#### Overview of this book

Python, one of the world's most popular programming languages, has a number of powerful packages to help you tackle complex mathematical problems in a simple and efficient way. These core capabilities help programmers pave the way for building exciting applications in various domains, such as machine learning and data science, using knowledge in the computational mathematics domain. The book teaches you how to solve problems faced in a wide variety of mathematical fields, including calculus, probability, statistics and data science, graph theory, optimization, and geometry. You'll start by developing core skills and learning about packages covered in Python’s scientific stack, including NumPy, SciPy, and Matplotlib. As you advance, you'll get to grips with more advanced topics of calculus, probability, and networks (graph theory). After you gain a solid understanding of these topics, you'll discover Python's applications in data science and statistics, forecasting, geometry, and optimization. The final chapters will take you through a collection of miscellaneous problems, including working with specific data formats and accelerating code. By the end of this book, you'll have an arsenal of practical coding solutions that can be used and modified to solve a wide range of practical problems in computational mathematics and data science.
Preface
Basic Packages, Functions, and Concepts
Free Chapter
Mathematical Plotting with Matplotlib
Working with Randomness and Probability
Geometric Problems
Finding Optimal Solutions
Miscellaneous Topics
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# Forecasting from time series data using ARIMA

```        In the previous recipe, we generated a model for a stationary time series using an ARMA model, which consists of an autoregressive (AR) component and an moving average (MA) component. Unfortunately, this model cannot accommodate time series that have some underlying trend; that is, they are not stationary time series. We can often get around this by differencing the observed time series one or more times until we obtain a stationary time series that can be modeled using ARMA. The incorporation of differencing into an ARMA model is called an ARIMA model, which stands for Autoregressive (AR) Integrated (I) Moving Average (MA).

Differencing is the process of computing the difference of consecutive terms in a sequence of data. So, applying first-order differencing amounts to subtracting the value at the current step from the value at the next step (ti+1 - ti). This has the effect of removing the underlying upward or downward...```