SMOOTHING SPLINE TECHNIQUE FOR TIME SERIES DATA WITH AUTOCORRELATION
Loading...
Date
2023-03-10
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
Lambert Academic Publishing
Abstract
Spline smoothing is a technique used to filter out noise in time series observations when predicting nonparametric regression models. Its performance depends on the choice of smoothing parameter lambda. Most of the existing smoothing methods applied to time series data tend to overfit in the presence of autocorrelated errors. The aim of this study is to propose a smoothing method which is the arithmetic weighted value of Generalized Cross-Validation (GCV) and Unbiased Risk (UBR) methods The objectives of the study were to (i) determine the best-fit smoothing method for the time series observation; (ii) identify the best smoothing method that does not overfit timeseries data when autocorrelation is present in the error term;
(iii)establish the optimum value of the proposed smoothing method; (iv) compare GCV, GML and UBR smoothing methods to the proposed smoothing methods in terms of sample size; and (v)test the results of simulation using real life-data. A hybrid smoothing method of the Generalized Cross-Validation (GCV) and Unbiased Risk (UBR) was developed by adding the weighted values of Generalized CrossValidation (GCV) and Unbiased Risk (UBR). The Proposed Smoothing Method (PSM) was compared with Generalized Maximum Likelihood (GML), GCV and UBR smoothing methods. A Monte Carlo experiment of 1,000 trials was carried out at three different sample sizes (20, 60 and 100), three levels of the autocorrelation (02, 05 and 08), and four degrees of smoothing (1, 2, 3 and 4) Real-life data on Standard international Trade Classification (SITC) export and import price indices in Nigeria between 1970 2018 extracted from CBN 2019 edition were also used. The four smoothing methods' performances were estimated and compared using the Predictive Mean Squared Error (PMSE) criterion. The findings of the study revealed that:(i)for a time series observation with autocorrelated errors, Ǥ ሺ ൌͲͲሻ ൌ ͳ ሺ ሻൈሺ ሻ ൌͲͻͳǡ provides the besfit smoothing method for the model: (ii)he PM does not over-fit data at all the autocorrelation levels considered (ͲǤʹ Ǥͷ ǤͺሻǢ (iii) t optium value of the PSM was at the weighted value of 0.04, with the eqtion is given as ሺ ሻ ൌ ሺͲͲͶሻ ! ሾ$ ሺ &' ሻሿ( ሺͲͻሻ *+") (% &' (,) * ሼ% &' ሻሽ- (; (i wh thee is autocorrelation in the error term, PSM performed better than the GCVGML and UBR smoothing methods were considered at all-time series sizes (T =20, 60 d 100); (v) for the real-life data employed in the study, PSM proved to be the most efficit among the GCV, GML, PSM and UBR smoothing methods compare. The study concluded that the PSM method provides the best-fit as a smoothing method, works well atutocorrelation levels (=0.2, 0.5 and 0.8), and does not overfit time-series observations. The study recommended that the proposed smoothing is appropriate for time series observations with autorrelation in the error term and econometrics real-life data. This study can be applied to; non parametric regression, non – parametric forecasting, spatial, survival and econometrics
Description
PhD Statistics