{"id":3674,"date":"2023-11-14T15:22:28","date_gmt":"2023-11-14T15:22:28","guid":{"rendered":"https:\/\/eodhd.com\/financial-academy\/?p=3674"},"modified":"2025-02-05T11:53:51","modified_gmt":"2025-02-05T11:53:51","slug":"estimate-volatility-with-sma-and-ewma-in-python","status":"publish","type":"post","link":"https:\/\/eodhd.com\/financial-academy\/stocks-data-analysis-examples\/estimate-volatility-with-sma-and-ewma-in-python","title":{"rendered":"Estimate Volatility with SMA and EWMA in Python"},"content":{"rendered":"\n

Time series analysis is a critical component of understanding and predicting trends in various fields such as finance, economics, and environmental science. Two common methods used for smoothing time series data are simple, or equally weighted, Moving Averages (SMA)<\/a> and Exponentially Weighted Moving Averages (EWMA)<\/a>. In this article, we will delve into the characteristics, advantages, and applications of both approaches.<\/p>\n\n\n\n

Additionally, we will demonstrate the practical application of these techniques by deriving volatility estimates from financial time series. We will use the Euro Stoxx 50 market index<\/a> as an example and highlight the main differences by comparing the two results<\/p>\n\n\n\n

Register & Get Data<\/span><\/a><\/p>\n\n\n\n\n\n\n

An Introduction to Simple Moving Averages<\/h2>\n\n\n\n

A moving average is calculated on a rolling estimation sample. In other words, we can set a window of fixed length n<\/em>, roll it through time and then compute the mean of each sample obtained by adding a new (most recent) observation and taking off the oldest one. This window is often referred to as look-back period<\/em>. As the name suggests, the same weight is assigned to each observation in the sample. A simple formulation is:<\/p>\n\n\n\n

\"MA_{t}<\/p>\n\n\n\n

where \"X_{t}\" with \"t are the time series observations. <\/p>\n\n\n\n

The advantages of this method surely lie in its simplicity and easy interpretability. By equally weighting all data points within its chosen timeframe, SMAs provide a smooth, undisturbed trend line, effectively filtering out the noise inherent in day-to-day market fluctuations and allowing the identification of long-term trends.<\/p>\n\n\n\n

Despite being widely used by practitioners, SMAs also come with some pitfalls. One of the main issues is known as the leverage <\/em>effect<\/em>, indicating a phenomenon where sudden spikes or outliers in data have a long-lasting impact on the results of moving averages. Let’s consider an exceptionally high return occurring today. If tomorrow we compute the 30-day volatility based on closing prices and include the abnormal return, our volatility forecast will be very high. However, in exactly 30 days (or 22 if we consider only business days), it will suddenly drop to a much lower level on a day when absolutely nothing happened in the markets. This occurrence is simply because the extreme return dropped out of the moving estimation sample. As long as this extreme return stays within the data window, the volatility forecast remains high. We will explore this exact case in the example below.
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Exponentially Weighted Moving Averages<\/h2>\n\n\n\n

Unlike the equal weighting approach, exponentially weighted moving averages (EWMA) add more weight on recent observations. This characteristic makes EWMA particularly useful in capturing short-term volatility dynamics and less prone to the leverage effect <\/em>issues associated with SMA. By incorporating a smoothing factor  \ud835\udf06  that dictates the rate at which past data diminishes in relevance, the model can be tailored to reflect the desired responsiveness to recent market movements. The higher is  \ud835\udf06, the more weight would be attributed to past returns when computing the volatility. For constant \"0<\lambda, EWMAs are defined as:<\/p>\n\n\n\n

\"EWMA(x_{t-1},<\/p>\n\n\n\n

Following this approach, and assuming mean asset returns equal to zero, we can compute EWMA estimates of variances and covariances as follows:<\/p>\n\n\n\n

\"\hat{\sigma}_{t}^2<\/p>\n\n\n\n

\"\hat{\sigma}_{12t}<\/p>\n\n\n\n

The rightmost part of the last two equations shows a recursive closed-form formulation for variance and covariance in the EWMA case.<\/p>\n\n\n\n

An example<\/h2>\n\n\n\n

Data<\/h3>\n\n\n\n

For our example, we will use time series data of one of the most known market indices, the Euro Stoxx 50, to compute risk measures for this asset and highlight the main differences obtained by comparing the results of these two techniques. The data sample spans from January 2018 to November 2023, encompassing a total of 1509 observations. <\/p>\n\n\n\n

To retrieve our data through the EOD API service<\/a>, we first need to download and import the EOD Python package<\/a>, and then authenticate using your personal API key. It’s recommendable to save your API keys in the environment variable.<\/p>\n\n\n\n

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pip install eod<\/code><\/pre>\n\n                <\/div>\n                
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