Unit root problems in time series analysis

Purutcuoğlu, Vilda
In time series models, autoregressive processes are one of the most popular stochastic processes, which are stationary under certain conditions. In this study we consider nonstationary autoregressive models of order one, which have iid random errors. One of the important nonstationary time series models is the unit root process in AR (1), which simply implies that a shock to the system has permanent effect through time. Therefore, testing unit root is a very important problem. However, under nonstationarity, any estimator of the autoregressive coefficient does not have a known exact distribution and the usual t 6 statistic is not accurate even if the sample size is very large. Hence,Wiener process is invoked to obtain the asymptotic distribution of the LSE under normality. The first four moments of under normality have been worked out for large n. In 1998, Tiku and Wong proposed the new test statistics and whose type I error and power values are calculated by using three 6 moment chi 6 square or four 6 moment F approximations. The test statistics are based on the modified maximum likelihood estimators and the least square estimators, respectively. They evaluated the type I errors and the power of these tests for a family of symmetric distributions (scaled Student2s t). In this thesis, we have extended this work to skewed distributions, namely, gamma and generalized logistic.


Time series AR(1) model for short-tailed distributions
Akkaya, AD; Tiku, ML (Informa UK Limited, 2005-04-01)
The innovations in AR(1) models in time series have primarily been assumed to have a normal or long-tailed distributions. We consider short-tailed distributions (kurtosis less than 3) and derive modified maximum likelihood (MML) estimators. We show that the MML estimator of 0 is considerably more efficient than the commonly used least squares estimator and is also robust. This paper is essentially the first to achieve robustness to inliers and to various forms of short-tailedness in time series analysis.
Topological constraints on HMO heteroatom parameters
Türker, Burhan Lemi (1997-01-01)
Within the Huckel molecular orbital framework, the effect of topological factors on the selection of heteroatom parameters for heteroconjugated systems is discussed.
Pairwise multiple comparisons under short-tailed symmetric distribution
Balcı, Sibel; Akkaya, Ayşen; Department of Statistics (2007)
In this thesis, pairwise multiple comparisons and multiple comparisons with a control are studied when the observations have short-tailed symmetric distributions. Under non-normality, the testing procedure is given and Huber estimators, trimmed mean with winsorized standard deviation, modified maximum likelihood estimators and ordinary sample mean and sample variance used in this procedure are reviewed. Finally, robustness properties of the stated estimators are compared with each other and it is shown that...
Multiple linear regression model with stochastic design variables
İslam, Muhammed Qamarul (Informa UK Limited, 2010-01-01)
In a simple multiple linear regression model, the design variables have traditionally been assumed to be non-stochastic. In numerous real-life situations, however, they are stochastic and non-normal. Estimators of parameters applicable to such situations are developed. It is shown that these estimators are efficient and robust. A real-life example is given.
Representation of Multiplicative Seasonal Vector Autoregressive Moving Average Models
Yozgatlıgil, Ceylan (Informa UK Limited, 2009-11-01)
Time series often contain observations of several variables and multivariate time series models are used to represent the relationship between these variables. There are many studies on vector autoregressive moving average (VARMA) models, but the representation of multiplicative seasonal VARMA models has not been seriously studied. In a multiplicative vector model, such as a seasonal VARMA model, the representation is not unique because of the noncommutative property of matrix multiplication. In this articl...
Citation Formats
V. Purutcuoğlu, “Unit root problems in time series analysis,” M.S. - Master of Science, Middle East Technical University, 2004.