Nonparametric and Non-Linear Models and Data Mining in time Series: A Case-Study on the Canadian Lynx Data

Abstract

Nonparametric regression methods are used as exploratory tools for formulating, identifying and estimating non-linear models for the Canadian lynx data, which have attained benchmark status in the time series literature since the work of Moran in 1953. To avoid the curse of dimensionality in the nonparametric analysis of this short series with 114 observations, we con®ne attention to the restricted class of additive and projection pursuit regression (PPR) models and rely on the estimated prediction error variance to compare the predictive performance of various (non-) linear models. A PPR model is found to have the smallest (in-sample) estimated prediction error variance of all the models ®tted to these data in the literature. We use a data perturbation procedure to assess and adjust for the effect of data mining on the estimated prediction error variances; this renders most models ®tted to the lynx data comparable and nearly equivalent. However, on the basis of the mean-squared error of out-of-sample prediction error, the semiparametric model X t 1X08 1X37X tÀ1 f (X tÀ2 ) e t and Tong's self-exciting threshold autoregressive model perform much better than the PPR and other models known for the lynx data.

An artificial neural network (p,d,q) model for timeseries forecasting

“…The data set has 114 observations, corresponding to the period of 1821-1934. It has also been extensively analyzed in the time series literature with a focus on the nonlinear modeling (Campbell & Walker, 1977;Cornillon, Imam, & Matzner, 2008;Lin & Pourahmadi, 1998;Tang & Ghosal, 2007) see Wong and Li (2000) for a survey. Following other studies (Subba Rao & Sabr, 1984;Stone & He, 2007;Zhang, 2003), the logarithms (to the base 10) of the data are used in the analysis.…”

An orthogonal projection and regularization technique for magnetospheric radio tomography

“…The snapshots whose projections are too far from the true measurements are inconsistent with the data and should not be used. This is similar to the cross validation widely used in statistical model selection literature [ Lin and Pourahadi , 1998]. The main difference is that magnetospheric tomographic imaging is an ill‐conditioned inverse problem with few path‐integrated measurements, while the statistical model selection is a well‐conditioned but overdetermined problem.…”

Combining domain knowledge and statistical models in time series analysis

“…Based on the average of these 12 absolute prediction errors (AAPE), FAR(2,2) performs slightly better than SETAR (2). Other nonparametric time series models for the Canadian lynx data include the projection pursuit regression (PPR) model fitted by Lin and Pourahmadi [36] who found that SETAR outperforms PPR in terms of one-step-ahead forecasts, and neural network models which Kajitani, Hipel and McLeod [25] found to be "just as good or better than SETAR models for one-step out-of-sample forecasting of the lynx data. "…”