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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Tuning ARIMA/ETS for univariate time series

I am running auto.arima/ETS models from the forecast package in R on monthly seasonal time series. I see the following fitted ...
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Variance for exponential smoothing

I want to obtain the analytical expression of variance for simple exponential smoothing . Please help verify and see if the expression could be further simplified , thanks . Assume the discrete time ...
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Fixed-leg Kalman filter smoother (Rauch–Tung–Striebel) error bounds

Although very intuitive and with plenty of results that talk about the asymptotic convergence of the estimate I wasn't able to track down any paper stating explicitly convergence bounds based on the ...
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Does seasonality frequency matter in exponential smoothing?

I'm pretty new to time-series forecasting and I hope that someone could help me out. Referring to Holt-Winters' multiplicative method in https://otexts.com/fpp2/holt-winters.html, how does frequency ...
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Exponential fitting in R with fixed minimal value

I need approximate datapoints by exponential function with some type of lower limit (variable "y" is price in time and I need fixed minimal value, so asymptote of exponential function cant ...
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Good libraries for exponential time series smoothing

I've a pandas series which contains the daily load consumption of a city for a year. I wish to forecast the load consumption for next year.As a result , I'm making use of exponential time series. The ...
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Why does the level update equation change in triple exponential smoothing (but the trend equation does not)?

I'm confused on the level and seasonal update equations in Holt-Winters (aka Triple) Exponential Smoothing. Namely, the equations are as follows (in additive form): Level: $l_t =\alpha(y_t - s_{t-m}) +...
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How is the decay rate in exponential smoothing optimized?

For the sake of simplicity, I just want to focus on single/level exponential smoothing. When alpha, the decay rate, is near 1, the most recent observation has the highest weight and influence of ...
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How is the recursive function in exponential smoothing evaluated?

In exponential smoothing models, the most recent observation is weighted most heavily, while observations further back receive a smaller and smaller portion of weight. An alpha parameter will inform ...
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Correct form of multiplicative Holt-Winters

In forecasting principles and practice, the update equations are given as: $$l_t = \alpha\frac{y_t}{s_{t-m}} + (1-\alpha)(l_{t-1} + b_{t-1})$$ $$b_t = \beta^*(l_t-l_{t-1}) + (1-\beta^*)b_{t-1}$$ $$s_t ...
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Problem with ets function diagnostic for model with trend and seasonality

I have been meaning to fit an exponential smoothing model to a monthly series that looks like the one below: When I decompose the series it is almost evident that we have seasonality and also there ...
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What to do when model fails Ljung-Box test?

I have been learning time-series forecasting recently and I am trying to understand the procedure. I would like to find the best model for a daily time series, so far I tried exponential smoothing ...
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Rolling average plus exponential weighted average - Crazy?

Hi I am trying to predict covid data with neural network models for a Uni project. The covid death data is not reported in Scotland so a 7 day rolling average is definitely needed. No smoothing: 7 ...
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Combining Linear Regression and Exponential Smoothing

I am working on a forecasting model that predicts inventory levels of a certain item based on how far behind our production line is predicted to be on a given day. EDA showed a high level of ...
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Estimating average of a random variable with lower variance is faster to converge than a variable with higher variance?

I have a fallowing problem: I have to estimate average of 2 random variables $X$ and $Y$ based on average of two other. Where the $X$ and $Y$ are some $n$ by $n$ matrices. $$ X = 0.5\cdot(A+B) $$ $$ Y ...
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Hyperparameters of Exponential Smoothing

I have a large number of time series to forecast on which I would like to evaluate the potential of Exponential Smoothing. However, I am faced with a problem of parameter selection: I dont know how to ...
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Appropriate forecasting methods for only 20 observations [duplicate]

I am trying to forecast the regional GDP growth of our region in the next five years, I only have 20 observations in my data which is yearly, what forecasting model is appropriate? I tried ARIMA in r ...
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Check residuals---HoltWinters forecasting?

Currently I am forecasting for my master thesis. This forecast has been made with HoltWinters. However the graphic seems to be "weird" to me. Anyone some ideas?
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AIC comparison between ETS and ARIMA

I was wondering is it relevant to compare AICc on training set between ARIMA and ETS method.
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Differentiating data before exponential smoothing?

I know that to perform exponential smoothing you don't have to make your time series stationary, but I seem to get better results when I do it. Do you know anything about it?
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(How) Can you combine moving average and exponential smoothing filters to get smoother trends?

Goal: Have a machine perform smoothing on time series data set to have a smooth looking trend. The correctness of the trend is balanced by being optimal i.e., minimize the MSE (Mean Standard Error). ...
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Point Estimates using forecast in R for Multi-Step TS Forecast -- Sometimes Same/Sometimes Not -- Why?

I am using the simple forecast(data, h = 6) function in R - as I work through Hyndman's 'Forecasting: Principles and Practice" textbook - which returns forecasts from the ETS algorithm. I'm not ...
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Why does the exponential moving average equation divide with 1+(1-⍺)+...?

I am trying to understand an exponential moving average, reading its Wikipedia page: https://en.wikipedia.org/wiki/Moving_average#Weighted_moving_average In the middle of the explanation, the page ...
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What does span mean in exponential moving average?

To borrow from the documentation of pandas' ewm function: the center of mass, span, halflife and alpha of an exponential moving ...
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ets() function does not minimize AICc?

I have a question that is similar to this question: ETS function in forecast package is not choosing minimized AICc I see what the author of that question misunderstood but I basically have a reverse ...
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Performance of Holt-Winter´s seasonal method is different from Python to Excel

I have to code the "Forecast.ETS" function from excel in Python to predicts a future values based on existing (historical) values. In the Excel documentation they write that it is based on ...
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How to decide seasonality Period with 1 year Weather Data?

SO I have 1 year wind Data below composed of 365 daily data, I also tried to decompose it. I tried to do Holt-Winters Exponential smoothing. My plan was to forecast the last 2 months from the data. I ...
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Smoothing factor in $n$-day exponentially weighted average

I have read online that if we want an $n$-day exponentially weighted average we use the formula $$ \alpha = \frac{2}{n+1} $$ My question is why is this the case? Does this choice of factor turn out to ...
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Forecasting: AIC, AICc and BIC VS Cross Validation for model selection (cases for different horizons)

The majority of the automatic model selection algorithms like auto.arima and ets (https://robjhyndman.com/publications/automatic-...
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How to correctly transform a log-log graph into untransformed exponential graph?

I plotted my data on a natural log-log scale and I seem to get a okay fit to the data with y=1.19 - 0.116x with Rsq = 0.29 I want to use the parameters but plot the row data with an exponential curve....
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Forecast is simply equal to the lag of the original time series

I am currently dealing with the problem of short time series which often involves naive models as they already perform well enough. So I implemented an exponential smoothing that follows $$ F_t = \...
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How do I identify if my time series' seasonality is additive or multiplicative?

The "ExponentialSmoothing" function in Python's "statsmodels.tsa.holtwinters" library gives you the option to set trend equal to ...
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What do the values for initialization method mean in statsmodels simple exponential smoothing?

I'm trying to use Statsmodels' simple exponential smoothing for time series analysis. There are various methods available for initializing the recursions (estimated, heuristic, known). Can someone ...
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Trend Dampen with SARIMA

Trend dampen exists as a parameter for Holt-Winters in the ExponentialSmoothing class for statsmodels but how can I do something ...
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Why does prophet produce much tighter prediction intervals than ETS?

I'm currently working on a forecast problem, where narrow prediction intervals are preferred. When I look at the prediction intervals of ETS and prophet forecasts, I'm surprised that the prophet ...
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Low value on MAPE when using log CPI

I'm trying to evalute my Holt-Winter model using MAPE (mean absolut percent error) and I'm getting a low value at 0.2% which seems a bit too low. I'm using data on CPI from Belgium (per month) where I ...
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Is the Elo "rule of 400" a variation on EWMA?

tldr: The Elo rule looks like an ewma-style running average to me. Is that right? Details: The Elo rule of 400 (here) could be expressed this way: $$ rating_{N} = \frac{1}{N} \Sigma_{i=1}^{N}\left( ...
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What is the lag associated with Moving Average smoothing?

In a tutorial I came across this: "Recall that the forecast value is: $\hat{y}_{t+1} = \frac{y_t + y_{t-1} + ... + y_{t-m+1}}{m}$ It's worth pondering that formula for a minute. While easy to ...
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Analysis of housing price data with strong trend and seasonality

I am new to time series. I have monthly Zillow data from Chicago. Trying to build three good models here. Tried to make it stationary, but failed. If I understand correctly, I need to remove the ...
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Calculating EWMA & EWMV of concurrency from duration & interval

I'm looking to calculate the exponential moving average & exponential moving variance of a continuous series of request/responses, using each response's duration and the interval (time delta) ...
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How's the seasonal adjusted series calculated in Holt Winters method?

In the text book Forecasting: Principles and Practice in Exponential Smoothing chapter there is this part * ".. With the additive method, the seasonal component is expressed in absolute terms in ...
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ARIMA, Simple Moving Average, and Exponential Smoothing [closed]

I have time series data about a museum visitors in each month since 2011 to 2019. This data has seasonality. If I want to forecast the visitors in 2020, what forecasting method I should use? ARIMA, ...
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Can I hybridize between ARIMA model and exponential smoothing?

I have a time series that stabilized at the first difference (d=1) and the model was ARIMA(0.1.0), as I know it is a model that does not really predict. In this case I relied on hybridization as ...
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EWMA covariance matrix number of lags

When calculating an exponentially weighted covariance matrix for t observations, formula 10.2 here: https://www.oreilly.com/library/view/analysis-of-financial/9781118017098/c10_level1_1.xhtml Uses ...
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Exponential Smoothing for many time series

I have a detailed dataset with a lot of time series. If I apply exponential smoothing (using for instance R) it will take me to much time to calculate an $\alpha$ (level parameter) and $\beta$ (trend ...
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Holt-Winters yields same coefficients no matter what seasonality parameter level set to

really appreciate any help, i've been running HoltWinters on data below, using R. Initially i just used ...
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How to improve forecast

I have the number of hospitalizations due to a particular disease and I'm trying to forecast the number of hospitalizations for the next 3 months. I've been reading about ARIMA and time series but I'm ...
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How to calculate the MSE of exponential smoothing model in R?

I have a dataset of the daily stock price and volume, like this: ...
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Rolling Time Period for Exponential Forecast (Holt Method)?

I am curious in which cases (if any) you would force an exponential smoothing function to only incorporate data from the past year? Per Holt method, one would continue to use the full time series as ...
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How to update an ExponentialSmoothing model on new data without refitting

I'm trying to find the correct way to update an already fitted ExponentialSmoothing model on new data. My guess was like this: ...
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