Nonparametric estimation in a nonlinear cointegration type model

By H. A. Karlsen, Terje Myklebust, Dag Tjøstheim. 2007

169 citations recorded by the source corpus.

We derive an asymptotic theory of nonparametric estimation for an nonlinear transfer function model Z(t) = f (Xt) + Wt where {Xt} and {Zt} are observed nonstationary processes and {Wt} is a stationary process. IN econometrics this can be interpreted as a nonlinear cointegration type relationship, but we believe that our results have wider interest. The class of nonstationary processes allowed for {Xt} is a subclass of the class of null recurrent.. Markov chains. This subclass contains the random walk model and the unit root processes. WE derive the asymptotics of an nonparametric estimate of f(z) under two alternative sets of assumptions on {Wt}: i) {Wt} is a linear process ii) {Wt} is a Markov chain satisfying some mixing conditions. The latter requires considerably more work but also holds larger promise for further developments. The finite sample properties f(x) are studied via a set of simulation experiments.

Subfields: Artificial Intelligence, Finance, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/9628f05ddbe3a8bcdc4c81484880f3c2f9bed94c

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

1. Qi Li
2. Jiti Gao
3. Clark Glymour
4. Tianjiao Chu
5. Joon Y. Park
6. Zongwu Cai
7. Chaohua Dong
8. Dag Tjøstheim

In Finance

1. Jiti Gao
2. Qi Li
3. Dag Tjøstheim
4. Chaohua Dong
5. Degui Li
6. Joon Y. Park
7. Tianjiao Chu
8. Clark Glymour

In Statistics and Probability

1. Qi Li
2. Jiti Gao
3. Joon Y. Park
4. Degui Li
5. Chaohua Dong
6. Dag Tjøstheim
7. Tianjiao Chu
8. Clark Glymour

Citations in the corpus

• Search for Additive Nonlinear Time Series Causal Models (2008, methodology): “However, recent studies on applying nonparametric regression methods to nonstationary time series data (Phillips and Park, 1998; Karlsen and Tjøstheim, 2001; Bandi and Phillips, 2003; Karlsen et al., 2005) seem promising.”
• Estimation for single-index and partially linear single-index integrated models (2016, methodology): “Meanwhile, (c), (d) and (e) are extensively used in related papers such as Park and Phillips (2000), Wang and Phillips (2009a, 2009b, 2012), Gao et al.”
• Functional-coefficient models for nonstationary time series data (2009, methodology): “(1.1) becomes a standard univariate nonparametric regressionmodel as considered by Wang and Phillips (forthcoming, 2008) and Karlsen et al. (2007).”
• Estimating Smooth Structural Change in Cointegration Models (2017, background): “Most recently, therefore, attention has been given to flexible nonparametric and semiparametric approaches that can cope with the unknown functional form of responses in a nonstationary time series setting (Karlsen et al , 2007; Wang and Phillips, 2009a, 2009b, 2015; Gao and Phillips, 2013a).”
• ASYMPTOTIC THEORY FOR LOCAL TIME DENSITY ESTIMATION AND NONPARAMETRIC COINTEGRATING REGRESSION (2009, unknown): “As an example of their theory, Karlsen et al. (2007) established (3.6) for an I (1) time series xt .”