Department of Statistics - Scholarly Publications
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Item SMOOTHING SPLINE TECHNIQUE FOR TIME SERIES DATA WITH AUTOCORRELATION(Lambert Academic Publishing, 2023-03-10) Adams, Samuel OlorunfemiSpline 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 econometricsItem The Efficiency of the Proposed Smoothing Method over the Classical Cubic Smoothing Spline Regression Model with Autocorrelated Residual(Science Publications, 2023-03-18) Adams, Samuel OlorunfemiSpline 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 the smoothing parameter. Most of the existing smoothing methods applied to time series data tend to over fit in the presence of autocorrelated errors. This study aims to determine the optimum performance value, goodness of fit and model overfitting properties of the proposed Smoothing Method (PSM), Generalized Maximum Likelihood (GML), Generalized Cross-Validation (GCV), and Unbiased Risk (UBR) smoothing parameter selection methods. A Monte Carlo experiment of 1,000 trials was carried out at three different sample sizes (20, 60, and 100) and three levels of autocorrelation (0.2, 05, and 0.8). The four smoothing methods' performances were estimated and compared using the Predictive Mean Squared Error (PMSE) criterion. The findings of the study revealed that: for a time series observation with autocorrelated errors, provides the best-fit smoothing method for the model, the PSM does not over-fit data at all the autocorrelation levels considered ( the optimum value of the PSM was at the weighted value of 0.04 when there is autocorrelation in the error term, PSM performed better than the GCV, GML, and UBR smoothing methods were considered at all-time series sizes (T = 20, 60 and 100). For the real-life data employed in the study, PSM proved to be the most efficient among the GCV, GML, PSM, and UBR smoothing methods compared. The study concluded that the PSM method provides the best fit as a smoothing method, works well at autocorrelation levels (ρ=0.2, 0.5, and 0.8), and does not over fit time-series observations. The study recommended that the proposed smoothing is appropriate for time series observations with autocorrelation 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 observations.Item Modeling and Forecasting Cryptocurrency Returns and Volatility: An Application of GARCH Models(Scientific Publications, 2022-11-10) Adams, Samuel OlorunfemiThe future of e-money is crypocurrencies, it is the decentralize digital and virtual currency that is secured by cryptography. It has become increasingly popular in recent years attracting the attention of the individual, investor, media, academia and governments worldwide. This study aims to model and forecast the volatilities and returns of three top cryptocurrencies, namely; Bitcoin, Ethereum and Binance Coin. The data utilized in the study was extracted from the higher market capitalization at 31st December, 2021 and the data for the period starting from 9th November, 2017 to 31st December 2021. The Generalised Autoregressive conditional heteroscedasticity (GARCH) type models with several distributions were fitted to the three cryptocurrencies dataset with their performances assessed using some model criterion tests. The result shows that the mean of all the returns are positive indicating the fact that the price of this three crptocurrencies increase throughout the period of study. The ARCH-LM test shows that there is no ARCH effect in volatility of Bitcoin and Ethereum but present in Binance Coin. The GARCH model was fitted on Binance Coin, the AIC and log L shows that the CGARCH is the best model for Binance Coin. Automatic forecasting was perform based on the selected ARIMA (2,0,1), ARIMA (0,1,2) and the random walk model which has the lowest AIC for ETH-USD, BNB-USD and BTC-USD respectively. This finding could aid investors in determining a cryptocurrency's unique risk-reward characteristics. The study contributes to a better deployment of investor’s resources and prediction of the future prices the three cryptocurrencies.Item The Efficiency of the Proposed Smoothing Method over the Classical Cubic Smoothing Spline Regression Model with Autocorrelated Residual(Science Publications, 2023-11-21) Adams, Samuel OlorunfemiAbstract: 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 the smoothing parameter. Most of the existing smoothing methods applied to time series data tend to overfit in the presence of autocorrelated errors. This study aims to determine the optimum performance value, goodness of fit and model overfitting properties of the proposed Smoothing Method (PSM), Generalized Maximum Likelihood (GML), Generalized Cross-Validation (GCV), and Unbiased Risk (UBR) smoothing parameter selection methods. A Monte Carlo experiment of 1,000 trials was carried out at three different sample sizes (20, 60, and 100) and three levels of autocorrelation (0.2, 05, and 0.8). The four smoothing methods' performances were estimated and compared using the Predictive Mean Squared Error (PMSE) criterion. The findings of the study revealed that: for a time series observation with autocorrelated errors, Adj. R2(PSM λ =0.04) provides the best-fit smoothing method for the model, the PSM does not over-fit data at all the autocorrelation levels considered (ρ = 0.2, 0.5 and 0.8); the optimum value of the PSM was at the weighted value of 0.04 when there is autocorrelation in the error term, PSM performed better than the GCV, GML, and UBR smoothing methods were considered at all-time series sizes (T = 20, 60 and 100). For the real-life data employed in the study, PSM proved to be the most efficient among the GCV, GML, PSM, and UBR smoothing methods compared. The study concluded that the PSM method provides the best fit as a smoothing method, works well at autocorrelation levels (ρ=0.2, 0.5, and 0.8), and does not over fit time-series observations. The study recommended that the proposed smoothing is appropriate for time series observations with autocorrelation 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 observations