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on Econometric Time Series |
| By: | Donald W. K. Andrews; Ming Li |
| Abstract: | This paper considers nonparametric estimation and inference in first-order autoregressive (AR(1)) models with deterministically time-varying parameters. A key feature of the proposed approach is to allow for time-varying stationarity in some time periods, time-varying nonstationarity (i.e., unit root or local-to-unit root behavior) in other periods, and smooth transitions between the two. The estimation of the AR parameter at any time point is based on a local least squares regression method, where the relevant initial condition is endogenous. We obtain limit distributions for the AR parameter estimator and t-statistic at a given point $\tau$ in time when the parameter exhibits unit root, local-to-unity, or stationary/stationary-like behavior at time $\tau$. These results are used to construct confidence intervals and median-unbiased interval estimators for the AR parameter at any specified point in time. The confidence intervals have correct asymptotic coverage probabilities with the coverage holding uniformly over stationary and nonstationary behavior of the observations. |
| Date: | 2024–11 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2411.00358 |
| By: | Dierkes, Maik; Fitter, Krischan; Sibbertsen, Philipp |
| Abstract: | We extend the monitoring of structural breaks in classic cointegration proposed by Wagner and Wied (2017) to explicitly allow for fractional cointegration and breaks in these fractional relations with possible deterministic trends. To estimate the parameters we use a fully modified OLS estimator and we estimate the integration order by the exact local whittle. In order to build the test statistic we establish a CUSUM test for a break in parameters or a break in the order of integration and derive the limiting distribution of the cumulative sum of the modified OLS residuals by using representations by Davidson and Hashimzade (2009) and Fox and Taqqu (1987). Using these limiting results we propose a detector and its limiting distribution as a function of fractional Brownian motions and prove the consistency of our procedure against fixed and local alternatives. The critical values for the monitoring are derived by bootstrap. In a Monte-Carlo study we show the finite sample behavior of our test and compare it to the one by Wagner and Wied (2017) in different scenarios of fractional cointegration. To conclude we show the applicability of the test by presenting the results of applying the test in the context of momentum investing. |
| Keywords: | long-memory time series, fractional cointegration, structural change, monitoring |
| JEL: | C32 C12 C52 |
| Date: | 2024–11 |
| URL: | https://d.repec.org/n?u=RePEc:han:dpaper:dp-728 |
| By: | Florian Huber; Christian Matthes; Michael Pfarrhofer |
| Abstract: | We provide a framework for efficiently estimating impulse response functions with Local Projections (LPs). Our approach offers a Bayesian treatment for LPs with Instrumental Variables, accommodating multiple shocks and instruments per shock, accounts for autocorrelation in multi-step forecasts by jointly modeling all LPs as a seemingly unrelated system of equations, defines a flexible yet parsimonious joint prior for impulse responses based on a Gaussian Process, allows for joint inference about the entire vector of impulse responses, and uses all available data across horizons by imputing missing values. |
| Date: | 2024–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2410.17105 |
| By: | Fotso, Chris Toumping; Sibbertsen, Philipp |
| Abstract: | This paper proposes an estimator that accounts for time variation in a regression relationship with stochastic regressors exhibiting long-range dependence, covering weak fractional cointegration as a special case. An interesting application of this estimator is its ability to handle situations where the regression coefficient changes abruptly. The parametric formulation of this estimator is introduced using the Block-Whittle-based estimation. We analyze the asymptotic properties of this estimator, including consistency and asymptotic normality. Furthermore, we examine the finite sample behavior of the estimator through Monte Carlo simulations. Additionally, we consider a real-life application to demonstrate its advantages over the constant case. |
| Keywords: | Stochastic regressors, weak fractional cointegration, Block-Whittle-based estimation, consistency, asymptotic normality |
| JEL: | C13 C22 |
| Date: | 2024–11 |
| URL: | https://d.repec.org/n?u=RePEc:han:dpaper:dp-730 |
| By: | Tomonori Takahashi; Takayuki Mizuno |
| Abstract: | Despite its practical significance, generating realistic synthetic financial time series is challenging due to statistical properties known as stylized facts, such as fat tails, volatility clustering, and seasonality patterns. Various generative models, including generative adversarial networks (GANs) and variational autoencoders (VAEs), have been employed to address this challenge, although no model yet satisfies all the stylized facts. We alternatively propose utilizing diffusion models, specifically denoising diffusion probabilistic models (DDPMs), to generate synthetic financial time series. This approach employs wavelet transformation to convert multiple time series (into images), such as stock prices, trading volumes, and spreads. Given these converted images, the model gains the ability to generate images that can be transformed back into realistic time series by inverse wavelet transformation. We demonstrate that our proposed approach satisfies stylized facts. |
| Date: | 2024–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2410.18897 |
| By: | Liudas Giraitis (School of Economics and Finance, Queen Mary University of London); George Kapetanios (Kings College London); Yufei Li (Kings College London) |
| Abstract: | This paper introduces and analyses a setting with general heterogeneity in regression modelling. It shows that regression models with fixed or time-varying parameters can be estimated by OLS or time-varying OLS methods, respectively, for a very wide class of regressors and noises, not covered by existing modelling theory. The new setting allows the development of asymptotic theory and the estimation of standard errors. The proposed robust confidence interval estimators permit a high degree of heterogeneity in regressors and noise. The estimates of robust standard errors coincide with the wellknown estimator of heteroskedasticity-consistent standard errors by White (1980), but are applicable to more general circumstances than just the presence of heteroscedastic noise. They are easy to compute and perform well in Monte Carlo simulations. Their robustness, generality and ease of use make them ideal for applied work. The paper includes a brief empirical illustration. |
| Keywords: | robust estimation, structural change, time-varying parameters, non-parametric estimation |
| JEL: | C12 C51 |
| Date: | 2024–08–22 |
| URL: | https://d.repec.org/n?u=RePEc:qmw:qmwecw:983 |
| By: | Alex Li |
| Abstract: | Predicting volatility in financial markets, including stocks, index ETFs, foreign exchange, and cryptocurrencies, remains a challenging task due to the inherent complexity and non-linear dynamics of these time series. In this study, I apply TimeMixer, a state-of-the-art time series forecasting model, to predict the volatility of global financial assets. TimeMixer utilizes a multiscale-mixing approach that effectively captures both short-term and long-term temporal patterns by analyzing data across different scales. My empirical results reveal that while TimeMixer performs exceptionally well in short-term volatility forecasting, its accuracy diminishes for longer-term predictions, particularly in highly volatile markets. These findings highlight TimeMixer's strength in capturing short-term volatility, making it highly suitable for practical applications in financial risk management, where precise short-term forecasts are critical. However, the model's limitations in long-term forecasting point to potential areas for further refinement. |
| Date: | 2024–09 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2410.09062 |
| By: | Enzo D'Innocenzo (University of Bologna); Andre Lucas (Vrije Universiteit Amsterdam and Tinbergen Institute); Bernd Schwaab (European Central Bank); Xin Zhang (Sveriges Riksbank) |
| Abstract: | We propose a robust semi-parametric framework for persistent time-varying extreme tail behavior, including extreme Value-at-Risk (VaR) and Expected Shortfall (ES). The framework builds on Extreme Value Theory and uses a conditional version of the Generalized Pareto Distribution (GPD) for peaks-over-threshold (POT) dynamics. Unlike earlier approaches, our model (i) has unit root-like, i.e., integrated autoregressive dynamics for the GPD tail shape, and (ii) re-scales POTs by their thresholds to obtain a more parsimonious model with only one time-varying parameter to describe the entire tail. We establish parameter regions for stationarity, ergodicity, and invertibility for the integrated time-varying parameter model and its filter, and formulate conditions for consistency and asymptotic normality of the maximum likelihood estimator. Using four exchange rate series, we illustrate how the new model captures the dynamics of extreme VaR and ES. |
| Keywords: | dynamic tail risk, integrated score-driven models, extreme value theory |
| JEL: | C22 G11 |
| Date: | 2024–11–08 |
| URL: | https://d.repec.org/n?u=RePEc:tin:wpaper:20240069 |
| By: | Mustafa R. K{\i}l{\i}n\c{c}; Michael Massmann; Maximilian Ambros |
| Abstract: | This note proposes semi-parametric tests for investigating whether a stochastic process is fractionally integrated of order $\delta$, where $|\delta| |
| Date: | 2024–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2410.10749 |
| By: | Abhishek Pal Majumder |
| Abstract: | Examples of stochastic processes whose state space representations involve functions of an integral type structure $$I_{t}^{(a, b)}:=\int_{0}^{t}b(Y_{s})e^{-\int_{s}^{t}a(Y_{r})dr}ds, \quad t\ge 0$$ are studied under an ergodic semi-Markovian environment described by an $S$ valued jump type process $Y:=(Y_{s}:s\in\mathbb{R}^{+})$ that is ergodic with a limiting distribution $\pi\in\mathcal{P}(S)$. Under different assumptions on signs of $E_{\pi}a(\cdot):=\sum_{j\in S}\pi_{j}a(j)$ and tail properties of the sojourn times of $Y$ we obtain different long time limit results for $I^{(a, b)}_{}:=(I^{(a, b)}_{t}:t\ge 0).$ In all cases mixture type of laws emerge which are naturally represented through an affine stochastic recurrence equation (SRE) $X\stackrel{d}{=}AX+B, \, \, X\perp\!\!\!\perp (A, B)$. Examples include explicit long-time representations of pitchfork bifurcation, and regime-switching diffusions under semi-Markov modulated environments, etc. |
| Date: | 2024–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2410.15824 |