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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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69 views

Does smoothed data work better for time series forecasting with LSTMs?

I am training a 3-layer LSTM on time series data ($10^6$ training samples) to predict the next point in the time series, where there is no seasonality and the time series has been made stationary (...
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time series forecasting - predicting the next 24 hours

I have much the same problem as predict-the-next-24-hours, I have several years of hourly data of demand, and I would like to predict the next 24 hours. Ignoring the multi-seasonality issues - is it ...
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why is the level equation in the holt winters triple exponential model different from the other two?

the double exponential model is so simple: level: $s_t = \alpha x_t + (1-\alpha)(s_{t-1}+b_{t-1})$ trend: $b_t = \beta (s_t - s_{t-1}) + (1-\beta)b_{t-1}$ both intuitively weigh the new information ...
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Incorporate recent drop in number of units sold in a forecast using exponential smoothing

I'm trying to generate a one-year forecast for the number of units sold by a retail company. I'm using monthly data from 2017 and 2018. The forecast is for 2019, and I'm using the data from the months ...
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Is Box-Jenkins approach to time-series prediction and forecasting similar to Unobserved Components models approach?

How I understand the Box-Jenkins Method in a nut-shell is that a time-series model has signals that can be identified by weighting its own past lagged values, or weighting its owned past errors or ...
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16 views

Hyperparameter-free method for Moving Average/ Exponential smoothing?

I want to find hyperparameter-free method for Moving Average/ Exponential smoothing. Is there any related paper or python code? S(t)= alpha * F(t) + (1-alpha) * S(t-1) Any methods can avoid the ...
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38 views

Question about the weighting factor of Exponential Weighted Moving Average (EWMA/EMA)

Hiii, I have one question about the weighting factor of EMA. As I learned, Exponential Weighted Moving Average has a weighting factor, Lamda, and its formula is: S(t) = Lamda * Y(t) + (1-Lamda) * S(...
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Closest ARIMA models to Holt-Winter's Mixed Model and Time Series Decomposition Models

Can you please tell which ARIMA model will be closest to Holt-Winter's mixed model and Time Series Decomposition (additive/multiplicative) models And that ARIMA model maybe used in replacement of the ...
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2answers
42 views

How do I compare time series forecast models? (ARIMA vs HoltWinter)

I'm working on a toy problem to try and get a better understanding for time series forecasting. I have a sample data set, which I'll include, that shows daily e-commerce sales from 2015 through Feb, ...
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28 views

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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37 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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93 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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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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898 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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82 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
66 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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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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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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61 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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29 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
100 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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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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368 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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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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277 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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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
254 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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36 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
405 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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189 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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195 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
712 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
36 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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258 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
2k 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
308 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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96 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
89 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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662 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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298 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
80 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
989 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
196 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
844 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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6k 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 ...