# Double exponential smoothing example

Let us consider chapter 7 of the excellent treatise on the subject of Exponential Smoothing By Hyndman and Athanasopoulos . We will work through all the examples in the chapter as they unfold.

Forecasting: principles and practice. OTexts, Here we run three variants of simple exponential smoothing: 1. This is the recommended approach. Lets take a look at another example. We will fit three examples again. Lets look at some seasonally adjusted livestock data.

The below table allows us to compare results when we use exponential versus additive and damped versus non-damped.

All of the models parameters will be optimized by statsmodels. The plot shows the results and forecast for fit1 and fit2. The table allows us to compare the results and parameterizations. Note that these values only have meaningful values in the space of your original data if the fit is performed without a Box-Cox transformation. By using a state space formulation, we can perform simulations of future values. The mathematical details are described in Hyndman and Athanasopoulos  and in the documentation of HoltWintersResults. Similar to the example in , we use the model with additive trend, multiplicative seasonality, and multiplicative error.

We simulate up to 8 steps into the future, and perform simulations. As can be seen in the below figure, the simulations match the forecast values quite well.

## Exponential smoothing

Forecasting: principles and practice, 2nd edition. Simulations can also be started at different points in time, and there are multiple options for choosing the random noise. We have included the R data in the notebook for expedience. Series dataindex. Figure 7. DataFrame np.Time Series. Moving Average. Exponential Smoothing. Double Exponential. Like the regression forecast, the double exponential smoothing forecast is based on the assumption of a model consisting of a constant plus a linear trend.

For the purposes of a forecast where the parameters of the model may change, it is more convenient to express the model as a function ofwhere is the positive displacement from a reference time T.

The estimate a and b at time T are based in the observation at time T and the estimates for the previous period, T Here we have both the constant and trend coefficients estimated by exponential smoothing. The forecasting parameters, for the constant term and for the trend term can be set independently. Both paremeters must be between 0 and 1.

Forecasting: Exponential Smoothing, MSE

The forecast for the expected value for future periods is the constant plus a linear term that depends on the number of periods into the future. With a linear term as part of the forecast, this method will track trends in the time series. We use the same data as for the other forecasting methods for illustration. We repeat the data below. Recall that the simulated data begins with a constant mean of At time 11 the mean increases with a trend of 1 until time 20 when the mean becomes a constant again with value The noise is simulated using a normal distribution with mean 0 and standard deviation 3.

The values are rounded to the nearest integer. At any time Tonly three pieces of information are necessary to compute the estimates, and. We illustrate the computations for time 20, using the estimated coefficients for time 19 and the data for time We investigate three different forecasts. For simplicity we base the forecasting parameters on a single parameter.

Of course the parameters need not be related in this way. The parameters are set with three different values of as in the table below. The estimates of the model for three cases are shown together with the mean of the time series in the figure below. The figure shows the estimate of the mean at each time and not the forecast.

The estimate with the larger value of follows the trend more accurately but has more variability. The forecast with the smaller value of is considerably smoother, but never corrects entirely for the trend. Compared to the regression model, the exponential smoothing method never entirely forgets any part of its past. Thus it may take longer to recover in the event of a perturbation in the underlying mean. This is illustrated in the figure below where the variance of the noise is set to 0.

The Forecasting add-in implements the double exponential smoothing formulas. The example below shows the analysis provided by the add-in for the sample data in column B. We use the parameters of the second case.The name of the indicator might be a bit misleading. The forecasting method usually used with it is a sort of linear forecasting. Like the regression forecast, the double exponential smoothing forecast is based on the assumption of a model consisting of a constant plus a linear trend.

For the purposes of a forecast where the parameters of the model may change, it is more convenient to express the model as a function ofwhere is the positive displacement from a reference time T. The estimate a and b at time T are based in the observation at time T and the estimates for the previous period, T Here we have both the constant and trend coefficients estimated by exponential smoothing.

The forecasting parameters, for the constant term and for the trend term can be set independently. Both parameters must be between 0 and 1. The forecast for the expected value for future periods is the constant plus a linear term that depends on the number of periods into the future. As usual with the forecasting parts, it is strongly advised not to use it in signaling mode. The forecasting part is a subject of change and should be used only as an estimation of trend component of the double smoothing, not as signal.

TrendFlex x 2 — indicator for MetaTrader 5. Reflex — indicator for MetaTrader 5. On Dec 16, Related Posts. Download Now. Leave a comment. Sign in. Welcome, Login to your account. Forget password? Remember me. Sign in Recover your password. A password will be e-mailed to you.Learn about exponential smoothing and the characteristics of time series data to create and validate time series forecasts in R.

In this blog post, I will show you how to create and validate exponential smoothing time series forecasts with the statistical software R. The post uses website traffic data from organic search as real-world example and R code snippets throughout. Depending on the type of online business, web traffic forecasts are usually of interest in regard to customer acquisition, advertisement revenues, and brand awareness. Exponential smoothing is one of the most popular time series forecasting techniques.

It uses historical data with its inherent characteristics more on that later as input for the forecasting model, which means that time series forecasting techniques like this are generally most suitable and accurate if:. Forecasting is equally an art as it is a science. However, this post will also address how the validity of an exponential smoothing forecast with its underlying assumptions can be evaluated and understood. In summary, the post aims to educate on:.

The post is organized as follows:. Characteristics of time series data. Exponential smoothing for time series forecasts. Evaluating and using exponential smoothing forecasts. Disclaimer: Note that the image links as part of the book recommendation below are affiliate links and as an Amazon Associate I earn commission from qualifying purchases at no additional costs of your own in case of subsequent purchase through that link. Know that I only recommend products that I have personally used and and believe are genuinely helpful not because of the small commissions I earn if you decide to purchase them.

This chapter addresses the characteristics of time series data. Examples from the business world include annual profits, quarterly sales revenue and monthly website traffic from organic search as used for forecasts later.

The described characteristics and components of time series data are important as they represent factors of the later introduced exponential smoothing forecasting technique. Real-world time series data commonly contains several components or recognizable patterns. Those time series components can be divided into systematic components and non-systematic components.

### Holt’s Linear Trend

Systematic time series components are those that allow modeling as they have some consistent or recurring pattern. Examples for systematic time series components are 1 trend and 2 seasonality.

Any other observation in the data is categorized as unsystematic and is called 3 error or remainder. A trend is a consistent increase or decrease in units of the underlying data. Consistent in this context means that there are consecutively increasing peaks during a so-called uptrend and consecutively decreasing lows during a so-called downtrend.

Also, if there is no trend, this can be called stationary. The trend component can also sometimes additionally reflect a cycle. A cyclic pattern is usually longer than a trend.Exponential Smoothing in Excel is an inbuilt smoothing method used for Forecasting, Smoothing the data, trend projection.

This will smoothen the select input range number by the percentage of dumping factor we choose. Start Your Free Excel Course. It is found under Analysis ToolPak in Excel.

This add-in is not loaded automatically on excel. Before using this first, we need to load it. We need to add this feature in Excel for analyzing business by using Excel Add-Ins. To add this feature in Excel follow below steps:.

Exponential Smoothing in Excel is very simple and easy to use. We have assigned the number to the month period. For Exponential Smoothing to this time series data, follow the below steps:.

Now if we compare the results of all the above 3 Excel Exponential Smoothing examples, then we can come up with below conclusion:. This has been a guide to Exponential Smoothing in Excel. Here we discuss how to use an Exponential Smoothing in Excel along with excel examples and downloadable excel template.

### A Gentle Introduction to Exponential Smoothing for Time Series Forecasting in Python

You may also look at these useful charts in excel —. Your email address will not be published. Forgot Password? Popular Course in this category. Course Price View Course. Leave a Reply Cancel reply Your email address will not be published. Free Excel Course. By continuing above step, you agree to our Terms of Use and Privacy Policy.We pick up on our discussion of exponential smoothing methods, focusing today on double exponential smoothing.

Single exponential smoothing, which we discussed in detail last week, is ideal when your time series is free of seasonal or trend components, which create patterns that your smoothing equation would miss due to lags. Single exponential smoothing produces forecasts that exceed actual results when the time series exhibits a decreasing linear trend, and forecasts that trail actual results when the time series exhibits an increasing trend.

Double exponential smoothing takes care of this problem. Y t is the actual value of the current period, t.

Now, three equations must be used to create a forecast: one to smooth the time series, one to smooth the trend, and one to combine the two equations to arrive at the forecast:.

Recall that these processes are judgmental, and constants closer to a value of 1. Sales Y t. The time series exhibits an increasing trend. Hence, you must use double exponential smoothing. You must first select your initial values for C and T. One way to do that is to again assume that the first value is equal to its forecast. Actual sales in period 3 wereand our constant-smoothing equation is:.

Mean Absolute Deviation has been computed for you. As with our explanation of single exponential smoothing, you need to experiment with the smoothing constants to find a balance that most accurate forecast at the lowest possible MAD.

Now, we need to forecast for period As with single exponential smoothing, you see that your forecasted curve is smoother than your actual curve. Notice also how small the gaps are between the actual and forecasted curves. Next week, we begin a multi-week discussion of regression analysis. During the course of the next few Forecast Fridayswe will discuss the issues that occur with regression: specification bias, autocorrelation, heteroscedasticity, and multicollinearity, to name a few.

There will be some discussions on how to detect — and correct — these violations. Once the regression analysis miniseries is complete, we will be set up to discuss ARMA and ARIMA models, which will be written by guest bloggers who are well-experienced in those approaches.

Tags: AnalysightsARIMAARMAbusiness forecastingcausal modelingdouble exponential smoothingeconometriceconometric forecastingexponential smoothingforecastForecast FridayForecastingregression analysissales forecastingsingle exponential smoothingtime seriestime series analysis.

You can follow any responses to this entry through the RSS 2.The data in Figure 3 of Simple Exponential Smoothing as well as previous figures on that webpage shows a distinct upwards trend.

This is accomplished by adding a second single exponential smoothing model to capture the trend either upwards or downwards. The result is shown in Figure 1. The next five values are shown in range SS We get the other four values by highlighting the range SS23 and pressing Ctrl-D.

Hello, The predicted value at each time depends on the value at the previous time. The first row corresponds to time 1 the first time period. All solutions seem to be forecasting in the same period. What about, if being asked to build a model that will forecast sales for the NEXT two years using Holt winter method.

How do I go about it? See Holt-Winter. Paul, Glad you like the post. The only real acceptance criteria for the Holt model or any other model is to see how good a job it does in correctly predicting future values. ETS function because I am a bit wary of the quality of the forecast.

Stephen, 1. ETS is supposed to be the same as Holt-Winter, although the algorithm used seems to be different. Your email address will not be published. RSS - Posts. RSS - Comments.

Real Statistics Using Excel. Skip to content. The result is shown in Figure 3. May 27, at pm. Why it should leave a blank in first row of the column of the forecast? Charles says:.

May 28, at am. Miel says:.