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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Choice of time-series model for store sales prediction

I have a data set of weekly sales for a range of stores (all belonging to one company). I am trying to predict weekly/monthly use of several ingredients in the individual stores. The choice for what ...
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Best practices for dealing with shifting, inconsistent seasonality

This question is related to a previous post I've looked at (Calculation of seasonality indexes for complex seasonality), but deals with more granular data (daily instead of weekly), and transforming ...
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How to learn beta in (this)variation of Brown's Simple Exponential Smoothing?

I have the below equation: Y' = Y + β Y1 + β^2 Y2 + β^3 Y3 This is time-series data where ...
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0answers
135 views

Holt-Winters: Can I use more than one seasonal cycle for SSE minimisation?

I am minimising SSE to estimate the parameters and starting values for a Holt-Winters model. I.e. "forecasting" the values using different parameters, measuring the sum of squared errors of these "...
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0answers
698 views

Exponentially Weighing Moving Average (EWMA) for weekly data

I'm aware that the typical EWMA approach is applied over larger time periods (say for Volatility, where lambda = 94% and all weights add up to 100% for stock returns data from last 5 years). ...
3
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0answers
233 views

How to select the exponential decay constant for weighting in proc logistic?

I am trying to predict the sales conversion using proc logistics in SAS. Right now I have around 3 months of data, and it will gradually grow to more than an year over time. My intuition is that the ...
3
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0answers
410 views

Exponential moving average with sub-interval relevance / varying timeframe

I need to calculate an exponential moving average for a series of data. The intended sampling interval is fixed (say 1s) but the data stream has varying intervals (data intervals vary from 0.01s to ...
2
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0answers
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 ...
2
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30 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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0answers
274 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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258 views

How much do the parameters in the Holt-Winters model matter?

When fitting a Holt-Winters model, I usually take the approach of retrospectively "predicting" some known historical values for the series, and optimising the coefficients for the parameters by ...
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0answers
474 views

Alternatives to Holt-Winters models when the seasonality pattern has changed

I am forecasting a series of daily volumes in terms of units processed for a particular time period (the period around Christmas). Historically, I have used a Holt-Winters model, with the minor ...
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0answers
254 views

Adjust decay rate dynamically

Say I have a stream of values $\langle s_1, s_2,\ldots\rangle$ coming in and a function $$E_{s_1:s_n}(t) = E_{s_1:s_{n-1}}(t-1) + \alpha\cdot (s_t-E_{s_1:s_{n-1}}(t-1))$$ that compute their ...
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Does it make sense to think about steady state forecast error for Kalman filter with time-varying parameters?

The environment: We have a state equation: $$ \xi_t =F\xi_{t-1} + v_t $$ and a measurement equation $$ y_t = H\xi_t + w_t $$ with $$ E\Bigg[\begin{pmatrix}v_t\\w_t\end{pmatrix}\begin{pmatrix}v_t'&...
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3answers
485 views

Can simple exponential forecasting be used for a non stationary series?

I have a non stationary series with trend and seasonal components. I want to use simple exponential smoothing ONLY for forecasting. Does the series need to converted to stationary before using SES? If ...
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0answers
27 views

'Level' still seems periodic after Season Decomposition

I've used tbats for this transformation: Exponential smoothing state space model with Box-Cox transformation, ARMA errors, Trend and Seasonal components My (...
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0answers
825 views

pandas.ewma to be used to make prediction

I would like to implement EWMA to be able to make prediction based on historical data. I am using EWMA in pandas. After playing with com and span, it seems like predictions are not based on ...
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981 views

R: Calculating prediction intervals (95%, seasonal naive and holt winters)

Could somebody explain to me the theory behind how R calculates the 95% prediction intervals for my 12 step ahead forecasts in (1) a seasonal naive model and (2) a Holt-Winters forecast. My code is ...
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Constant in arima model whether to include or exclude?

I have a very basic question on including constant in Arima models. I'll illustrate this by an example. I have the following ACF and PACF of a weekly time series that is differenced at lag 1 (trend) ...
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833 views

Which method of implementing the Brown's linear exponential smoothing is correct?

I am trying figure out what is the difference between Brown's linear model for double exponential smoothing and Holt's model. So the differences can be implemented into a Holt model using if ...
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0answers
3k views

How to derive the variance of a weighted moving average?

I have a problem understanding a piece of a paper. Greatly appreciate any hint or help. It says: A sensor records $Z(i)$ at intervals of 1 second and calculates background values $U(i)$ using ...
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96 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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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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0answers
1k 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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1answer
99 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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109 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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206 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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41 views

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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106 views

What does the ACF tell me here?

I have a time series of monthly sales data that is incomplete. That is, the product was partly out of stock and the sales of those periods are too low. I manually fixed this and wanted to plot the ...
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80 views

What to make of a declining amplitude of a time series trend?

I am forecasting demand using the Holt-Winters model for a particular product class. I have been examining its performance so far this quarter (I only ever forecast Q4), and was surprised to note ...
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0answers
64 views

Forecasting a series with changes in growth rate

I have a particular time series (demand in units for a particular product category), which I forecast each year (specifically, at/for Christmas, although the data runs all year round. Historically, ...
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206 views

How is the Ornstein-Uhlenbeck process related to the error of an exponential moving average?

Is anyone aware of a direct relationship between the residual of an exponential moving average and the Ornstein-Uhlenbeck process? For example, assume a series, $Y_{t}$, that follows a geometric ...
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417 views

Does “level” in exponential smoothing stand for the “mean”?

In triple exponential smoothing it is said that there are estimates for 3 components: level, trend and seasonal. Does "level" here stand for "mean"? In single exponential smoothing is only the level ...
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216 views

How come Exponential Smoothing without trend producing astonishing results when there is trend in the time series

I have a time series and a plot of it is presented below for consideration. A linear trend was identified in the series both visually and using statistical tests such as Cox-Stuart and ManKendall. ...
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862 views

Holt-Winters Method & Triple Exponential Smoothing

what the different about HW method & triple exponential smoothing? Some people say it same. but I still confused about the formula, its look the different.. Please help me, I need for my first ...
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64 views

Formula to estimate parameter in double seasonal exponential smoothing

I have read the Taylor's Journal of double seasonal exponential smoothing, in his journal he said that the parameter of double seasonal exponential smoothing is estimate by the common procedure of ...
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231 views

smoothing nodes values on a graph given adjacency matrix

I am currently looking for a method to smooth values on a graph (composed of vertices and edges). For example I have a graph with a set of nodes V and I want to be able to smooth it. I could have ...
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0answers
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Improving Python Exponential smoothing

I am going to improve my code to the Exponential smoothing I submitted to Statsmodel which can be found here. The code handles 15 different variation Standard Exponential Smoothing models including ...
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Time series Exponential smoothing by Holt winters method

I have basic questions with respect to exponential smoothing techniques, from statsmodels.tsa.holtwinters import ExponentialSmoothing add_model = ExponentialSmoothing(traindata,seasonal_periods=12 ,...
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Forecasting method for different cohorts with large seasonal swings but otherwise stable data

I am attempting to forecast percentage of churn for different cohorts. However, I am unsure how to proceed after selecting an initial method. The churn is fairly stable except for large seasonal ...
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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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22 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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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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34 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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1answer
107 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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0answers
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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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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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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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67 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 ...