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)

Modeling higher-order exponential smoothing


The concept can be further extended to higher-order exponential smoothing with an nth order polynomial model:

Here, error εt ∼ N(0,σ2) is normally distributed with 0 mean and σ2 variance. The exponential smoothers used for higher order are as follows:

...

Here, is weights for smoothers. Usually, higher-order exponential smoothing is not used in time as even for second order smoothing, the computation becomes very hard and approaches such as Autoregressive Integrated Moving Average (ARIMA) are utilized. It will be further discussed in Chapter 4, Auto Regressive Models.

Another very popular exponential smoothing is triple exponential smoothing. The triple exponential smoothing allows you to capture seasonality with level and trend. The relationship between levels, trends, and seasonality is defined using the following set of equations:

In these equations, Ft captures levels of observation at time t. Similarly, Tt and St captures trend and seasonality...