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Questions tagged [exponential-smoothing]

A basic forecasting technique for time series data, optionally including trend and/or seasonality, but (usually) excluding causal influences.

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How to get a forecast equation for $\hat{y}$ using ETS state space model

The ets(AAA) state space model (Rob Hyndman's handbook) is as below State equation is \begin{equation} Y_t = L_{t-1} + b_{t-1} + S_{t - m} + \varepsilon_t \end{equation} The measurement equations ...
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1answer
24 views

Search for optimal alpha in EWMA

All literature about finding the best alpha for a EWMA points to use RMSE to measure the fit between the EWMA and the signal. As alpha increases, the series get less and less smoothed out, and as a ...
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1answer
42 views

Holt-winters method, outlier day of week

Hopefully this isn't too off topic. I've just received test results and disagree with some explanations of a question. The TA and I can't seem to resolve our differences and I'm starting to think ...
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11 views

What is the best calculation method to account for individual change, volatility, observation windows and time decays in time series data? ARIMA, ETS?

I am looking at applying a theoretical best calculation method to some particular time series (ts) data. Ideally the calculation method would encompass relative change in individual ts, volatility of ...
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286 views

Prediction intervals exponential smoothing statsmodels

I've been reading through Forecasting: Principles and Practice. I am working through the exponential smoothing section attempting to model my own data with python instead of R. I am confused about how ...
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53 views

How to forecast individual customer's spend (for millions of customers)?

Which forecasting model fits better to forecast the customers spend in the next upcoming visit? We have millions of customers, so ARIMA or any other time series modeling for each of the customers is ...
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1answer
47 views

method for predicting a curve

I have data on several curves. the data is of the form: curve_id x y and there are many x/y pairs for each curve and x is limited to some known range. overall, the curves look quite similar in ...
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29 views

When we are proving why ARIMA(0,1,1) is equal to simple exponential smoothing, why can we considered theta to be equal to (1-alpha)

I know this is a very basic question, but its not clarified within my lectures. Essentially when you have ARIMA(0,1,1) You can simplify the theta 1 term in order to obtain SES via stating its (1-...
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21 views

Historical average with exponential smoothing model [duplicate]

This topic similar with this one R Time Series Analysis forecast result always remains same But I perfrom exponential smoothing model in R. ...
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43 views

Derivation of Brown's High Order Exponential Smoothing Equations

Can anyone help me to find how the local slope ($\hat{a}_1(t)$) and acceleration ($\hat{a}_2(t)$) equations in Brown's high order (3rd in this case) exponential smoothing is derived? I can easily ...
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25 views

How to tune an exponential smothing function pon implicit feedback collaborative filtering recommenders

I am developing a recommender based on implicit feedback. The feedback is mainly the time someone spends on a product in a day. Then I transform this feedback to a rating matrix in order to implement ...
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1answer
70 views

Understanding Intuition for ETS Damping Selection via AIC/BIC

I'm trying to understand how ETS selects whether to use a damped model via information criteria (I'm not sure which of AIC, AICc or BIC are used). I have a time series and I'm comparing two ETS ...
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24 views

Get forecast after modelling on differenced series

I'm trying to apply exponential smoothing methods for a forecasting exercise in R. Since the data has seasonality component, I differenced and got a time series that is stationary. I tried to perform ...
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3answers
273 views

Negative Forecast using Holt-Winters

I tried to use Holt-Winters for forecasting, but it gives me negative values, but since these are demand quantities they cannot be negative. ...
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94 views

Intuition about Exponential Smoothing parameters?

If I use Triple Exponential Smoothing with Additive Seasonality and let a statistical program optimize alpha, beta and gamma for me, is there something I can conclude about my data based on the ...
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27 views

Any book containing a collection of exponential smoothing papers from 1950s/1960s such as those by Holt?

I would like to read the originally published papers to see how the structure of the equations is justified. I would especially like to read Holt, Charles C. (1957). "Forecasting Trends and Seasonal ...
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175 views

Robust alternative to exponential smoothing?

Despite being easy to calculate and understand, exponential smoothing is excessively affected by outliers and thus performs poorly when the data has a non-Gaussian probability distribution, such as a ...
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1answer
34 views

Can I say Holt-Winters Method is an example of interpolation?

I believe it fits under the definition from wiki: In the mathematical field of numerical analysis, interpolation is a method of constructing new data points within the range of a discrete set of ...
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1answer
168 views

What exactly is the exponential smoothing model?

I see the term "exponential smoothing" model used a lot in different applications but I never understood what exactly it is. Is it just a MA(1) model? Or is it any moving average model, meaning it ...
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32 views

Exponential forecasting with non-constant variance

I want to use exponential forecasting to detect outliers, but my data are means of samples of different sizes. The series was formed by taking the average, every five minutes, of measurements ...
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1answer
311 views

How to handle multiple periods in data when using Triple Exponential Smoothing (Holt-Winters method)?

Let's say I've got the the following time series (duration = 2.5 years) grouped by hour: ...
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136 views

When optimizing $\alpha$ in a simple exponential smoothing model, is there any benefit to using something more sophisticated than least squares?

I am trying to manually implement simple exponential smoothing, for which the formula is pretty straightforward: $\hat{Y}_{t+1} = \alpha Y + (1- \alpha) \hat{Y}_t$ In the original formulation, the ...
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154 views

Strange output while using Holt’s Linear Trend method

Here're the pictures of using Holt’s Linear Trend method: From tutorial (what it should be like): After running the code for my data Isn't it strange? Here's a code (method #5): ...
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Time series when the data are averages of different sample sizes

I am trying to analyse a collection of time series where the observations are averages of different sample sizes. I'm looking at measurements from a high volume system with many users.I get averages ...
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1answer
455 views

What are the prerequisites before running Holt Winters Model?

I just read Demand-Driven Forecasting: A Structured Approach to Forecasting(Wiley and SAS Business Series) and have a few doubts in Holt-Winters Model: 1) Unlike OLS Regression Modeling technique or ...
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1answer
19 views

How to calculate the average age of observations in forecasting models of various types?

Suppose you have a time series $\ Z_t$ that is used as a forecasting model for $\tau$ steps ahead from origin $T$. $\ Z_t$ is defined as: $\ Z_t = 0.05 Z_T + 0.10 Z_{T-1} + 0.15 Z_{T-2} + 0.20 Z_{T-...
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1answer
192 views

Time series forecasting: exponential smoothing, MA, or regression for future observations

Given a set of time series data from 0 to t as $x_t$, we would like to predict time series for t+1 and, say, t+2, using trend $m_{t+1}, ...$ Now, exponential smoothing trend is defined as: $m_{t+1} = ...
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1answer
1k views

Choosing between Holt-Winters additive and multiplicative methods

I am attaching the question, I am solving for context. The sales of the average price of Fiat cars sold in a garage in the Belgian province of Limburg for each month are listed below. The foreman, Mr ...
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3answers
236 views

Positive smoothing with the fda-package (Functional data analysis)

In the book Functional Data Analysis with R (Ramsay&Silverman) there is described the possibility to do the "positive smoothing" if it’s needed instead of the "normal smoothing". In the books ...
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188 views

Strange results while using ets function in R (package “forecast”) [closed]

Below is my code. The forecasts are obviously wrong in both examples. Both functions y and z are decreasing, but "ets" predicts 3 values equal to the last known value in both cases. If I replace <...
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1answer
85 views

Correct formula for converting the ARIMA MA(1) coefficient to the exponential smoothing $\alpha$ parameter?

Two crucial sources for time series analysis differ in a critical formula for equivalence between simple exponential smoothing (SES) and ARIMA(0, 1, 1). From Hyndman's F:PP: $\theta_1 = \alpha - 1$ ...
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1answer
72 views

Does an exponential smoothing model have roots the way ARIMA models do?

I read elsewhere in this forum a comment (which I have since been unable to find again) about Exponential Smoothing models not having unit roots. I (sort of) know how to figure out the roots of an ...
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1answer
2k views

Is it OK to use Holt-Winters to predict longer-term future sales?

I have a full year of 2017 daily sales data and am looking forward to predicting the daily sales for next month. It has strong seasonality of 7, so what I did is to use Holt-Winters to calculate the ...
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1answer
612 views

Are both ARIMA and Exponential Smoothing special cases of State Space models?

From the literature I gather that exponential smoothing models can be recast as special cases of state space models. I haven't seen similar references w/r to ARIMA being considered state space models,...
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1answer
262 views

R - Holt-Winters - irregular frequency

I originally posted this on Stack Overflow, and it was suggested that this question would be better suited for CV: With reference to the HoltWinters function in R, how does one deal with time ...
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What are the differences between two different EWMA estimator?

Someone just showed me a different way of recursively estimating EWMA based on the exponential sum. The estimator has two different recursions: one for the sum and another for the weight. $$ \alpha=e^...
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1answer
78 views

What is a recommended forecasting method for predicting air passenger numbers?

I am doing a forecasting project for school and trying to predict air passenger numbers based on 18 months of historical data from the airport. I have considered applying Holt-Winters seasonal ...
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1answer
697 views

Seasonal or non-seasonal? ETS and auto-arima disagree?

I am working with the following monthly time series to build forecasting models: From this plot, it's quite tricky to identify if there is some kind of seasonality or not. When I use the ...
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1answer
2k views

Holt-Winters prediction intervals

I noticed that the Holt-Winters function in the "forecast" package in R contains prediction intervals. This was interesting, as it is not intuitively obvious to me how prediction intervals could be ...
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1answer
155 views

What data generation process corresponds to exponential moving average prediction?

For each ARMA process formulation, there is an optimal prediction. E.g.: When you believe that $y_{t+1}=\alpha y_t + \varepsilon_{t+1}$, where $\varepsilon_{t+1}$ are IID, you predict $\hat{y}_{t+1}=\...
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1answer
693 views

Level and trend in Holt's linear trend method

I'm studying about exponential smoothing methods and something I still can not understand is the behavior of level and trend components when you increase and decrease level and trend smoothing ...
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2answers
5k views

Time series prediction: Neural Network (nnetar) vs. exponential smoothing (ets)

When I make a forecast for the univariate time series $x_1=1, x_2=2, \dots, x_{14} = 14$, why does the nnetar() function in R (which uses a neural network) not ...
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1answer
323 views

Implementation Difference between HoltWinters and hw functions of R's forecast package

While searing for examples for implementing Holtwinters with R, I came across following two functions: hw function from forecast package HoltWinters function from R-Core For the same data set, ...
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1answer
846 views

Deciding inital values of trend, season and level for Holt winter's seasonal additive smoothing

I am following this for understanding Holt winter's seasonal additive smoothing. I am not able to find any explanation for deciding initial values for trend, level and season for seasonal additive ...
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3answers
2k views

Alternatives to Using ARIMA for forecasting

I've been dealing with mostly univariate time series data and am wondering what alternative models exist for forecasting instead of ARIMA, ARMA, AR and MA processes, I know about exponential ...
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1answer
290 views

Applying EWMA to first difference of a time series

I am trying to fit an EWMA to the first difference but I am unsure how to properly fit the EWMA and how to assess if one model is better than another. I am trying to use the EWMA described in the <...
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Forecasting methods to work globally on a series of datasets

Forecasting a numeric time-series is providing an estimator $\hat y(t+1)$ of $y(t+1)$ computed from $(y(1),y(2)...y(t))$. You want it to be close to $y(t+1)$ (say in terms of squared distance). Now ...
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239 views

Is there any interpretation of parameters in Holt Winters method?

I am doing forecast on time series on R and I use exponential smoothing method Holt Winters. Does a value of $\alpha$ close to $0$ or $1$ "mean" something particular about the series? Same question ...
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421 views

Techniques to improve accuracy of time series use case

I am working on forecasting weekly revenue of 10,000 sectors. Applied basic time series models and average RMSE(in thousands) on hold-out set (last 32 weeks) as below. In my view, ma12 and ETS(ANN) ...