Also, not all time series have a seasonal component, as mentioned for audio or video data. An example of a trend would be a long term increase in a companies sales data or network usage.

Below, we have a figure that displays Zillows jumbo 30 year fixed mortgage rates from data. When a series contains a trend, seasonality, and noise, then you can define that series by the way those components interact with each other. These interactions can be reduced to what is called either a multiplicative or additive time series. A multiplicative time series is when the fluctuations in the time series increase over time and is dependent on the level of the series:.

Therefore, the seasonality of the model would increase with the level over time.

## Introduction to Time Series Analysis and Forecasting, 2nd Edition

In the graph below, you can see that the seasonality of airplane passengers increases as the level increases:. Below is a graph of births in New York where you can see that although the level increases, the seasonality stays the same:. Knowing whether your series data is multiplicative or additive is important if you want to decompose your data into its various parts such as trend, or seasonality. Decomposition is the deconstruction of the series data into its various components: trend, cycle, noise, and seasonality when those exist.

Two different types of classic decomposition include multiplicative and additive decomposition. The purpose of decomposition is to isolate the various components so you can view them each individually and perform analysis or forecasting without the influence of noise or seasonality.

For example, if you wanted to only view the trend of a real estate series, you would need to remove the seasonality found in the data, the noise due to randomness, and any cycles such as economic expansion. To get seasonally adjusted data, you can subtract the seasonal component from the decomposed data, most statistical packages have functions to do this for you. We already talked about how there is randomness, or noise in our data, and how to separate it with decomposition, but sometimes we simply want to reduce the noise in our data and smooth out the fluctuations from the noise in order to better forecast future data points.

## How To Identify Patterns in Time Series Data: Time Series Analysis

A moving average model leverages the average of the data points that exist in a specific overlapping subsection of the series. An average is taken from the first subset of the data, and then it is moved forward to the next data point while dropping out the initial data point.

A moving average can give you information about the current trends, and reduce the amount of noise in your data. Often, it is a preprocessing step for forecasting. The way a SMA is calculated is that it takes the subset of the data mentioned in the moving average model description, adds together the data points, and then takes the average over the subset of data. Here is the SMA graphed of the mortgage rate data, where you can see how the noise is smoothed out to better detect the trend:.

Note, that you can host your data for free on our platform or use Dropbox or Amazon S3 data connectors.

## ISBN 13: 9781475777505

In a cumulative moving average, the mean is calculated from a data stream up to the current data point, which gets updated with each new data point that comes in from the stream. This is often used to smooth data when analyzing stock market data, network data, and even social media data that has some numeric value such as sentiment scores. With smoothing, it becomes easier to detect trends. The key difference between the cumulative moving average and a simple moving average is that because the cumulative moving average is applied to a data stream versus static data, the average is updated as each new data point comes in through the stream.

In the above graph you can see the actual data points, along with the blue line that represents the cumulative moving average and recall that the average gets updated with each new data point. Unlike the simple moving average that moves forward one data point and drops the oldest data point to take the average from, an exponential moving average EMA uses all data points before the current data point.

Weights are associated with each data point and those further away from the current point are given less weight, in an exponentially decreasing fashion, than the data points closest to the current point. When the most current data has the most influence, you can better determine trends that matter most in real time which is why EMA is used in evaluating stock prices. Exponential moving average is also used in trading to identify support and resistance levels of stock prices as mentioned earlier in our discussion of Moving Averages.

But, this model is not only used in trading. In healthcare, the EMA has been used for identifying baselines for influenza outbreaks. Below is a graph of our mortgage series data that shows the daily rates for mortgage rates between and and includes the EMA for 50 and days which can be used to detect long-term trends. If you wanted to detect short-term trends you can use shorter periods. If you have data that you want to test an EMA on, such as a stock series, fisheries time series, or even sentiment score time series, check out Exponential Moving Average on Algorithmia.

Although you can forecast with SMA or EMA, another moving average model called Autoregressive Integrated Moving Average is popular for fairly accurate and quick forecasting of time series. ARIMA combines the models own past data points to determine future points versus a linear regression model that would rely on an independent variable to predict the dependent variable such as using treasury note rates to predict mortgage rates.

### 1st Edition

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