Introduction to Time Series Analysis
In this lesson, you’re expected to:
– learn how to conduct a time series analysis
– understand the characteristics of a time series
– discover the best techniques to analyze a time series
Most commonly, a time series is a sequence collecting data at successive equally spaced points in time.
For example, the minimum and maximum temperatures of Madrid over the last year.
In all these examples, each observation corresponds to a different timestamp, and analyzing the temporal variation of the variable will be meaningful.
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.
The main characteristics or components of a time series are the following:
Seasonality: cyclic variations around the trend-cycle.For example, the demand of swimsuits will have a cyclical trend that will be repeated every year. The demand will increase in summer and reach its minimum values during winter.
Cyclicaleffects refer to the impact of the business cycle. For example, the sales of cars is significantly reduced when an economy falls into recession.
Noise component or Irregular effects refer to the impact of random events such as strikes, sudden changes in the weather etc.
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.
Use specific time series analysis methods to find trends and patterns in the data.
We will see these methods in the following slides.
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.
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.
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.
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.
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.
http://www.climate4you.com/DataSmoothing.htm
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.
The mean is taken from an equal number of data on either side of the central value and all the points have the same weight in the fitting.