scholarly journals A persistence‐based Wold‐type decomposition for stationary time series

10.3982/qe994 ◽  
2020 ◽  
Vol 11 (1) ◽  
pp. 203-230 ◽  
Author(s):  
Fulvio Ortu ◽  
Federico Severino ◽  
Andrea Tamoni ◽  
Claudio Tebaldi
Keyword(s):  
Time Series ◽  
Stationary Process ◽  
Financial Time Series ◽  
Variance Decomposition ◽  
Stationary Time Series ◽  
Wold Decomposition ◽  
Process Innovations ◽  
Financial Time ◽  
Stationary Time ◽  
Type Decomposition

This paper shows how to decompose weakly stationary time series into the sum, across time scales, of uncorrelated components associated with different degrees of persistence. In particular, we provide an Extended Wold Decomposition based on an isometric scaling operator that makes averages of process innovations. Thanks to the uncorrelatedness of components, our representation of a time series naturally induces a persistence‐based variance decomposition of any weakly stationary process. We provide two applications to show how the tools developed in this paper can shed new light on the determinants of the variability of economic and financial time series.

A note on the asymptotic eigenvalues and eigenvectors of the dispersion matrix of a second-order Stationary Process on a d-dimensional Lattice

1986 ◽  
Vol 23 (02) ◽  
pp. 529-535 ◽  
Author(s):  
R. J. Martin
Keyword(s):  
Time Series ◽  
Stationary Process ◽  
Second Order ◽  
Stationary Time Series ◽  
Stationary Processes ◽  
Dispersion Matrix ◽  
Eigenvalues And Eigenvectors ◽  
Dimensional Lattice ◽  
Stationary Time

A sufficiently large finite second-order stationary time series process on a line has approximately the same eigenvalues and eigenvectors of its dispersion matrix as its counterpart on a circle. It is shown here that this result can be extended to second-order stationary processes on a d-dimensional lattice.

A note on the asymptotic eigenvalues and eigenvectors of the dispersion matrix of a second-order Stationary Process on a d-dimensional Lattice

1986 ◽  
Vol 23 (2) ◽  
pp. 529-535 ◽  
Author(s):  
R. J. Martin
Keyword(s):  
Time Series ◽  
Stationary Process ◽  
Second Order ◽  
Stationary Time Series ◽  
Stationary Processes ◽  
Dispersion Matrix ◽  
Eigenvalues And Eigenvectors ◽  
Dimensional Lattice ◽  
Stationary Time

A sufficiently large finite second-order stationary time series process on a line has approximately the same eigenvalues and eigenvectors of its dispersion matrix as its counterpart on a circle. It is shown here that this result can be extended to second-order stationary processes on a d-dimensional lattice.

BOOTSTRAP INFERENCE FOR MULTIPLE CHANGE-POINTS IN TIME SERIES

2021 ◽  
pp. 1-41
Author(s):  
Wai Leong Ng ◽  
Shenyi Pan ◽  
Chun Yip Yau
Keyword(s):  
Time Series ◽  
Change Point ◽  
Financial Time Series ◽  
Change Point Detection ◽  
Stationary Time Series ◽  
Change Points ◽  
Finite Sample ◽  
Sample Distribution ◽  
Stationary Time ◽  
Point Estimators

In this paper, we propose two bootstrap procedures, namely parametric and block bootstrap, to approximate the finite sample distribution of change-point estimators for piecewise stationary time series. The bootstrap procedures are then used to develop a generalized likelihood ratio scan method (GLRSM) for multiple change-point inference in piecewise stationary time series, which estimates the number and locations of change-points and provides a confidence interval for each change-point. The computational complexity of using GLRSM for multiple change-point detection is as low as $O(n(\log n)^{3})$ for a series of length n. Extensive simulation studies are provided to demonstrate the effectiveness of the proposed methodology under different scenarios. Applications to financial time series are also illustrated.

scholarly journals Sarima-arch versus genetic programming in stock price prediction

2021 ◽  
pp. 110-122
Author(s):  
Gulder KEMALBAY
Keyword(s):  
Time Series ◽  
Stock Price ◽  
Time Series Data ◽  
Financial Time Series ◽  
Stationary Time Series ◽  
Series Data ◽  
Arch Model ◽  
Sarima Model ◽  
Financial Time ◽  
Price Series

In financial time series, one of the most challenging problems is predicting stock prices since the data generally exhibit deviation from the assumptions of stationary and homoscedasticity. For homogenous non-stationary time series, the Autoregressive Integrated Moving Average (ARIMA) model is the most commonly used linear class including some transformation such as differencing and variance stabilizing process. However, stock market data is often nonlinear, which indicates that more advanced methods are necessary. Genetic Programming (GP) is one of the evolutionary computational methods that could capture both linear and nonlinear patterns in time series data. The present study aims to build a machine learning tool using GP for prediction The Istanbul Stock Exchange National 100 (XU100) index and compare the obtained results with conventional seasonal ARIMA(SARIMA) and ARCH models. In order to achieve this goal, it was first modeled with the SARIMA model after appropriate transfor- mations were made to the stock price series and the diagnostic control result showed that the residual of the SARIMA model have the heteroscedasticity problem. Then, the ARCH model was applied to SARIMA residuals to eliminate this effect and an integrated SARIMA-ARCH model is obtained. Since it is possible and capable to model nonlinear and non-stationary time series using GP without any pre-assumptions, we proposed GP to predict the stock price series. The function set of GP consists of not only arithmetic but also trigonometric functions. To the best of our knowledge, this study is the first to predict XU100 stock price data using GP. In this experiment, the data set consists of the daily closing prices of the XU100 index over 775 days from the beginning of 2017 until the end of January 2020. The experimental results obtained show that the accuracy metrics used in the study are lower in the proposed GP model compared to other models. These results reveal that the GP method provides better predictive results for the financial time series data of the XU100 index than traditional methods.

scholarly journals HURST EXPONENTS AND DELAMPERTIZED FRACTIONAL BROWNIAN MOTIONS

2019 ◽  
Vol 22 (05) ◽  
pp. 1950024
Author(s):  
MATTHIEU GARCIN
Keyword(s):  
Time Series ◽  
High Frequency ◽  
Hurst Exponent ◽  
Stationary Process ◽  
Financial Time Series ◽  
Mean Reversion ◽  
Foreign Exchange Rates ◽  
Medium Term ◽  
Fractional Brownian Motions ◽  
Financial Time

The inverse Lamperti transform of a fractional Brownian motion (fBm) is a stationary process. We determine the empirical Hurst exponent of such a composite process with the help of a regression of the log absolute moments of its increments, at various scales, on the corresponding log scales. This perceived Hurst exponent underestimates the Hurst exponent of the underlying fBm. We thus encounter some time series having a perceived Hurst exponent lower than [Formula: see text], but an underlying Hurst exponent higher than [Formula: see text]. This paves the way for short- and medium-term forecasting. Indeed, in such series, mean reversion predominates at high scales, whereas persistence is overriding at lower scales. We propose a way to characterize the Hurst horizon, namely a limit scale between these opposite behaviors. We show that the delampertized fBm, which mixes persistence and mean reversion, is relevant for financial time series, in particular for high-frequency foreign exchange rates. In our sample, the empirical Hurst horizon is always above 1[Formula: see text]h and 23[Formula: see text]min.

Sign in / Sign up

Export Citation Format

Share Document