Book Image

Practical Time Series Analysis

By : Avishek Pal, PKS Prakash
Book Image

Practical Time Series Analysis

By: Avishek Pal, PKS Prakash

Overview of this book

Time Series Analysis allows us to analyze data which is generated over a period of time and has sequential interdependencies between the observations. This book describes special mathematical tricks and techniques which are geared towards exploring the internal structures of time series data and generating powerful descriptive and predictive insights. Also, the book is full of real-life examples of time series and their analyses using cutting-edge solutions developed in Python. The book starts with descriptive analysis to create insightful visualizations of internal structures such as trend, seasonality, and autocorrelation. Next, the statistical methods of dealing with autocorrelation and non-stationary time series are described. This is followed by exponential smoothing to produce meaningful insights from noisy time series data. At this point, we shift focus towards predictive analysis and introduce autoregressive models such as ARMA and ARIMA for time series forecasting. Later, powerful deep learning methods are presented, to develop accurate forecasting models for complex time series, and under the availability of little domain knowledge. All the topics are illustrated with real-life problem scenarios and their solutions by best-practice implementations in Python. The book concludes with the Appendix, with a brief discussion of programming and solving data science problems using Python.
Table of Contents (13 chapters)

Time series decomposition


The objective of time series decomposition is to model the long-term trend and seasonality and estimate the overall time series as a combination of them. Two popular models for time series decomposition are:

  • Additive model
  • Multiplicative model

The additive model formulates the original time series (xt) as the sum of the trend cycle (Ft) and seasonal (St) components as follows:

xt = Ft + St + Єt

The residuals Єt obtained after adjusting the trend and seasonal components are the irregular variations. The additive model is usually applied when there is a time-dependent trend cycle component, but independent seasonality that does not change over time.

The multiplicative decomposition model, which gives the time series as product of the trend, seasonal, and irregular components is useful when there is time-varying seasonality:

xt = Ft x St x Єt

By taking logarithm, the multiplicative model is converted to an additive model of logarithm of the individual components. The multiplicative...