Introduction to Time Series Analysis

Other examples could be the vote intention during an electoral campaign or the number of mentions received on Twitter by each candidate.

In all these examples, each observation corresponds to a different timestamp, and analyzing the temporal variation of the variable will be meaningful.

Time Series Analysis

In time series, a variable evolves with time, and the objective is to predict its future values. Hence, we assume that there is a pattern in the series and also a noise component. We want to find and isolate the hidden patterns.

1) Exploratory Analysis 

The first step is to gain intuition about our data. Hence, we will visualize the time series and compute some basic statistics.

For example, if analyzing temperature, we would expect temperatures to be higher in summer than in winter. Thus, though we do not know when summer or winter occurs in the given city, after visually exploring the data, we will be able to identify both periods.

2) In-Depth Analysis

Use specific time series analysis methods to find trends and patterns in the data.

We will see these methods in the following slides.

3) Time Series Forecasting

Build models that are able to predict the future values of the time series.

We will not be able to produce a high quality model without steps 1 and 2.

When analyzing time series, usually our aim is to forecast future values, and we do so by learning from the already observed time series, and the patterns identified in it. This is a difficult task.

However, economists and investors have always attempted to predict future values of stock prices, real estate prices, interest rates, exchange rates etc. Trading strategies rely on models that learn from historical data and predict future values.

Usually time series contain a noise component. Though there might be a pattern in the signal, we can usually find a lot of noise around these signals.

Therefore, in order to explore the trend and seasonality of the time series, we usually need to smooth the curve.

Once the time series is smoothed, it is much easier to analyze it, identify patterns and derive conclusions.

Smoothers

This is the basic tool used for estimating the components of a time series in decomposition and smoothing models.

Smoothing a time series is to approximate it by a function that attempts to capture the important patterns while removing the noise.

Smoothers create an estimation for each point of the series by fitting an auxiliary model with the data of a local window.

Smoothers

This is the basic tool used for estimating the components of a time series in decomposition and smoothing models.

Smoothing a time series is to approximate it by a function that attempts to capture the important patterns while removing the noise.

Smoothers create an estimation for each point of the series by fitting an auxiliary model with the data of a local window.

In a smoother, we have to define the following:

Auxiliary Model: In the simplest case it will just be the mean, but it could be a linear regression or polynomial model.

The size of the window: The larger, the more smoothed the signal will be, and the more noise we will remove. However, if the windows is too wide, we can lose part of the signal.

Center of the window: Is the window centered at the considered point, or to the right or left.

Weights: This is the importance of each point in the model. In the simplest case, all observations in the window have the same weight. But, we could weight more observations closer to the center, or observations from the past.