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)

Introduction to time-series smoothing


Time series data is composed of signals and noise, where signals capture intrinsic dynamics of the process; however, noise represents the unmodeled component of a signal. The intrinsic dynamics of a time series signal can be as simple as the mean of the process or it can be a complex functional form within observations, as represented here:

xt = f(xi) + εt for i=1,2,3, ... t-1

Here, xt is observations and εt is white noise. The f(xi) denotes the functional form; an example of a constant as a functional form is as follows:

xt = μ + εt

Here, the constant value μ in the preceding equation acts as a drift parameter, as shown in the following figure:

Figure 3.1: Example of time series with drift parameter

As εt is white noise, this smoothing-based approach helps separate the intrinsic functional form from random noise by canceling it. The smoothing forecasting methods can be considered as filters that take inputs and separate the trend and noise components, as...