Adaptive Student's t-distribution with method of moments moving estimator for nonstationary time series
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866909586777178112 |
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| author | Duda, Jarek |
| author_facet | Duda, Jarek |
| contents | The real life time series are usually nonstationary, bringing a difficult question of model adaptation. Classical approaches like ARMA-ARCH assume arbitrary type of dependence. To avoid their bias, we will focus on recently proposed agnostic philosophy of moving estimator: in time $t$ finding parameters optimizing e.g. $F_t=\sum_{τ<t} (1-η)^{t-τ} \ln(ρ_θ(x_τ))$ moving log-likelihood, evolving in time. It allows for example to estimate parameters using inexpensive exponential moving averages (EMA), like absolute central moments $m_p=E[|x-μ|^p]$ evolving for one or multiple powers $p\in\mathbb{R}^+$ using $m_{p,t+1} = m_{p,t} + η(|x_t-μ_t|^p-m_{p,t})$. Application of such general adaptive methods of moments will be presented on Student's t-distribution, popular especially in economical applications, here applied to log-returns of DJIA companies. While standard ARMA-ARCH approaches provide evolution of $μ$ and $σ$, here we also get evolution of $ν$ describing $ρ(x)\sim |x|^{-ν-1}$ tail shape, probability of extreme events - which might turn out catastrophic, destabilizing the market. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_03069 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Adaptive Student's t-distribution with method of moments moving estimator for nonstationary time series Duda, Jarek Methodology Machine Learning Econometrics The real life time series are usually nonstationary, bringing a difficult question of model adaptation. Classical approaches like ARMA-ARCH assume arbitrary type of dependence. To avoid their bias, we will focus on recently proposed agnostic philosophy of moving estimator: in time $t$ finding parameters optimizing e.g. $F_t=\sum_{τ<t} (1-η)^{t-τ} \ln(ρ_θ(x_τ))$ moving log-likelihood, evolving in time. It allows for example to estimate parameters using inexpensive exponential moving averages (EMA), like absolute central moments $m_p=E[|x-μ|^p]$ evolving for one or multiple powers $p\in\mathbb{R}^+$ using $m_{p,t+1} = m_{p,t} + η(|x_t-μ_t|^p-m_{p,t})$. Application of such general adaptive methods of moments will be presented on Student's t-distribution, popular especially in economical applications, here applied to log-returns of DJIA companies. While standard ARMA-ARCH approaches provide evolution of $μ$ and $σ$, here we also get evolution of $ν$ describing $ρ(x)\sim |x|^{-ν-1}$ tail shape, probability of extreme events - which might turn out catastrophic, destabilizing the market. |
| title | Adaptive Student's t-distribution with method of moments moving estimator for nonstationary time series |
| topic | Methodology Machine Learning Econometrics |
| url | https://arxiv.org/abs/2304.03069 |