# Weighted Moving Average (WMA)

The Weighted Moving Average is a valuable tool for traders, as it provides a clear signal of trend changes and smoothes out price volatility, thereby helping traders make informed trading decisions and identify potential opportunities

9 minutes

A moving average is a simple but powerful tool that can help you identify the trend direction, support and resistance levels, and momentum of a security. It is calculated by taking the average price of a security over a specified number of periods, such as days, weeks or months. By doing so, it smooths out the random fluctuations and noise in the price data and reveals the underlying trend.

There are different types of moving averages that can be used for technical analysis, each with its own advantages and disadvantages. In this blog post, we discuss the Weighted Moving Average.

#### Introduction

A weighted moving average is a type of moving average used to analyze a time series by assigning varying weights to each data point. Unlike a simple moving average, which treats each data point equally, a weighted moving average places more emphasis on recent or significant data points.

To calculate a weighted moving average, each data point is multiplied by a weight and the sum of these products is divided by the sum of the weights. The weights can be determined in different ways, such as linear or exponential, depending on the analyst’s preference.

Using a weighted moving average offers several benefits, including the ability to smooth out short-term fluctuations in data and identify underlying trends. It can also identify changes in trend direction and forecast future values of the time series.

Overall, a weighted moving average is a valuable tool for analysts and traders seeking to gain insights into a time series’ behavior and make informed decisions based on their analysis.

#### Selecting the weights to be used in the WMA

When selecting weights for a weighted moving average, there are several common approaches that analysts use:

Linear weights

This method assigns weights in a linear fashion, with recent data points given more weight. For example, a five-period moving average could use weights of 1, 2, 3, 4, and 5, with the most recent period given a weight of 5.

Exponential weights

This method assigns weights in an exponentially decreasing fashion, with recent data points given more weight than older data points. The weights are determined by a smoothing factor, usually represented by the symbol “α” (alpha). The formula for an exponential moving average with a smoothing constant of α is: EMA(t) = α * Xt + (1 – α) * EMA(t-1), where EMA(t) is the current period’s exponential moving average, Xt is the current period’s data point, and EMA(t-1) is the previous period’s exponential moving average.

Other methods

While less common, some analysts use other weight assignment methods such as using a triangular or Gaussian distribution.

Choosing the period length is an important consideration when using a weighted moving average. Shorter periods respond more quickly to changes but may be more susceptible to noise, while longer periods provide a smoother estimate but may not capture short-term changes as effectively.

Using multiple moving averages with different period lengths can help to identify trends and changes in trend more effectively than a single moving average. This can also provide signals for entering or exiting positions based on the relationship between the different moving averages.

Ultimately, the choice of weighting method, period length, and number of moving averages will depend on the goals of the analysis and the characteristics of the time series being studied.

#### The origin of the Weighted Moving Average

The concept of the weighted moving average has been in use for a long time, and its origins cannot be attributed to a single individual or entity.

Moving averages have been used in financial analysis and time series forecasting since at least the early 20th century, with early references found in the work of British economist Frederick Macaulay. Over the decades, many researchers and practitioners have contributed to the development and refinement of moving average methods, including weighted moving averages. For instance, J. Welles Wilder Jr. introduced the exponential moving average, a type of weighted moving average, in his 1978 book “New Concepts in Technical Trading Systems.”

Today, weighted moving averages are widely employed in finance, economics, and other fields for tasks such as smoothing noisy time series data, identifying patterns and trends, and making predictions.

#### Computing the Weighted Moving Average

To calculate a weighted moving average, the following formula is used:

WMA = (w1 * y1 + w2 * y2 + ... + wn * yn) / (w1 + w2 + ... + wn)

where:
WMA represents the weighted moving average;
y1 through yn represent the data points in the time series, with y1 being the most recent and yn being the oldest; and
w1 through wn represent the weights assigned to each data point, with w1 being the weight assigned to y1 and wn being the weight assigned to yn

The specific weights used depend on the chosen weighting method, as discussed above. For example, if a linear weighted moving average with a period of five was being used, the weights would be 1, 2, 3, 4, and 5, with the most recent period (y1) being assigned a weight of 5. To illustrate, if the data points for the past five periods (looking back) were 106, 112, 110, 108, and 113, the weighted moving average would be calculated as follows:

WMA = (5 * 111 + 4 * 110 + 3 * 112 + 2 * 109 + 1 * 106) / (5 + 4 + 3 + 2 + 1) = 110.33

It is important to note that in this example, the most recent data point (106) is given the highest weight, while the oldest data point (113) is given the lowest weight. Consequently, the weighted moving average places more emphasis on recent data and responds more quickly to changes in the time series.

ChartAlert ships with the Weighted Moving Average.

#### How to use the Weighted Moving Averagein trading?

Using a weighted moving average can be a valuable tool for identifying trends and potential trading opportunities. To make the most of this method, consider these practical tips:

Identify trends

The slope and direction of the moving average can help determine whether an asset’s price is trending upward or downward. Use this information to make informed trading decisions and identify potential entry and exit points.

Determine the period length

The appropriate period length for a weighted moving average depends on the asset and trading strategy. Experiment with different lengths to see how the moving average performs in various market conditions.

Confirm signals

Use the weighted moving average to confirm signals generated by other technical indicators. If the price is above the moving average and it’s sloping upward, it may be a good time to buy. If the price is below the moving average and it’s sloping downward, it may be a good time to sell.

Establish support and resistance levels

The moving average can help establish support and resistance levels. It is possible that the moving average could function as a support level if the price is above it. If the price is below the moving average, it may serve as a resistance level.

Combine multiple moving averages

Using multiple weighted moving averages with different periods can help identify trends and confirm signals.

Use the moving average as a support or resistance level

The moving average can serve as a reference level for potential support or resistance.

Combine the moving average with other technical indicators

Use the moving average in conjunction with other technical indicators to confirm signals or identify trading opportunities.

Be aware of market conditions

The effectiveness of the weighted moving average will depend on market conditions. Consider factors such as volatility, news events, and market sentiment when using this method.

Use fundamental analysis

Avoid relying solely on the moving average

Consider multiple factors, including market conditions, technical indicators, and fundamental analysis, when making trading decisions. Additionally, maintain discipline and stick to a trading plan.

Overall, the key to using a weighted moving average effectively in trading is to experiment with different parameters, combine it with other technical indicators, and adapt to changing market conditions. It’s important to have a solid understanding of technical analysis principles and risk management strategies, and to integrate the moving average into a broader trading strategy that incorporates multiple indicators and analytical methods.

#### Advantages & Limitations of the Weighted Moving Average

The usage of Weighted Moving Average (WMA) is widespread in trading and it comes with its own set of advantages and limitations. Allow us to examine this more closely:

• Sensitivity to recent price action: WMA places more weight on recent price data, providing a more timely signal of changes in trend direction compared to a simple moving average.
• Smoothing of price volatility: WMA helps to smooth out the volatility of the price series, making it easier to identify trends and potential trading opportunities.
• Clear signals: The slope and direction of a WMA can provide clear signals for entry and exit points, as well as potential support and resistance levels.
• Customizable: Traders can adjust the weightings used in a WMA to suit their individual preferences and trading style.

Limitations

• Subject to lag: While WMA is more sensitive to recent price data compared to a simple moving average, it can still be subject to lag in identifying trend changes.
• Affected by outliers: WMA can be more susceptible to being affected by outliers or sudden price spikes.
• May generate false signals: Like any trading indicator, a WMA can generate false signals, particularly during periods of high volatility or when there is a lack of clear trend direction.
• Unsuitable for certain market conditions: WMA may not work well in choppy or range-bound markets, where the price is oscillating back and forth between support and resistance levels. Other indicators or trading methods may be more effective in such markets.

The WMA is a widely used tool for technical analysis that can assist traders in recognizing trends and potential trading opportunities. Unlike simple moving averages, WMA emphasizes recent price data, which enhances its responsiveness to shifts in trend direction. Furthermore, WMA can dampen price volatility, provide unambiguous signals for entering and exiting positions, and be tailored to match a trader’s particular preferences and trading style.

Although the WMA is a valuable tool for traders, it’s crucial to acknowledge that no single strategy or indicator can guarantee success in trading. In making trading decisions, traders must weigh a variety of factors, such as market conditions, technical indicators, and fundamental analysis. It is also essential to exercise discipline and follow a trading plan rather than making impulsive decisions based solely on WMA signals. Furthermore, traders should bear in mind that past performance doesn’t guarantee future results and should be adaptable to changing market conditions by adjusting their strategies accordingly.