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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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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17 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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35 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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18 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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38 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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20 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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24 views
Comparing two sets of exponential data $T(t)=−e^{−kt}$
I have two sets of exponential data (temperature measurements) of the form:
$T(t)=−e^{−kt}$.
k is a constant that determines the rate of temperature change. 1 temperature measurement was taken every ...
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3answers
152 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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25 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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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
29 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
110 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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29 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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188 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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65 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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83 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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0answers
20 views
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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Simple Forecasting methods like SES
Please have a look at the below chart. It seems stationary to me. I didn't apply any transformations and the original data itself is stationary.
Can you suggest a time series plot.
I tried SES, but ...
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1answer
280 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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What is the correlation between the order $\ N$ of a moving average process and the exponential smoothing factor $\alpha$?
Suppose you have a constant forecasting model, $\ X_T(\tau)$ for $\tau$ steps ahead at origin $\ T$ such as
$\ X_T(\tau)$ = $\mu + \epsilon_t$
and that $\ â_1$, the estimator of $\mu$, is a moving ...
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1answer
17 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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124 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
750 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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57 views
Implementation of Holt-Winters method for forecasting
This is regarding a simple implementation of Holt-Winters method for
forecasting.
Referring to this table :
This data this is based on is :
...
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14 views
Forecast with 2 time dimensions/Split forecast based on 2nd time dimension
My data Set consist of: Customer, Pay Month, Serv Month, Amount
where
Pay month is the actual calendar month of payment
Serv month is the service month
Data buckets -
Current Payment >> when Serv ...
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0answers
68 views
EWMA for financial time series
I'm trying to use ewma for outlier detection on financial time series historical data, but I am not able to apply the ranges at the term structure levels.
Is there a way I can identify outliers at ...
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1answer
130 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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163 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
63 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
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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
1k 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
558 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
216 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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113 views
When aggregate forecasts (yearly) matter: model choices and data frequency?
I'm attempting to build models for numerous time series (all are of the same frequency and periods, but for different countries) in order to forecast values 1-4 years into the future. The data goes ...
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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
75 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
419 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
1k 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
118 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
537 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
4k 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
224 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
496 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
1k 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
170 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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0answers
200 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 ...
