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)

Chapter 5. Deep Learning for Time Series Forecasting

So far in this book, we have described traditional statistical methods for time series analysis. In the preceding chapters, we has discussed several methods to forecast the series at a future point in time from observations taken in the past. One such method to make predictions is the auto-regressive (AR) model, which expresses the series at time t as a linear regression of previous p observations:

 

Here, Єt is the residual error term from the AR model.

The idea underlying the linear model can be generalized that the objective of time series forecasting is to develop a function f that predicts xt in terms of the observations at previous p points of time:

xt = f(xt-1,xt-2, ... ,xt-p)

In this chapter, we will explore three methods based on neural networks to develop the function f. Each method includes defining a neural network architecture (in terms of the number of hidden layers, number of neurons in every hidden layer, and so on) and then...