Efficiency of 4253HT smoothers in extracting signal from noise and their applications in forecasting

Compound smoother is a non-linear smoothing technique that has the ability to reduce heavy noise from signal and at the same time, is resistant to sudden changes and impulse in a data series. The compound smoother of 4253HT has been studied and modified in the algorithm, specifically to estimate the middle point of running median for even span size by applying the following types of means; geometric, harmonic, quadratic and contraharmonic. The stability of running median of even span with modification toward the positive and negative block pulse were discussed. The modified 4253HT using harmonic mean works best in preserving edge at sudden changes point from down to upward and negative block pulse. Modified 4253HT using contraharmonic mean on the other hand, has been found to preserve edge of upward point and positive block pulse. The combination of modified 4253HT using harmonic and contraharmonic means adaptively, produce a new smoother with more resistance to block pulse and better preservation of the edge. The performance of the modified compound smoothers was assessed via simulation. The signal of sinusoidal and special functions; Doppler, HeavySine, Bumps and Block was generated with non-Gaussian noise added that produced high volatility and disturbed by outliers. The performance were measured by regression coefficient, Estimated Integrated Mean Square Error (EIMSE) and variance reduction. The 4253HT has the ability to capture the signal from heavy noise data. In general, 4253HT performs best at smaller frequency and the recovery of signal from heavy noise at high frequency using 4253HT is fairly good. This is asserted by the smooth value which was close to the signal, indicating its capability to extract signal from highly fluctuating noise. The modified 4253HT using adaptive mean showed the most effective, compared to others, in extracting low, moderate and high frequency of sinusoidal signal from the noise with 10%, 25%, 50% and 75% contaminated normal distribution. The Doppler, Block, Bumps and Heavy Sine signal show the modified 4253HT using adaptive mean also managed to recover those signal from noise better than other modified 4253HT and the existing one. The extracted signal was then used for better forecasting which was facilitated by seasonal Holt-Winters, ARAR and seasonal ARIMA algorithm.

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