This lesson was adapted from educational material written by Dr. Kateri Salk for her Fall 2019 Hydrologic Data Analysis course at Duke University. This is the first part of a two-part exercise focusing on time series analysis.

Introduction

Time series are a special class of dataset, where a response variable is tracked over time. The frequency of measurement and the timespan of the dataset can vary widely. At its most simple, a time series model includes an explanatory time component and a response variable. Mixed models can include additional explanatory variables (check out the `nlme` and `lme4` R packages). We will be covering a few simple applications of time series analysis in these lessons.

Opportunities

Analysis of time series presents several opportunities. In aquatic sciences, some of the most common questions we can answer with time series modeling are:

* Has there been an increasing or decreasing trend in the response variable over time?
* Can we forecast conditions in the future?

Challenges

Time series datasets come with several caveats, which need to be addressed in order to effectively model the system. A few common challenges that arise (and can occur together within a single dataset) are:

* Autocorrelation: Data points are not independent from one another (i.e., the measurement at a given time point is dependent on previous time point(s)).

* Data gaps: Data are not collected at regular intervals, necessitating *interpolation* between measurements. There are often gaps between monitoring periods. For many time series analyses, we need equally spaced points.

* Seasonality: Cyclic patterns in variables occur at regular intervals, impeding clear interpretation of a monotonic (unidirectional) trend. Ex. We can assume that summer temperatures are higher.

* Heteroscedasticity: The variance of the time series is not constant over time.

* Covariance: the covariance of the time series is not constant over time. Many of these models assume that the variance and covariance are similar over the time-->heteroschedasticity.

Learning Objectives

After successfully completing this notebook, you will be able to:

1. Choose appropriate time series analyses for trend detection and forecasting

2. Discuss the influence of seasonality on time series analysis

3. Interpret and communicate results of time series analyses