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How do you evaluate the accuracy of exponential smoothing forecasts?

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Exponential smoothing is a popular method for forecasting future values of a time series, such as sales, demand, or inventory. It works by assigning different weights to the past observations, with more recent ones getting higher weights. This way, the forecast can capture the trends and patterns in the data, while smoothing out the random fluctuations. But how do you choose the right type of exponential smoothing for your data? And how do you evaluate the accuracy and reliability of your forecasts?

Read on for the main types of exponential smoothing, their advantages and disadvantages, and how to use them in practice.

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1 Simple exponential smoothing

Simple exponential smoothing, also known as single exponential smoothing, is the simplest form of exponential smoothing. It only uses one parameter, called the smoothing factor or alpha, which determines how much weight is given to the most recent observation. The forecast for the next period is calculated as a weighted average of the current observation and the previous forecast. The formula is:

<code>Forecast(t+1) = alpha * Observation(t) + (1 - alpha) * Forecast(t)</code>

Simple exponential smoothing is suitable for time series that have no trend or seasonality, and have a constant level. It can produce smooth and stable forecasts, but it cannot adapt to changes in the data. It also requires a reasonable initial value for the forecast, which can be tricky to estimate.

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Richard DiPilla

I create stories about life, love, nature, relationships and friendships. #storytelling #influencers #branding #leadership LinkedIn Weekly Avg. Reach- 10 Million + Views
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Although there are obviously many advantages to exponential smoothing, I have a hard time getting past in inability to handle new and unexpected trends. I believe that better AI formulas are on the near horizon. A decade ago trends developed over long periods of time. This gave forecasters sufficient time to make necessary adjustments. In today's world a trend can be created and promoter through social media in less than 24 hours. Already burdened by lag time issues, I can't see this modeling as anything but a lose bandaid that carries huge potential liabilities.

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George Nisotel

* SEMI-RETIRED SENIOR FINANCE & OPERATIONS ANALYST *
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If there’s no discernible trend, you may want to look for other independent variables that could logically be underlying drivers of the observed data.

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Fernando Jesús Alba Marín

Ingeniero Industrial
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La suavización exponencial simple no siempre puede utilizarse en la práctica debido a que presenta la desventaja de que los cambios van a la zaga del comportamiento real de los datos durante un incremento o disminución, pero se dispara cuando ocurre un cambio de dirección. Cuando se presentan estos efectos se puede ajustar el valor de alfa en cada período utilizando una variante de la suavización exponencial simple conocida como suavización exponencial adaptativa o ARRSES por las siglas en inglés (Adaptative Response Rate Single Exponential Smoothing).

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2 Holt's linear exponential smoothing

Holt's linear exponential smoothing, also known as double exponential smoothing, extends the simple exponential smoothing by adding another parameter, called the trend factor or beta, which captures the slope of the time series. The forecast for the next period is calculated as a weighted average of the current observation, the previous forecast, and the previous trend. The formula is:

<code>Forecast(t+1) = (alpha * Observation(t) + (1 - alpha) * (Forecast(t) + Trend(t))) + Trend(t+1)</code>

<code>Trend(t+1) = beta * (Forecast(t+1) - Forecast(t)) + (1 - beta) * Trend(t)</code>

Holt's linear exponential smoothing is suitable for time series that have a linear trend, but no seasonality. It can capture the direction and magnitude of the trend, and adjust to changes in the data. However, it assumes that the trend is constant over time, which may not be realistic for some data. It also requires two reasonable initial values for the forecast and the trend, which can be difficult to estimate.

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Michai Mathieu Morin

CEO @ Coeus Institute | Leading the Future of Autonomous Data Systems | Automating Open-Source Intelligence for Strategic Impact
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This method, by incorporating a trend factor, captures the slope of the time series and adjusts for changes in the data. However it assumes a constant trend over time, which is not always realistic -- at least in the real world. Also, determining reasonable initial values for the forecast and trend(s) is always difficult. Only if you use Holt's smoothing with specific types of datasets can it be a powerful tool for forecasting. The key takeaway here is how important it is to pair the rule with the right data, otherwise you'll not garner the highest fidelity forecast.

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3 Holt-Winters exponential smoothing

Holt-Winters exponential smoothing, also known as triple exponential smoothing, further extends the Holt's linear exponential smoothing by adding another parameter, called the seasonal factor or gamma, which captures the periodic fluctuations of the time series. The forecast for the next period is calculated as a weighted average of the current observation, the previous forecast, the previous trend, and the previous seasonal component. The formula is:

<code>Forecast(t+1) = (alpha * Observation(t) / Seasonal(t-m) + (1 - alpha) * (Forecast(t) + Trend(t))) + Trend(t+1)</code>

<code>Trend(t+1) = beta * (Forecast(t+1) - Forecast(t)) + (1 - beta) * Trend(t)</code>

<code>Seasonal(t+1) = gamma * Observation(t) / Forecast(t) + (1 - gamma) * Seasonal(t-m)</code>

where m is the length of the seasonal cycle. Holt-Winters exponential smoothing is suitable for time series that have a trend and a seasonality. It can capture the shape and amplitude of the seasonal pattern, and adjust to changes in the data. However, it assumes that the trend and the seasonality are additive, which may not be true for some data. It also requires three reasonable initial values for the forecast, the trend, and the seasonal component, which can be challenging to estimate.

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Jeremy Boudreau

Problem Solving Optimist | WFM Professional | Excel Guru | Efficiency Expert
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To me this just feels like a basic understanding of what needs to be done when forecasting. If you're in a simple environment with no variation (coughHIRE MEcough) there is always going to be variation. Just looking at the numbers requires multiple variables in order to generate a new number for the future. Seasonality needs to be considered in any forecast.

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4 Evaluating exponential smoothing forecasts

To evaluate the accuracy and reliability of exponential smoothing forecasts, you can use various measures, such as the mean absolute error (MAE), the mean squared error (MSE), the root mean squared error (RMSE), or the mean absolute percentage error (MAPE). These measures compare the actual values of the time series with the forecasted values, and quantify the magnitude of the errors. The lower the error, the better the forecast. However, these measures do not tell you how well the forecast captures the dynamics of the data, such as the trend and the seasonality. For that, you can use graphical methods, such as plotting the actual and forecasted values over time, or plotting the forecast errors over time. These methods can help you identify any systematic biases, patterns, or outliers in the forecast errors, and suggest ways to improve the forecast model.

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Hans Levenbach PhD CPDF
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Your statement "do not tell you how well the forecast captures the dynamics of the data, such as the trend and the seasonality" does have a constructive solution. It is called Profile Analysis and is documented in my books Change & Chance Embraced (Chapter 3) and Four P's in a Pod (Chapter 20), available on Amazon websites. Hans Levenbach, PhD

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5 Here’s what else to consider

This is a space to share examples, stories, or insights that don’t fit into any of the previous sections. What else would you like to add?

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Ricardo Chang

| Strategic Business Manager | BDM | Sales & Commercial | B2B & B2C | Disruptive Innovator | Mentor
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La evaluación de la precisión de los pronósticos de suavizado exponencial se puede realizar a través de diferentes métodos. Algunos de los métodos comunes incluyen el cálculo de la raíz del error cuadrático medio (RMSE) y la comparación de los valores predichos con los valores reales. El RMSE es una medida de la diferencia entre los valores predichos por un modelo o un estimador y los valores observados. También se puede utilizar la validación cruzada para evaluar el rendimiento del modelo de suavizado exponencial. Este método implica dividir los datos en conjuntos de entrenamiento y prueba, y luego evaluar el rendimiento del modelo en el conjunto de prueba.

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Fernando Jesús Alba Marín

Ingeniero Industrial
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De manera general, los pronósticos de una suavización exponencial simple son muy conservadores debido a que se basan únicamente en la última estimación del nivel y no en una estimación de la tendencia, por lo que presentan otra desventaja debido a la propensión que tienen los datos a mostrar tendencias y variaciones estacionales. Para esos casos, pueden utilizarse suavizaciones de segundo orden y de tercer orden.

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How do you evaluate the accuracy of exponential smoothing forecasts?

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1 Simple exponential smoothing

2 Holt's linear exponential smoothing

3 Holt-Winters exponential smoothing

4 Evaluating exponential smoothing forecasts

5 Here’s what else to consider

Forecasting

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