Portfolio selection in non-stationary markets

2021 ◽  
pp. 1-13
Author(s):  
Eyal Kenig
Keyword(s):  
Stochastic Process ◽  
Portfolio Selection ◽  
Time Series Prediction ◽  
Stationary Stochastic Process ◽  
Learning Approach ◽  
Generalization Error ◽  
Time Step ◽  
Large Numbers ◽  
Stationary Markets ◽  
Short Time

We consider the task of portfolio selection as a time series prediction problem. At each time-step we obtain prices of a universe of assets and are required to allocate our wealth across them with the goal of maximizing it, based on the historic price returns. We assume these returns are realizations of a general non-stationary stochastic process, and only assume they do not change significantly over short time scales. We follow a statistical learning approach, in which we bound the generalization error of a non-stationary stochastic process, using analogues of uniform laws of large numbers for non-i.i.d. random variables. We use the learning bounds to formulate an optimization algorithm for portfolio selection, and present favorable numerical results with financial data.

scholarly journals Time series analysis of trial-to-trial variability of MEG power spectrum during rest state, unattented listening and frequency-modulated tones classification

2021 ◽  
Author(s):  
Lech Kipiński ◽  
Wojciech Kordecki
Keyword(s):  
Stochastic Process ◽  
Time Series ◽  
Power Spectrum ◽  
Spectral Density ◽  
Cognitive Task ◽  
Clinical Neuroscience ◽  
Rest State ◽  
Short Time ◽  
Low Complex ◽  
Dominant Frequencies

AbstractThe nonstationarity of EEG/MEG signals is important for understanding the functioning of human brain. From the previous research we know that even very short, i.e. 250—500ms MEG signals are variance-nonstationary. The covariance of stochastic process is mathematically associated with its spectral density, therefore we investigate how the spectrum of such nonstationary signals varies in time.We analyze the data from 148-channel MEG, that represent rest state, unattented listening and frequency-modulated tones classification. We transform short-time MEG signals to the frequency domain using the FFT algorithm and for the dominant frequencies 8—12 Hz we prepare the time series representing their trial-to-trial variability. Then, we test them for level- and trend-stationarity, unit root, heteroscedasticity and gaussianity and based on their properties we propose the ARMA-modelling for their description.The analyzed time series have the weakly stationary properties independently of the functional state of brain and localization. Only their small percentage, mostly related to the cognitive task, still presents nonstationarity. The obtained mathematical models show that the spectral density of analyzed signals depends on only 2—3 previous trials.The presented method has limitations related to FFT resolution and univariate models, but it is not computationally complicated and allows to obtain a low-complex stochastic models of the EEG/MEG spectrum variability.Although the physiological short-time MEG signals are in principle nonstationary in time domain, its power spectrum at the dominant frequencies varies as weakly stationary stochastic process. Described technique has the possible applications in prediction of the EEG/MEG spectral properties in theoretical and clinical neuroscience.

scholarly journals Vector Autoregressive Weighting Reversion Strategy for Online Portfolio Selection

2020 ◽  
Author(s):  
Xia Cai
Keyword(s):  
Portfolio Selection ◽  
Moving Average ◽  
Time Series Prediction ◽  
Vector Autoregressive ◽  
Practical Applications ◽  
Public Datasets ◽  
Dynamic Relationships ◽  
Online Portfolio ◽  
Online Portfolio Selection ◽  
Sharp Ratio

Aiming to improve the performance of existing reversion based online portfolio selection strategies, we propose a novel multi-period strategy named “Vector Autoregressive Weighting Reversion” (VAWR). Firstly, vector autoregressive moving-average algorithm used in time series prediction is transformed into exploring the dynamic relationships between different assets for more accurate price prediction. Secondly, we design the modified online passive aggressive technique and advance a scheme to weigh investment risk and cumulative experience to update the closed-form of portfolio. Theoretical analysis and experimental results confirm the effectiveness and robustness of our strategy. Compared with the state-of-the-art strategies, VAWR greatly increases cumulative wealth, and it obtains the highest annualized percentage yield and sharp ratio on various public datasets. These improvements and easy implementation support the practical applications of VAWR.

A deep learning approach for hydrological time-series prediction: A case study of Gilgit river basin

2020 ◽  
Vol 13 (3) ◽  
pp. 915-927 ◽  
Author(s):  
Dostdar Hussain ◽  
Tahir Hussain ◽  
Aftab Ahmed Khan ◽  
Syed Ali Asad Naqvi ◽  
Akhtar Jamil
Keyword(s):  
Time Series ◽  
Deep Learning ◽  
River Basin ◽  
Time Series Prediction ◽  
Learning Approach
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