A Detailed & Easy Explanation of Smoothing Methods

Introduction

Smoothing is a powerful method that is used across data analysis. Synonyms of smoothing are curve fitting and low pass filtering. The motive to use smoothing is to detect trends in the presence of noisy clumsy data in cases in which the shape of the trend is unknown. The smoothing methods are used in conditional expectations/probabilities can be thought of as trends of unknown shapes that we need to estimate in the presence of uncertainty.

Forecasting or prediction is belonging to those powers which everyone wants to possess. The satisfaction of prediction is attained if the prediction turns out to be true, and that too with maximum accuracy. Similarly, this accuracy in forecasting is required in the prediction of the output through the time series data. 

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The forecasting methods of time series have many members of their family. One member is the Smoothing method. It is reducing noise by averaging previous values of the time series. It is further divided into two smoothers; one is moving average smoothing and another is simple exponential smoothing. They both can find implementation into series forecasting that does not have trend and seasonality. The series history length and the weights used differentiate both these methods. Another important point about the smoothing method is that in this method, averaging of the values is done over multiple times. Let's now have a deeper look into the two smoothers:

The Moving Average Smoothing - An Easy but Unworthy Method:

It is the simplest form of the smoothing method. In this method, a consecutive window is chosen after a period, to produce an average's series. Suppose a window of w consecutive value is considered as averaged, then this means that width of the window is w. Here the value of w is decided by the user. The moving average can be computed by placing the window at the centre of the time t and then averaging w values within that window, which is known as Centered Moving Average for Visualization. This type of moving average technique helps visualize the trends.

Code of Moving average method is:

import java.util.*; 

public class SimMovAvg { 

    private final Queue<Double> Dataset = new LinkedList<Double>(); 

    private final int prd; 

    private double s;

    public SimMovAvg(int prd) 

    { 

       this.prd = prd; 

    } 

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    public void addData(double n) 

    { 

        s += n; 

        Dataset.add(n); 

        if (Dataset.size() > prd) 

        { 

            s -= Dataset.remove(); 

        } 

    } 

    public double getMean() 

    { 

        return s / prd; 

    } 

    public static void main(String[] args) 

    { 

        double[] data = {1, 3, 5, 6, 8,

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                                              12, 18, 21, 22, 25}; 

        int prd = 3; 

        SimMovAvg ob = new SimMovAvg(prd); 

        for (double i : data) { 

            ob.addData(i); 

            System.out.println("Number added is " + 

                                i + ", SMA = " + ob.getMean()); 

        } 

    } 

}

Output

Figure 1: Output of Moving Average

But through the centred moving average, forecasting cannot be done as in this case the average computing is done using the data of the past as well as future of the given time. But for forecasting the future must be unknown. To overcome this issue, we have to place the window of width w over the recently arrived values of the series. Hence, this technique is called Trailing Moving Average for Forecasting.

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The Simple Exponential Smoothing a Popular Smoother:

It is similar to moving average smoothing, but not completely. In this smoothing method, recent information is considered more important than the older one. To do so, a weighted average of the past is taken such that there is a decrease in weight exponentially while going back into the past, instead of taking a simple average of the w most recent values as in moving average method. Hence, fulfilling the idea to give priority to recent values, and also not completely neglecting the past values. This is a popular forecasting method in business due to its cost-effective computation, better performance, flexibility, and it is easy to use for automation.

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Model-Based or Data-Driven Methods - Who is The Most Effective?

There is a rough division of forecasting methods into model-based methods and data-driven methods:·Model-based method is one in which there is an application of statistical, mathematical, or another scientific model for forecasting of the data series, whereas Data-driven method is a technique in which there are certain algorithms that learn patterns from the given data.

A model-based method is advantageous when the series at hand is very short, whereas, in the case of a data-driven method, the advantage is when the model assumption Is likely to be violated or when time series structure changes over time. Data-driven method's advantage is that it requires less user input and hence more automated, while this is not true in the case of a model-based method. Another difference between model-based and data-driven approaches are that model-based methods prefer forecasting series with global patterns, that extends throughout the period, whereas data-driven methods prefer local patterns for forecasting series. Multiple linear regression, autoregressive model, logistic regression model etc. are some model-based methods, whereas, regression tree, neural network, and naïve forecasting are some example of data-driven methods.

Extrapolation Methods — A Simple but Carefree Method:

When the forecast for a given time-series is created based on its history, then such a forecast has been known as extrapolation methods. This method is applicable even if multiple related time series are to be forecasted simultaneously because even in such cases most popular forecasting practice is to forecast each series using only its historical values. The simplicity of this method is its advantage, whereas the disadvantage is this method does not bother about the relationship between the series if any.

Econometric Models — Best Endorsed Model in Tourism Bout:

Econometric models are based on the assumption of the causality that is derived from the theoretical models. These include information from one or more series inputs into other series. These types of methods most probably make controlling assumptions about the data and the cross-series structure. For multivariate time series, the statistics literature contains a model that directly models the cross-correlation between a set of series.  

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External Information — Best, But Require Information all the Time:

When the main purpose is to forecast time series, another alternative is to gain access to external information that more heuristically correlates with a series. The most important factor that must be kept in mind while implementing this method is, whatever external information is integrated into the forecasting method that must be available during the prediction time. Further, it is worth adding that smoothing methods are strictly extrapolation methods, whereas regression models and neural networks can be adapted to capture external information.

Manual and Automated Forecasting - Who will Rule?

The level of automation depends on how forecasting will be used in the practice and nature of the forecasting task. When many time series are to be forecasted continuously, and there is a shortage of forecasting experts to be allocated to the process, then automation role comes into play.  

Model-based methods vary in their applicability for automation. Like the models that are based on many assumptions for producing adequate forecasts favours being manual rather automated. This is because they require constant observation of whether the assumptions are met or not.

Data-driven methods such as smoothing methods prefer automated forecasting. Here this is possible because it requires less tweaking, its range of trends and seasonal are suitable.

Combining methods are one of the suitable candidates of the automation. One of them is discussed in the next sub-heading.  

But even if the automated system is in place, it is suggested that proper monitoring of the forecast and errors in the forecast, that are produced by an automated system, is performed and periodic examining and updating of the automated system is done.

Ensemble Modeling - Best Endorsed model in Netflix Bout:

In general, ensemble modelling is the way toward running at least two related yet unique analytical models, and afterwards combining the outcomes into a solitary score or spread to improve the exactness of predictive analytics and data mining application. For forecasting different horizons or periods one can use different methods. Ensembles are useful for predicting cross-sectional settings.

One of the best examples of the implementation of the Ensemble modelling is that it played a major role in a million-dollar Netflix Prize contest, in which there was a competition of creating the most accurate prediction of the movie preferences by Netflix DVD rental service users. For improvement of the precision in forecast via ensemble modelling is a similar principle that underlies the advantage of portfolios and diversification in financial investment. Negative correlation or at least uncorrelated forecast can lead to the greatest improvement. 

Conclusion

After going through all the methods only one thing can be inferred, and it is that Smoothing Method is a composition of all the methods mentioned here, whether it be a moving average method, the three E's of forecasting methods, also constitutes of Automated as well as Manual forecasting control system. This is the last suggests that it is one of the kinds of Ensemble Modeling which helps to carve-out the best graph so that there may not arise the condition of over as well as underfitting. 

Please leave the query and comments in the comment section.

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