Assessing Stationarity in Univariate Time Series with Applications in Physics and Finance

Assessing Stationarity in Univariate Time Series with Applications in Physics and Finance

Ooms, J.C.

Den Dekker, A.J. (mentor)
Tejada, A. (mentor)
Bombois, X.J.A. (mentor)

Applied Sciences

Delft Center for Systems and Control

Bachelor of Science Applied Physics

2012-11-30

This thesis investigates methods to assess stationarity in a given time series. It is assumed that such a time series is generated by one of the autoregressive and moving average models, with optional deterministic and/or stochastic trends. The problem subjected here, will be to characterize if this stochastic process is stationary or non-stationary. To answer this, different known hypothesis tests under various assumptions are introduced. In particular, the Dickey-Fuller and Phillips-Perron tests, that test for a unit root under the null hypothesis, are compared in performance by experiments using simulated data. From the results of these experiments, it will be shown that the augmented Dickey-Fuller test with specified parameter k12 for the lag length performs best. Following this conclusion, an automated testing procedure is developed where this unit root test is applied complementary to the KPSS stationarity test. Next, this procedure is applied to different physical and financial data to show that most realizations are I(1) level-stationary. That is, the data will become stationary around a non zero mean when the unit root is removed by differencing once.

time series analysis
ARMA model
unit root
stationarity
hypothesis testing
Dickey-Fuller
KPSS

http://resolver.tudelft.nl/uuid:90850971-73e5-444a-8384-bf99d2d5e8fb

Student theses

bachelor thesis

(c) 2012 Ooms, J.C.