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)

Moving average models


The moving average models use dependency between residual errors to forecast values in the next time period. The model helps you adjust for any unpredictable events such as catastrophic events leading to a share market crash leading to share prices falling, which will happen over time and is captured as a moving average process.

The first-order moving average denoted by MA(1) is as follows:

xt = α - θ1Єt-1 + Єt

The second-order moving average denoted by MA(2) is as follows:

xt = α - θ1Єt-1 - θ2Єt-2+ Єt

The qth order moving average denoted by MA(q) is as follows:

xt = α - θ1Єt-1 - θ2Єt-2 - ... - θqЄt-q+ Єt

Here, Єt is the identically independently-distributed error at time t and follows normal distribution N(0,σ2Є) with zero mean and σ2Є variance. The Єt component represents error in time t and the α  and Є notations represent mean intercept and error coefficients, respectively. The moving average time series model with qth order is represented as MA(q). The preceding relations...