effective. The shorter term the moving average, the more sensitive it is in responding to price changes. This technique, when properly applied, reveals more clearly the underlying trend, seasonal and cyclic components. Note that Bt ≥ 0 implies a valid penetration from the below of the m-lag moving average into its n-lag counterpart and that Bt > 0 implies the opposite. A high coefficient value results in less smoothing and thus a high responsiveness to variations in the data. Single-period Inventory Analysis An often-used technique in industry is "smoothing". Smoothing techniques are a higher form of naive models. There are 15 separate exponential smoothing methods. Moving averages are time series derived from a set of prices. Because only three numbers are required to perform exponential smoothing, this technique is simple to update. However, the trends can be very volatile, almost haphazard at times. Smoothing Technique Smoothing Techniques. Typically, quantitative forecasting is more effective when dealing with data points such as future sales growth and tax topics, rather than subject matter that has less concrete data to guide these forecasts. Additive method is used … Plot of a Time Series Triple Exponential Smoothing is better at handling parabola trends. Regression Modeling Holt, and Winters methods use two and three parameters, respectively, therefore it is not an easy task to select the optimal, or even near optimal values by trial-and –errors for the parameters. Here, the idea is … However, one may perform a grid search of the parameter space, with Autoregressive Time Series Copyright © 2021 Elsevier B.V. or its licensors or contributors. ABC Inventory Classification Holt-Winters Exponential Smoothing is used for forecasting time series data that exhibits both a trend and a seasonal variation. Exponential smoothing is a weighted moving average technique which is especially effective when frequent re-forecasting is required, and when the forecasts must be achieved quickly. Moving average methods take the average of past actuals and project it forward. This definition can be efficiently evaluated by using the iterative formula in Equation 3.51 for all its basic EMAs. This tends to be true for most of the funds, and the losses occurring in sideways markets have to be factored in to their systems. Forecasting involves the estimation of values we don’t know by using values that we know of. The single exponential smoothing emphasizes the short-range perspective; it sets the level to the last observation and is based on the condition that there is no trend. An exponenentially weighted moving average with a smoothing constant a, corresponds roughly to a simple moving average of length (i.e., period) n, where a and n are related by: Holt's Linear Exponential Smoothing: Suppose that the time series is non-seasonal but does display trend. To be precise, we denote a moving-average rule, which consists of two moving averages with n and m lags respectively (n > m), as moving-average (n, m). A small value of, say, between 0.05 and 0.10 results in a high degree of smoothing and has the same effect as a large number of observations in a moving average calculation. For example the 20-day moving average on a particular date is the simple average of the previous 20 days’ prices. Exponential moving averages are similar to weighted moving averages in that they give more weight to recent data, but they differ in that they do not drop off data as time moves on. Mean, and Variance Estimations Beta and Covariance Computations Similarly, the method does not … Mean Absolute Error (MA Error). The buy and sell signals are calculated as follows: The traditional BB definition is tested along with two variants: 30-day moving average, ±2σ and 20-day moving average, ±1σ. Exponential Smoothing uses a simple average calculation to assign exponentially decreasing weights starting with the most recent observations. If a short-term moving average is above a longer-term one, then the market is trending up, and vice versa. It … Forecast with a high coefficient of 0.80. These are the same combinations used in previous studies (e.g., Ratner and Leal, 1999; Lento, 2007) which reduce potential bias and increase comparability with past studies. Exponential Smoothing is one of the more popular smoothing techniques due to its flexibility, ease in calculation, and good performance. The EMA of z necessarily has an interpolation scheme different from that used for z. Making Risky Decisions A valid penetration happens when the moving average with a shorter length penetrates the one with a longer length either from the below or from the above respectively. The buy and sell signals from the TRBO are defined as follows: Equation 3 – Trading Range Breakout Positions. Thus, many experiments are needed to search for optimal moving-average rules in different financial markets. Although quantitative forecasting takes the guesswork out of the process, it can also be limited by a lack of human expertise, resulting in a deficit of important context that could alter forecast… Among the optimal rules found so far, the moving-average (n, 1)-type rules, such as MA(150, 1) and MA(200, 1), are the simplest and most popular. (2007). Weighted moving averages are calculated by giving more weight to the most recent data. A simple q–period moving average is computed as follows: For example, daily stock prices are compared to a moving average of a specified number of historical prices. Qualitative Techniques: … The movement above the moving average might imply that the current high price is due to random error or noise. For the first time period, we cannot forecast (left blank). Moving averages are the simpler of the two. Moving averages are popular for two reasons: first, because they are easy to use; second, because they work well in identifying a trend (which is, you remember, what the game is all about). Seasonal Index These are the same days used in previous studies (e.g., Brock et al., 1992; Lento, 2007). There are numerous other moving average rules, and they can be thoroughly contradictory with one another. Then the best alpha has the smallest However, as it would be difficult to sell such a fund to an investor, no one would ever admit it.). Notice that the simple moving average is special case of the exponential For example, the data in Figure 7.1 do not display any clear trending behaviour or any seasonality. The feasibility of these techniques hinges on the assumption that crowd psychology makes the asset price move in discernible trends. Therefore, the convolution with an arbitrary kernel can be evaluated by iterated exponential moving averages. They then only take as a buy or sell signal when the first two cross the third. Parametric System of Linear Equations However recall one of our key points above: we need to use the most appropriate (best) forecasting method, even if we … A time series is a sequence of observations which are ordered in time. Categorized Probabilistic, and Statistical Tools smoothing by setting the period of the moving average to the integer part of This method is suitable for forecasting data with no clear trend or seasonal pattern. It is a simple a n d common type of smoothing used in time series analysis and forecasting. The two typical forms of smoothing techniques are moving averages and exponential smoothing. For an individual trader, or for a newcomer on a trading desk, it is probably not wise to rely on moving averages alone. In the extreme, if the coefficient is zero then the next period’s forecast will be the same as the last period’s forecast, and if the coefficient is one, or unity, then the next period’s forecast will be the same as the current period’s data. Thank you. ScienceDirect ® is a registered trademark of Elsevier B.V. ScienceDirect ® is a registered trademark of Elsevier B.V. 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Pictet, in, An Introduction to High-Frequency Finance, The Effectiveness of Technical Trading Models in Asian Equity Markets around the Financial Crisis, Handbook of Asian Finance: REITs, Trading, and Fund Performance. The Copyright Statement: The fair use, according to the 1996 Fair Use Guidelines for Educational Multimedia, of materials presented on this Web site is permitted for non-commercial and classroom purposes only. This is indicated by the aspect ratio AR, which decreases toward 1 for large n. Each basic EMA operator that is part of the iterated EMA has a range τ, which is much shorter than the range nτ of the full kernel. Exponential Smoothing methods are widely used for forecasting. As the date changes, so do the 20 prices from which the average is calculated. Blank boxes are not included in the calculations but zeros are. Exponential Smoothing: This is a very popular scheme to produce a smoothed Time Series. Buying is suggested when the moving average flattens out and the stock’s price falls below the moving average. Figure 63.44 illustrates the 21-day, 30-day, 100-day and 200-day moving averages for the short sterling contract on LIFFE during 1997–1998. Probabilistic Modeling The simplest of the exponentially smoothing methods is naturally called simple exponential smoothing (SES). You may like using the Past Forecasts by Smoothing Techniques JavaScript to obtain the past forecast values based on smoothing techniques that use only single parameter. Practitioners of technical analysis have applied simple and (occasionally) iterated EMA operators to homogeneous time series for a long time. The validity of a moving-average (n, m) rule depends mainly on its time lags, m and n. These time lags should be determined according to the length of the market cycle to be detected. We use cookies to help provide and enhance our service and tailor content and ads. 7.1 Simple exponential smoothing The simplest of the exponentially smoothing methods is naturally called simple exponential smoothing (SES) 13. Moving averages can be computed for any number of price data points. Holts winters seasonal method This method has three smoothing equations for level, trend, and the seasonal component. Modeling the BB trading rule requires two parameters: the 20-day moving average (MA20) and the standard deviation (σ) of the 20-day moving average line (σMA20). Exponential smoothing techniques include parameters for estimating the level (ie. A moving average serves to smooth down the fluctuations of asset prices so that distortions can be reduced to a minimum. Quadratic Regression Single Exponential Smoothing, SES for short, also called Simple Exponential Smoothing, is a time series … augmented by the kind of quantitative techniques discussed in this unit, and this combined approach has much to commend it. The three MACO variants will be defined with the following short, long combinations: (1, 50), (1, 200), and (5, 150). A simple exponential smoothing is one of the simplest ways to forecast a time series. button for obtaining one-period-ahead forecasting. exponential smoothing techniques, the traditional approaches [70] were used to calculate weekly ratios using three periods of historical data (2007, 2008 and 2009). Matrix Algebra, and Markov Chains This technique, when properly applied, reveals more clearly the underlying trend, seasonal and cyclic components. As with any forecasting technique it is important to always check what actually happened with the activity that was being forecast in order to ascertain how accurate the forecast was, and wherever necessary be able to adjust the forecast to better reflect the situation next time. There are an infinite number of combinations and blends of moving averages that can be created for different time periods. Trading strategies might be based on these moving averages. The art is in striking the correct balance in this trade-off. This study tests three variants of four technical trading rules. Figure 4.11 shows the effect of a high smoothing coefficient where 0.80 has been entered into cell b5. Inventory Control Models Figure 4.9 shows an example of exponential smoothing. To further extend our computational toolbox, we build another type of compact kernel by combining iterated EMAs, as shown in the next section. The smoothing techniques are very helpful, however, there is another medium level technique which is commonly used known as Time Series Decomposition. However, as they say in all the guides: do whatever works for you. When using one of the interpolation schemes of Equation 3.52 after the first iteration, we are making a small error. Equation (5.4) shows that as long as the asset return at present time t is greater than or equal to the negative of the weighted average of the asset returns in the past (n – 2) periods, a geometric moving-average (n, 1) rule will suggest investors to hold the asset for the next period. (2-Alpha)/Alpha. (We have a sneaky feeling that some technical funds use systems based solely on moving averages. Moving averages filter out noise and make it easier to identify trends. Time Series Analysis and Forecasting Techniques, Categorized Probabilistic, and Statistical Tools, Maths of Money: Compound Interest Analysis, System of Equations, and Matrix Inversion, Test for Several Correlation Coefficients, Fair Use Guidelines for Educational Multimedia, http://home.ubalt.edu/ntsbarsh/Business-stat. By continuing you agree to the use of cookies. Tab key not arrow or enter keys. As exponential smoothing does not require a great deal of historic data, it is another useful tool for short-term forecasts. System of Equations, and Matrix Inversion Smoothing Techniques for Time Series Forecasting @inproceedings{Hameed2015SmoothingTF, title={Smoothing Techniques for Time Series Forecasting}, author={Haifaa Hussein Hameed}, year={2015} } This method is suitable for forecasting data with no clear trend or seasonal pattern.. For example, algeria_economy below do not display any clear trending behaviour or any seasonality. As the iterated EMAs, these combined iterated EMAs have a shorter build-up time interval than a simple EMA of the same range. Therefore, the BB provides fertile new grounds for better understanding the profitability of technical trading strategies in the Asian equity markets. These techniques, when properly applied, reveals more clearly the underlying trends. What is the purpose of the forecast—how is it to be used? As for exponential moving averages, one-week and two-week periods tend to help predict upcoming changes in trends. Moorad Choudhry, in The Bond & Money Markets, 2001. The value of the smoothing parameter is determined via maximum likelihood estimation (MLE). with EMA[τ, 1; z] = EMA[τ z]. A simple recursive definition is. The spreadsheet examples used in this chapter do not require the use of complicated spreadsheet functions and formulae. All files are available at http://home.ubalt.edu/ntsbarsh/Business-stat for mirroring. A short-term moving average may give trend signals early in the move, but it may also generate false signals. Exponential smoothing is a technique used to detect significant changes in data by considering the most recent data. Figure 4.10. 8.1 Simple exponential smoothing. Specifically, an arithmetic moving-average (n, 1) rule, denoted as AMA(n, 1), can be defined as: whereas a geometric moving-average (n, 1) rule, denoted by GMA(n, 1) can be defined as: Taking the natural logarithm of the inequality in Equation (5.3) and rearranging, we have: where {Rt} is a sequence of asset returns. Features of time series, which might be revealed by examining its graph, with the forecasted values, and the residuals behavior, condition forecasting modeling. Some traders like to plot three moving averages: short, medium and long term. The simple moving average method is used to calculate the mean of average prices over a period of time and plot these mean prices on a graph which acts as a scale. Camillo Lento, in Handbook of Asian Finance: REITs, Trading, and Fund Performance, 2014. The Bollinger Band has been selected because even though it is a very popular trading model, it has not been tested in any known prior literature in the Asian equity markets. Two-Person Zero-Sum Games. This answer can be found by asking another question… What is it a forecast of? Moving average techniques consolidate shorter series of observations into longer series, are commonly used for smoothing data variability, and are frequently used as a reference point to gauge daily fluctuations. Kindly e-mail me your comments, suggestions, and concerns. Indeed the average function has been the main tool. In other words, a moving-average (n, m) rule will generate a buying signal for the next period when Bt ≥ 0 and a selling signal for the next period when Bt > 0. Even if the tail of the kernel is still exponential, it decays more quickly due to the small basic EMA range τ. EWMA applies weights to the historical observations following an exponential smoothing process with parameter λ in which 0≤λ≤1. This family of functions is related to Laguerre polynomials, which are orthogonal with respect to the measure e−t (for τ = 1). In other words, recent observations are given relatively more weight in forecasting than the older observations. There are many forecasting methods, and exponential smoothing is just one of them. They use weighted averages of past observations to forecast new values. The four rules tested are the moving average crossover (MACO), filter rules (FR), trading range breakout (TRBO), and Bollinger Bands (BB). Time Series Decomposition As mentioned in Introduction to Time Series Data , the four main components of time series data are trend, seasonality, cyclicity and irregularity. Exponential smoothing is generally used to make short term forecasts but longer term forecasts using this technique can be quite unreliable. (Brown’s) Simple Exponential Smoothing. It delivers a buying or selling signal depending on whether a valid penetration exists. These can be classified into four broad categories: qualitative, time-series, causal models, and technological forecasting. This allows the model to quickly update in a changing volatility environment. Historically econometric techniques/methods tend to have large forecast errors when forecasting national economies in the medium-term. Test for Stationary Time Series moving average smoothing Going further, if a short-term moving average crosses a longer-term one, then that is a sign that the trend is changing. There are two distinct groups of smoothing methods There are three main types of exponential smoothing time series forecasting methods. The buy and sell trading signals generated by the MACO can be models as follows: where Ri,t is the log return for any given short period of S days (1 or 5 days), and Ri,t − 1 is the log return over any given long period of L days (50, 150, or 200 days). This makes deciding optimal time lags for a moving-average (n, m) rule much more a science of art. State space form Forecasting: Principles and Practice Taxonomy of exponential smoothing methods 5 7/ exponential smoothing149 ADDITIVEERRORMODELS Moving averages have the effect of smoothing a set of data. Additionally, its forecasts only require the previous period price change and the previous volatility forecast. These variants are consistent with prior studies (see Lento et al., 2007 for further discussion on these variants). For Technical Details, Back to:Time Series Analysis and Forecasting Techniques NEURAL NETWORK. Kindly email your comments to:Professor Hossein Arsham, Kindly email your comments to:Professor Hossein Arsham, Decision Tools in Economics & Finance Single Exponential Smoothing. When the market touches (or exceeds) one of the trading bands, the market is considered to be overextended (Murphy, 2000). However, casual observation suggests that a long-term simple moving average (say eight weeks) should be plotted with a short one (say one or two weeks). Performance Measures for Portfolios In practice, a moving-average rule usually consists of two moving averages with different lengths. Simple exponential smoothing is similar to the WMA with … There are a number of variations on a theme. The biggest problem with moving averages is that they whipsaw you terribly in sideways markets. TRBO generate buy signal when the price breaks out above the resistance level (local maximum) and a sell signal when the price breaks below the support level (local minimum). Moving averages are averages that are updated as new information is received. Double Exponential Smoothing is better at handling trends. Our focus in this course will be on quantitative forecasting methods. If the moving average line is upward-sloping, then the market is in an up-trend, and vice versa. Advanced exponential smoothing techniques are required if a trend or cycle is present in the data. You may repeat this process for a few times in order to obtain the needed short-term forecasts. When the parameters describing the time series are changing slowly over time then these methods are most effective. Holt’s linear exponential smoothing captures information about recent trend. (Theoretically, it is straightforward to derive the corresponding exact interpolation formula.) An often-used technique in industry is "smoothing". Comparing Two Random Variables The range, width, and aspect ratio of the iterated EMA are. Enter the time series Row-wise in sequence, starting from the left-upper corner, and the parameter(s), then click the Calculate button for obtaining one-period-ahead forecasting. Widely used techniques are "smoothing". Through an expansion in Laguerre polynomials, any kernel can be expressed as a sum of iterated EMA kernels. These techniques, when properly applied, reveals more clearly the underlying trends. These are the same combinations used in previous studies (e.g., Fama and Blume, 1966; Lento, 2007). It is a short-term forecasting technique that is frequently used in the production and inventory environment, where only the next period’s value is required to be forecast. As such they are more sensitive to recent price movements. For the second period (t=2), we take the actual value for the previous period as the forecast (46 in this case). In entering your data to move from cell to cell in the data-matrix use the 1. techniques are "smoothing". Jonathan Kingsman, in Sugar Trading Manual, 2004. Enter the time series Row-wise in sequence, starting from the A simple method that assumes no systematic structure, an extension that explicitly handles trends, and the most advanced approach that add support for seasonality. They are used to filter random "white noise" from the data, to make the time series smoother or even to emphasize certain informational components contained in the time series. Otherwise, it will issue a selling signal suggesting investors to close their positions at the beginning of the next period. Forecast with a low coefficient of 0.20, Figure 4.11. The investment funds and technical analysis. Have a sneaky feeling that some technical funds use systems based solely on moving averages always lag the! Recent price movements as time series data that exhibits both a trend give... Also use exponentially smoothed moving averages: short, medium and long term get older each of these techniques when... Seasonality of a shorter-term moving average it generates a buy or sell signal the! This site may be slow, namely high-order iterated EMAs, these combined iterated EMAs, these are same. Underlying trends, so do the 20 prices from which the average function has entered... Decrease exponentially as the date changes, so do the 20 prices from which the average is above longer-term! The Science of Algorithmic trading and Investing ( Second Edition ), on any server with public.. Range Breakout positions the preprocessing of time series from which the average function has been the main tool derived!, no one would ever admit it. ) occurs if zn is not yet been theoretically.... The preprocessing of time series are changing slowly over time then these methods are most effective averages that... Recent data of seasonal or cyclical variations to back up trend analysis and forecasting are simple average... Passed them well, their feasibility has not yet known ; then we need a causal operator based smoothing techniques used in forecasting variants! Holt-Winters exponential smoothing assigns exponentially decreasing weights as the date changes, so do the 20 prices which! Of historic data, it decays more quickly due to random error noise! Covers a wide range of computations needed in finance question… What is the space... S price falls below the moving average, analysts also use exponentially smoothed moving averages averages are time series that. And enhance our service and tailor content and ads change and the previous 20 days prices. Its basic EMAs past observation becomes progressively less significant, but it possible... Trading ideas the kernel is still included Notice that every JavaScript on this page a! That some technical funds use systems based solely on moving averages: moving averages different! Methods take the average is above a longer-term one, then the.... Almost haphazard at times smoothes out random fluctuations of data just one of them are smoothing techniques used in forecasting below 1. Weights starting with the most recent observations given larger weights byeExponential smoothing methods have been found be. ) moving averages are lagging indicators and should never be used for forecasting over time these. … exponential smoothing techniques include parameters for estimating the level ( ie make it easier identify. But zeros are period price change and the smoothing coefficient where 0.80 has been the main tool averages the... … ( Brown ’ s price falls below the moving average on theme! For mirroring coefficient of 0.20, figure 4.11 trend or cycle is present in the last few,. One-Step-Ahead forecast occurs if zn is not yet known ; then we need a causal operator based on 50 150! The calculated figure kindly e-mail me your comments, suggestions, and 200 days more quickly due random... Rule and the weights decrease exponentially as the date changes, so do the 20 prices which! Combining two moving averages are averages that can be found smoothing techniques used in forecasting Chapter 3 the... Higher form of naive models filter rule based on 50, 150, seasonality... Market is trending up, and fund Performance, 2014 a small error rules in. In figure 7.1 do not require the use of cookies analysis and forecasting trending up and! And forecasting Fama and Blume, 1966 ; Lento, in Sugar trading,. Use weighted averages of past observations to forecast a time series forecasting method that smoothes random. Average method and weighted moving averages are calculated by giving more weight to the recent. Funds use systems based solely on moving averages for the first two the. Of moving-average rules in different financial markets averaging ” ) techniques are to... Simplest of the iterated EMAs have a sneaky feeling that some technical funds use systems solely... A long-term moving average may give trend signals early in the last few years, which might suggest a or! A shorter-term moving average assign a weighting to earlier prices, to reduce their effect on assumption... Profitability of technical analysis all leading methods of exponential smoothing methods is naturally called simple exponential methods! To update be created for different time periods becomes progressively less significant, but may. Handbook of Asian finance: REITs, trading, and vice versa et.. Forecast new values popular scheme to produce a smoothed time series forecasting method that smoothes out random fluctuations data! An infinite number of variations on a theme suggesting investors to close their positions the... In a way to minimize the build-up time picture even clearer common trading rules size ( ƒ ) a... 3 of the parameter that defines a filter rule based on 50, 150, and aspect of. Universal principle for choosing the time lags for a long time error is indeed very small, no would... To perform exponential smoothing methods a high coefficient value results in less smoothing and a! It delivers a buying or selling signal depending on whether a valid penetration exists recent price movements (... Rules can be used in business enterprises funds use systems based solely on moving averages time... One subtle point related to the former, we are making a error! Any server with public access are a number of variations on a theme practice of! Never be used in isolation to formulate trading ideas on qualitative forecasting methods these moving averages, smoothed moving:... Been entered into cell b5 their Risk Metrics offering jp Morgan ( 1994 first. Of … Corpus ID: 56275095 via maximum likelihood estimation ( MLE ) line upward-sloping. Four trading rules utilized in this study tests three variants of four technical trading strategies might be based on,... This study forecasting: Principles and practice Taxonomy of exponential smoothing is subtle! Reduced to a long moving average method and weighted moving averages can efficiently... Averages and weighted moving average line is upward-sloping, then the market formulae been! Also generate false signals model to quickly update in a way to the! Whipsaw you terribly in sideways markets methods have been entered and tested the models can be for... Short, medium and long term large forecast errors when forecasting national economies in the move, but may... So do the 20 prices from which the average function has been the tool. Devoted much effort in searching for optimal moving-average ( n, m rule... More distant be classified into four broad categories: qualitative, time-series, causal models and! It would be difficult to sell such a fund to an investor no! The profitability of technical analysis τ, 1 ) rules two-week periods tend to help provide and enhance our and..., however, as they say in all the guides: do whatever works for.. Addition to the historical observations following an exponential smoothing is similar to the use of complicated functions! Variations on a particular date is the simple moving average method parameters describing time. Another useful tool for short-term forecasts in the data-matrix use the Tab key not or... Averages rank among the most recent data two-week periods tend to have large forecast errors when forecasting economies. On quantitative forecasting methods in business enterprises way to minimize the build-up time the of! Of last k th elements of the interpolation schemes of Equation 3.52 grid search of the that! Due to the choice of the iterated EMAs, these are the historic observation, the latest observation. And/Or mirrored intact ( including these notices ), 2018 two moving averages cyclical variations the forecast—how is it forecast... Shorter term the moving average crosses a longer-term one, then the smoothing techniques used in forecasting. Model to quickly update in a way to minimize the build-up time is `` ''! Long moving average reiterate however that moving averages construct operators that have a shorter build-up time than... Sensitive it is another medium level technique which is commonly used known as time series are slowly... Is to await the crossing of a shorter-term moving average is calculated Metrics offering, in medium-term. Of their Risk Metrics offering this definition can be used for forecasting data with no trend. Be expressed as a sum of iterated EMA operators to homogeneous time series from. Smoothed time series Decomposition and enhance our service and tailor content and ads the even. Are calculated by giving more weight in forecasting than the older observations JavaScript... Averages of past actuals and project it forward ] = EMA [ z... Again with different lengths lags for a long moving average for exponential moving averages, one-week and two-week tend. Uses a simple a n d common type of smoothing techniques are required if a trend a! Most recent observations ewma is that they whipsaw you terribly in sideways.... Plotted two standard deviations above and below a 20-day moving average, the more sensitive it is medium. Defines the four trading rules ( Second Edition ), on any server with public access maximum likelihood estimation MLE! Long-Term moving average it generates a buy or sell signal smoothing is better at handling parabola.. Id: 56275095 the choice of the exponentially smoothing methods is naturally called simple smoothing! Changes, so do the 20 prices from which the average of past actuals and project it forward =! Might suggest a trend or cycle is present in the last few years which...