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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Detailed derivation of Multiplicative and Additive Holts & Winter triple exponential smoothing forecasting variance
I'm not able to found any website or textbook or scientific paper with the detailed derivation of of Multiplicative and Additive Holts & Winter triple exponential smoothing forecasting variance...
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Exponential Averaging using Simple averaging
Mathematically what is the expression that is close to a 10 Day Exponential moving average (span of 10 means decay factor of 0.818181) that is created using averaging over Simple moving averages. E.g. ...
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Check exponential smoothing forecasts for significant changes
Suppose I have a time series that I model with double exponential smoothing as implemented in the R package forecast via the ets ...
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Mixed Effect Regression and Time Series Data
I have $5$ groups containing $30$ people. Every week, a person in a group plays a person in the same group at a game (so $15$ games in total for the entire group, but only one per person). This goes ...
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Implemented model over the smoothing value in timeseries
I am working with the demand forecasting project using time series. The problems is that there are too many items that need demand forecasting model. So I want to use the most general ways that can ...
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Holt-Winters forecasting method
Holt-Winters forecasting equations for quarterly observations are
$\alpha_t = \alpha.\frac{y_t}{s_{t-4}} + (1-\alpha) . (\alpha_{t-1} + g_{t-1} )$
$g_t=\gamma.(\alpha_{t}-\alpha_{t-1})+(1-\gamma).g_{t-...
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Holt-Winters and multiple seasonal components
My use case involves daily data, in which there are both weekly and monthly seasonal components. Can Holt-Winters be applied in this case, or be easily adapted to handle multiple seasonal components?
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exponential moving average taking into account different time intervals
i want to calculate the exponential moving average with the following formula
EMAt = valt * α + EMAt - 1 * (1 - α)
but i don't have all the data, i only have some data with a big gap in time. while ...
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Confusion between the meaning of seasonality and seasonal patterns in time-series forecasting
According to Forecasting: Principles and Practice
Seasonality is always of a fixed and known frequency.
If it is a fixed and known frequency, does that mean every series with monthly or quarterly ...
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Predicting the date of the next action from previous dates
I have the date in which a customer made the last purchases. What approach could I use to predict the date of the next purchase?
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Why does Exponential Smoothing model on all data produces NAN forecasts when given parameters from Training and Testing model in Python s
I am using statsmodels.tsa.holtwinters.ExponentialSmoothing to perform Holt Winters' Additive method, first on training dataset and later on the whole dataset. After training and testing, I take the ...
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How to apply exponentially decaying weights to converge PD estimates after 4-5 (or 7-10) years?
I have conditional Probability of Default (PD) estimates for 5 risk grades and for 6 year horizon using Markov Chain. I need to calibrate the first year to long run average and therefore change the ...
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Forecasting - Review Volume & Average Rating
I just want to confirm -
our review volume has an upward trend but no seasonality. I can use holt's exponential smoothing. Right?
for average ratings, no trend, and no seasonality. simple exponential ...
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Method to model exponential fit line coefficients based on main function parameters
I have a quite complicated trigonometric equation I was able massage into a parametric function that takes four parameters as inputs/arguments, say: $a$, $b$, $c$, and $d$. Regardless of the ...
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What is $h$ in the Holt-Winters model as denoted in Hyndman, R.J., & Athanasopoulos, G. (2018)?
The Holt-Winters additive method model is defined to be
\begin{align*}
\hat{y}_{t+h|t} &= \ell_{t} + hb_{t} + s_{t+h-m(k+1)} \\
\ell_{t} &= \alpha(y_{t} - s_{t-m}) + (1 - \alpha)(\ell_{t-1}...
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How to fix exponential smoothing straight line with R
I'm a novice in using R and in forecasting. Right now I'm using a dataset with daily precipitation(mm) data from 2001 to mid 2022.
Using STL decomposition seems to suggest the data has a yearly ...
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How to use the initial values computed for the Holt-Winters model to update the model to time t=n?
I have followed the technique for determining the initial level, trend and seasonal components for the Holt-Winters model as detailed by Rob Hyndman on https://robjhyndman.com/hyndsight/hw-...
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Calculating the Standard Deviation for EWMA
I'm building an EWMA chart based on the predicted mortality of patients admitted to hospital. I'm working with some previous R code to calculate the standard deviation of the EWMA which work, but I ...
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Exponential time series model usecases
When do we need to use following ETS models: additive seasonality model, multiplicative seasonality model, additive error model, multiplicative error model?
Is there any study available regarding when ...
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Time series model in production - Re-train on the fly as as batch process?
Let's say I've a time series of phone calls per day over the last three years. I could train a model using exponential smoothing (e.g. HoltWinters) for predicting the future amount of phone calls per ...
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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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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:
$$l_t = \alpha\frac{y_t}{s_{t-m}} + (1-\alpha)(l_{t-1} + b_{t-1})$$
$$b_t = \beta^*(l_t-l_{t-1}) + (1-\beta^*)b_{t-1}$$
$$s_t ...
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Problem with ets function diagnostic for model with trend and seasonality
I have been meaning to fit an exponential smoothing model to a monthly series that looks like the one below:
When I decompose the series it is almost evident that we have seasonality and also there ...
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What to do when model fails Ljung-Box test?
I have been learning time-series forecasting recently and I am trying to understand the procedure. I would like to find the best model for a daily time series, so far I tried exponential smoothing ...
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Estimating average of a random variable with lower variance is faster to converge than a variable with higher variance?
I have a fallowing problem:
I have to estimate average of 2 random variables $X$ and $Y$ based on average of two other. Where the $X$ and $Y$ are some $n$ by $n$ matrices.
$$
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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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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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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