Chapter 8
Time Series
Abstract This chapter introduces the Box-Jenkins methodology to analyze timeseries data, which first removes trend and seasonality, before trying to explain the
residual time series through moving average or auto-regressive models. In order to
determine the order of a process, autocorrelation and partial autocorrelation functions
are introduced. They are then used to construct a suitable model for the dynamics.
All concepts are illustrated with environmental data. Later in the chapter, the basic
ideas behind forecasting applications are developed. A discussion of various types
of models, ARIMA, EWMA, and GARCH among them, concludes the presentation.
Raw data in physics, finance, and other fields are often produced at a constant rate.
Examples are share prices that are updated daily, hourly, or even by the fraction of a
second and we seek to extract information from the data. We might either try to
• determine a model to characterize the dynamics of the system;
• predict or forecast the next data points;
• deduce inherent characteristics of the data, for example its volatility.
In the following sections, we will address these points one at a time. Inspired by the
discussion from the NIST web site [1, 2], we base our discussion on measurements
of the CO 2 concentration from the Mauna Loa observatory in Hawaii. Time series
of the averaged monthly measurements from 1958 until today are available in the
file co2_mm_mlo.txt from [3]. We reformat the data in this text file, extract data for
the period between 1995 and 2008, and generate a file that contains three columns:
the date in decimal form, the averaged monthly CO 2 concentration expressed in
μmole/mole of dry air, and the month as a number (Jan = 1,…, Dec = 12). We show
the first few lines to illustrate that format.
Electronic supplementary material The online version of this chapter
(https://doi.org/10.1007/978-3-030-63643-2_8) contains supplementary material, which is
available to authorized users.
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2021
V. Ziemann, Physics and Finance, Undergraduate Lecture Notes in Physics,
https://doi.org/10.1007/978-3-030-63643-2_8
91
Time Series
Abstract This chapter introduces the Box-Jenkins methodology to analyze timeseries data, which first removes trend and seasonality, before trying to explain the
residual time series through moving average or auto-regressive models. In order to
determine the order of a process, autocorrelation and partial autocorrelation functions
are introduced. They are then used to construct a suitable model for the dynamics.
All concepts are illustrated with environmental data. Later in the chapter, the basic
ideas behind forecasting applications are developed. A discussion of various types
of models, ARIMA, EWMA, and GARCH among them, concludes the presentation.
Raw data in physics, finance, and other fields are often produced at a constant rate.
Examples are share prices that are updated daily, hourly, or even by the fraction of a
second and we seek to extract information from the data. We might either try to
• determine a model to characterize the dynamics of the system;
• predict or forecast the next data points;
• deduce inherent characteristics of the data, for example its volatility.
In the following sections, we will address these points one at a time. Inspired by the
discussion from the NIST web site [1, 2], we base our discussion on measurements
of the CO 2 concentration from the Mauna Loa observatory in Hawaii. Time series
of the averaged monthly measurements from 1958 until today are available in the
file co2_mm_mlo.txt from [3]. We reformat the data in this text file, extract data for
the period between 1995 and 2008, and generate a file that contains three columns:
the date in decimal form, the averaged monthly CO 2 concentration expressed in
μmole/mole of dry air, and the month as a number (Jan = 1,…, Dec = 12). We show
the first few lines to illustrate that format.
Electronic supplementary material The online version of this chapter
(https://doi.org/10.1007/978-3-030-63643-2_8) contains supplementary material, which is
available to authorized users.
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2021
V. Ziemann, Physics and Finance, Undergraduate Lecture Notes in Physics,
https://doi.org/10.1007/978-3-030-63643-2_8
91