2020/03/04 by Jarek Duda, Duda, Jarek · 2 citations
Computer Science · Economics, Econometrics and Finance · Engineering · Mathematics · #FOS: Computer and information sciences #FOS: Economics and business #Fault Detection and Control Systems #Financial Risk and Volatility Modeling #Machine Learning (stat.ML) #Statistical Finance (q-fin.ST) #Time Series Analysis and Forecasting #q-fin.ST #stat.ML
paper · pdf · doi:10.48550/arxiv.2003.02149
6 pages, 4 figures
openalex publication_date 2020/03/04 · arxiv created 2020/03/23 · arxiv updated 2020/03/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
While standard estimation assumes that all datapoints are from probability distribution of the same fixed parameters θ, we will focus on maximum likelihood (ML) adaptive estimation for nonstationary time series: separately estimating parameters θT for each time T based on the earlier values (xt)t<T using (exponential) moving ML estimator θT=argmaxθlT for lT=∑t<T ηT-t ln(ρθ(xt)) and some η∈(0,1]. Computational cost of such moving estimator is generally much higher as we need to optimize log-likelihood multiple times, however, in many cases it can be made inexpensive thanks to dependencies. We focus on such example: ρ(x)∝ exp(-|(x-μ)/σ|κ/κ) exponential power distribution (EPD) family, which covers wide range of tail behavior like Gaussian (κ=2) or Laplace (κ=1) distribution. It is also convenient for such adaptive estimation of scale parameter σ as its standard ML estimation is σκ being average ‖x-μ‖κ. By just replacing average with exponential moving average: (σT+1)κ=η(σT)κ+(1-η)|xT-μ|κ we can inexpensively make it adaptive. It is tested on daily log-return series for DJIA companies, leading to essentially better log-likelihoods than standard (static) estimation, with optimal κ tails types varying between companies. Presented general alternative estimation philosophy provides tools which might be useful for building better models for analysis of nonstationary time-series.