Ionospheric Delay Investigation and Forecasting by N. A. Elmunim & M. Abdullah
Author:N. A. Elmunim & M. Abdullah
Language: eng
Format: epub
ISBN: 9789811650451
Publisher: Springer Singapore
5.1 HoltâWinter Method
The HoltâWinter method is a statistical short-term method that utilises mathematically recursive functions to forecast the behavioural trend of ionospheric delay [15]. It uses a time-series with a repeated trend and a seasonal pattern to forecast under the assumption that the future will follow a similar pattern. The exponential smoothing function method is used to minimise the data fluctuations of a time-series to offer a clear perspective of the time-series. Moreover, it can forecast the values of future data in a time-series by giving the best way to derive accurate readings. Three smoothing constants or weight constants, including level (α), trend (β), and seasonal (γ). These smooth constants are suitable for a certain period in updating the component t. The value of the constant in the basic equation is usually 0.2. However, this value can vary between 0 and 1. The HoltâWinter method, when modelled by using the identified parameters, can provide forecasts with increased accuracy [8].
The HoltâWinter forecasting process proceeds as follows: firstly, the data are modified seasonally. Then, forecasts are made for the seasonally controlled data via linear exponential smoothing. Lastly, the forecasts that are modified seasonally are âreseasonalisedâ to generate forecasts for the appropriate series. The first step in seasonal modification is the computation of a centred moving average by taking the average of 3 h of data. The ratio is then estimated to a moving average, i.e. the reference data divided by the moving average in each period. The computed seasonal index for each season is determined by estimating the average of all of the ratios for that season and averaging. Subsequently, the ratios are averaged separately for each hour of the day to obtain the non-normalised seasonal indices.
The HoltâWinter method involves two main models in accordance with the type of seasonality: the additive (A-HW) and multiplicative (M-HW) models. The A-HW model is unaffected by changes in data-series and thus works best when the seasonal pattern does not change over time. By contrast, the M-HW model is dependent on data size. For example, ionospheric delay is affected by several factors, such as solar activity. When these factors increase ionospheric delay, the seasonal component of the M-HW model also increases. The A-HW model is applied by using the following equations:
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