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No Time to Lose: Time Series Analysis
Published in Jesús Rogel-Salazar, Advanced Data Science and Analytics with Python, 2020
We can also consider giving greater importance to more recent past values than older ones. It sounds plausible, right? Well, this is actually what exponential smoothingenables us to do. The weighting is performed via constant values called smoothing constants. The simplest method is appropriately called simple exponential smoothing (SES) and it uses one smoothing constant, α. Exponential smoothing works by weighting past observations.
Forecasting
Published in José Manuel Torres Farinha, Asset Maintenance Engineering Methodologies, 2018
The exponential smoothing method uses an estimate of historical (past) values to make a forecast for the current period. As a consequence, the calculation of the next period value requires only the actual value for the current period and the corresponding forecast value for this period. Additionally, it is necessary to apply a smoothing parameter α that corresponds to the weight history that should be given in the calculation of the value for the next period. The value of this parameter is located in the interval between 0 and 1: α∈[0,1].
Forecasting in the air transport industry
Published in Bijan Vasigh, Ken Fleming, Thomas Tacker, Introduction to Air Transport Economics, 2018
Bijan Vasigh, Ken Fleming, Thomas Tacker
A third smoothing technique that can be used to forecast time-series data is exponential smoothing. Unlike a moving average which uses multiple historical values to help forecast, exponential smoothing only uses data from the previous period. Exponential smoothing indirectly takes into consideration previous periods by using the previous period’s forecast value to determine the forecasted value. This creates a situation where the weighting for a value gets exponentially smaller as time moves on. The general formula for exponential smoothing is:
Performance of recycled concrete aggregate pavements based on historical condition data
Published in International Journal of Pavement Engineering, 2020
Farhad Reza, W. J. Wilde, B. I. Izevbekhai
The basic idea of exponential smoothing is that in determining the moving average, past observations are assigned an exponentially decreasing weight based on their age. In triple exponential smoothing, in addition to the smoothing, two other factors related to trend and seasonality (or periodicity) are included. The approach can be summarised by the following equations:where: x is the observation, s is the smoothed observation, b is the trend factor, c is the seasonal index, F is the forecast at m periods ahead, t is an index denoting a time period, L is the number of periods in a season and α, β, γ are constants (that typically range from 0.1 to 0.3) that must be estimated to minimise the mean squared errors.
Individual and combination approaches to forecasting hierarchical time series with correlated data: an empirical study
Published in Journal of Management Analytics, 2019
Hakeem-Ur Rehman, Guohua Wan, Azmat Ullah, Badiea Shaukat
Here, we are interested in generating forecasts at 1st, 2nd and 3rd level of the hierarchy. To generate the forecast at all levels of the hierarchy, firstly direct forecasts are generated for each series at Level 1, 2 and 3 using appropriate forecasting method. Exponential smoothing (Hyndman, Koehler, Snyder, & Grose, 2002) methods are used to forecast the individual time series as these methods are relatively simple but robust, and they perform quite well in forecasting competition against more sophisticated methods (Makridakis & Hibon, 2000). The ‘forecast’ package (Hyndman et al., 2015) of the statistical software R, 3.2.3, is used to implement these methods. We refer to these as ‘base’ forecasts; these base forecasts are then combined to produce the desired hierarchical forecasts in a manner that is consistent with the structure of the hierarchy.
iSDS: a self-configurable software-defined storage system for enterprise
Published in Enterprise Information Systems, 2018
Wen-Shyen Eric Chen, Chun-Fang Huang, Ming-Jen Huang
The short-term prediction is complementary to the long-term prediction. The long-term prediction requires larger data set for ANN to generate a confident model. Therefore, the generated prediction is not sensitive to recent changes of data. For example, when the enterprise organisation is reformed, the storage performance metrics of the VDI application may change dramatically due to people accessing the iSDS cluster from different physical locations, which may invalidate the previous model generated by ANN. In this situation, before the long-term prediction becomes stable for generating new predictions, short-term prediction is more suitable based on the short period of monitored performance records. In current implementation of DAS, the exponential smoothing algorithm is used. The exponential smoothing algorithm places decreasing weights over older data. Therefore, newer data are more significant than older data (Chatfield 1978). An example of short-term prediction generated by Holt–Winters algorithm is depicted in Figure 16.