Practical Time-Series Analysis: Master Time Series Data Processing, Visualization, and Modeling using Python by unknow

Author:unknow
Language: eng
Format: azw3
Tags: COM062000 - COMPUTERS / Data Modeling and Design, COM051360 - COMPUTERS / Programming Languages / Python, COM018000 - COMPUTERS / Data Processing
Publisher: Packt Publishing
Published: 2017-09-28T04:00:00+00:00

Solving the previous equation will lead to the following variance:

Here, T is the length of the time series. For unit variance of series xT, the variance captured by the forecasted series will vary based on the smoothing parameter α as follows:

Figure 3.10: Variance captured by simple exponential smoothing with varying alpha

Second order exponential smoothing

If first order exponential smoothing does not perform well, then there is a trend in the time series data. The trend is commonly observed in many domains such as when marketing campaigns are run by e-commerce companies, the sales rise or any good annual performance by a company will have a bullish effect on its stock prices. The linear trend can occur due to linear trend between time and response:

xt = constant + ωt + εt

Here, ω is the coefficient that leads to trend. The second order exponential smoothing helps capture the trend in time series data by including another term to the first order exponential smoothing as follows:

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