An extension of the iterated moving average

Area of Science:

• Data analysis
• Signal processing
• Time series analysis

Background:

• The Kolmogorov-Zurbenko (KZ) filter, an iterated simple moving average (SMA) filter, is valuable for time series and spatio-temporal analysis.
• Its application is limited by constraints on window length (positive odd integers), restricting its use in various data analysis tasks.
• This limitation hinders applications like time series component separation, signal reconstruction, and forecasting.

Purpose of the Study:

• To introduce the Extended Kolmogorov-Zurbenko (EKZ) filter, an advancement over the traditional KZ filter.
• To overcome the limitations of fixed window length selection in KZ filters.
• To provide enhanced control over filter characteristics for broader practical applications.

Main Methods:

• The Extended Kolmogorov-Zurbenko (EKZ) filter is developed by extending the argument selection for the filter window length.
• This extension allows for a wider range of filter parameters compared to the standard KZ filter.
• Simulations and real-world data examples are used to demonstrate the filter's efficacy.

Main Results:

• The EKZ filter permits an infinite number of filter choices, significantly expanding upon the discrete options of the KZ filter.
• This enhanced flexibility allows for finer tuning of filter properties, including the energy transfer function and cut-off frequency.
• The EKZ filter demonstrates improved practical applicability in diverse data analysis scenarios.

Conclusions:

• The Extended Kolmogorov-Zurbenko (EKZ) filter offers a more flexible and powerful approach to time series and spatio-temporal data analysis.
• Its extended window length selection enhances control over filter characteristics, facilitating a wider range of applications.
• The EKZ filter represents a significant improvement for data filtration, modeling, and forecasting tasks.