . . . . . 93 5.3.2 Residual-based CUSUM test . . . . . . . . . . . . . . . . . . . 93 5.4 Simulation study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 5.4.1 Test for Poisson INGARCH(1,1) models . . . . . . . . . . . . 95 5.4.2 Test for NB-INGARCH(1,1) models . . . . . . . . . . . . . . . 96 5.4.3 Test for binomial INGARCH(1,1) models . . . . . . . . . . . . 97 5.5 Real data analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98 5.6 Concluding remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98 5.7 Proofs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99Docto

Essays on testing for nonlinearity in time series : issues in nonlinear cointegration, structural breaks and changes in persistence

Besides obvious nonlinear relations like a nonlinear error correction model are nonlinearities in time series closely related to structural breaks and changes in persistence. Since both kinds of changes can induce regime-switching, they qualify well to capture the characteristic of time-variability. On the contrary, linear models are often an insufficient simplification of the real underlying DGP because they fail ro reproduce trends, shocks like finance crises and stylized facts such as long-range dependencies as well as volatility clustering. This is why testing for the presence of these nonlinear properties as the first step of any statistical analysis is very crucial, especially with regard to effective model building. Nonlinear Cointegration In the first chapter, a nonlinear cointegration test is proposed which builds on Kapetanios et al. (2006) who where the first who addressed cointegration in a nonlinear error correction framework under the alternative. The switch between regimes is modeled to follow a second order logistic smooth transition (D-LSTR) function and a null hypothesis of no cointegration is tested against globally stationary D-LSTR cointegration. From the nonlinear error correction regression, t-type and F-type statistics are derived and finite-sample investigations are conducted. The results of the modified nonlinear cointegration test are compared to a comparable linear cointegration test, namely the test proposed by Johansen (1991). The D-LSTR function qualifies well as an overall-generalization of transition functions and it is found that the D-LSTR error correction model has power against both alternatives, D-LSTR as well as 3-regime TAR nonlinearity which is nested for large gamma in the D-LSTR function. Structural breaks The topic of the second paper is to survey the most frequently applied volatility break tests when they are employed to a broad range of different DGPs. Within a simulation study, the break tests are applied to DGPs which can exhibit either single- or double-shifting or the process can experience a smooth increase in the magnitude of the volatility break. The surveyed tests are a CUSUM test in a version proposed by Deng and Perron (2008) and conventional Wald and LM tests. Besides size and power comparisons the break tests are empirically validated and it is found that more breaks are found in equity series than in exchange rate series. One main finding is that huge outliers in the data can impact the long-run variance of the squared return process to be no longer finite which renders non-monotonic power functions. Changes in Persistence Chapter three addresses the specific question whether either structural breaks or nonstationarity in the conditional volatility affect the testing decision of the R test proposed by Leybourne et al. (2007). The additional structural breaks in the conditional volatility process are not specified under the null hypothesis and may therefore lead to a non-pivotal limiting distribution. Hence, heteroskedasticity of an unknown form is encountered and in order to potentially robustify the testing procedure, a wild-bootstrapped version of Leybourne et al. (2007)'s R test is suggested. Within a simulation study, size and power of the originally proposed test and the wild-bootstrap analogue are compared for various constellations of simultaneous breaks in the AR parameter as well as the GARCH parameter. It is found that the Leybourne et al. (2007) test seems heavily impacted by additional structural breaks in the conditional volatility, especially in very finite sample sizes. In an empirical application the two testing procedures are applied and evaluated