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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6k views

Exponential Regression vs Exponential smoothing

I am very new to statistics (I am programmer). Can you, please, explain is this the same or these are different methods: Exponential Regression (http://www.xuru.org/rt/ExpR.asp) vs Exponential ...
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499 views

Holt-Winters for Imputation

I have found Holt-Winters seasonal method a very decent method for forecast, specifically for cases where more recent observations are more representative of the near future. The method equally sounds ...
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1answer
69 views

Smoothing intraday data when only looking at a certain time range

I have an intraday price series (5 minute) over several months. I want to smooth the data using an ema but also i am only interested in analysing the series between certain time periods eg between 8am ...
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55 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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101 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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76 views

Fitting a nonlinear regression $Y=1 - a^{-bx}$

I have the following dataset: where X:Y 1:0.81 2:0.86 4:0.9 6:0.93 8:0.96 10:0.98 12:0.99 14:0.99 16:1 18:1 20:1 ..:1 Since the limit of the regression ...
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1answer
507 views

How to compare ARIMA and exponential smooting model numerically?

The exponential smoothing method gives us values like SSE and $R^2$ for the entire model. The ARIMA model, however, does not give us these values. So, given the same data, how do one decide which ...
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2k views

time series forecasting using auto.arima and exponential smoothing

I am working with workers’ remittance quarterly data for Bangladesh. Here I am doing time series forecasting using R. I am applying auto.arima model and exponential smoothing model. I want to compare ...
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93 views

Strange results in Holt forecast

I am trying to understand what could be causing these strange values to appear on applying a Holt model to a vector. The data represents actual sales of an item. ...
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385 views

Simple exponential smoothing

I simulated a time series using expressions (3.10a), (3.10b) from (Hyndman et al., 2008). Next, I'd like to use a simple exponential smoothing method to forecast for the next period. For a given ...
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1answer
1k views

Standard error and p-values of exponential smoothing weights

Is there any justfification for producing a standard error of a single exponentially weighted coefficient? If yes, how can we interpret the p-value? Background I use SAS ETS to estimate a single ...
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1answer
114 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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461 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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1answer
3k 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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1answer
911 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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1answer
1k views

Why am I getting flat time series forecasts from most of the techniques?

I have a simple example time series: Data: ...
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1answer
731 views

Why are exponential smoothing forecasts exactly the same for the following 5 days in hourly sampled 30 days data? R ets forecast package

I would like to use exponential smoothing to forecast for 5 days, but forecasts look all same. I have read the documentation of ets package and tried different Additive, Multiplicative model, but ...
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1answer
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Selecting between exponential smoothing models: MAPE or AIC?

I have applied Exponential Smoothing methods on data (Quarterly electricity production in Australia million kilowatt hourly) and then I forecast the accuracy of my models, ...
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608 views

Why are forecasts from ARIMA and ETS equivalents different?

ETS models have ARIMA equivalents - this is described, eg, here and here. However when fitting pairs of ARIMA and ETS equivalents in R I sometimes get different results. For example, compare ...
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1answer
121 views

Interpreting Seasonality Component Exponential Smoothing Models

I am building an exponential smoothing model that has seasonality in it, I would like to analyze the data with the seasonal factor removed so I can tell if a performance one month was due to seasonal ...
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1answer
3k views

Using Holt-Winters formula, how do you choose which seasonality to begin your first forecast period with?

This is probably a pretty basic question but I'd like to understand how you choose a seasonality number for the first forecast period in a Holt-Winters model. If you need to forecast 8 months ahead ...
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1answer
59 views

Exponential Regression with x outside of exponential

I am trying to do exponential regression by matrix notation, and I am trying to figure out to create my $\mathbf{X}$ matrix to fit my model. I know that I need to use a model function of the form $c_1 ...
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1answer
178 views

Analyzing seasonality in data

In order to analyze the data in presence of seasonality, I used two methods: Proportional hazard model (Cox model) and time series method (Triple Exponential Smoothing (Holt Winters Method)). Now , my ...
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Multivariate exponential smoothing and Kalman filter equivalence

Suppose the time-series $X$ is hidden state Gaussian random walk and we observe $Y = X + e$, where $e$ is gaussian white noise independent of $X$. The Kalman estimator of $X$ in this case has a ...
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836 views

Do you think smoothing constant value, alpha, in SES method is a control parameter or process parameter?

There is a debate in selecting the smoothign constant in Single Exponentioan Smoothing method by practitioner or considering it as a process parameter? Could you please provide your opinion regarding ...
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583 views

use Exponential smoothing to forecast lead-time demand

I'd like to use Simple Exponential smoothing to forecast the lead-time demand for inventory control, I have monthly data and LT+1 is equal to 5 months, can I do a forecast using SES which gives me a ...
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Fitting a Local Poisson model (Exponential Smoothing) [closed]

I am working through "Forecasting with Exponential Smoothing". I am stuck on exercise 16.4 on the part that states: The data set partx contains a history of ...
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121 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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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
142 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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112 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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225 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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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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65 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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208 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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430 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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1answer
899 views

How can a 95% confidence interval not overlap with my trendline forecast?

I used holt winters in excel to forecast 12 moths ahead based on 40 months of historic data. Then I ran a monte carlo simulation to create 1000 scenarios and computed upper and lower bounds to create ...
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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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864 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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65 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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234 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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384 views

Holt-Winters seasonal method doesn't work in a small sample

I was following the examples provided by Forecasting: principles and practice. I have modified a little bit the Holt-Winters' example: ...
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1answer
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Values of $\alpha$, $\beta$ and $\gamma$ in ets in forecast package

I am using the forecast package in R. I wanted to know how the ets() function finds the value of $\alpha$, $\beta$ and $\gamma$? ...
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686 views

Why doesn't the exponential smoothing forecast package in R provide confidence intervals for the fitted values?

The upper and lower prediction intervals for the forecast periods are provided by the forecast() function. However, neither prediction or confidence intervals seem to be available for the fitted ...
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326 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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Results of stlf forecast prediction intervals change each run [closed]

Using stlf from Rob Hyndman's forecast package in R, I have noticed that the prediction intervals change each time I run it on a specific series of data (stays the same on other time series data as it ...
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How to pick coefficients for Holt Winters?

I'm using Holt Winters to predict sales revenue from past performance. Seasonality and changing trends exist in the data. One of the reasons chosen for Holt Winters is that it is fairly simple (...