A basic forecasting technique for time series data, optionally including trend and/or seasonality, but (usually) excluding causal influences.

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Forecast daily data with weekly and monthly seasonality using exponential smoothing

I have to forecast data that exhibits dual seasonality. For example, the first day of the week can show seasonality and also the first week of the month can show seasonality. I am planning to use ...
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1answer
2k views

Need clarity on alpha, beta, gamma optimization in Triple Exponential Smoothing Forecast

I asked a variation of this question, but I want to be more direct. Take the exact same Triple Exponential Smoothing Model (Holt-Winters with a moving level, trend, and seasonal component)--- Would ...
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18 views

Sales forecasting: Unsure about data grouping

I am trying to implement a simple, short-term (1-4 weeks) forecast of product revenue/sales. The data I have is brand category product revenue where ...
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1answer
421 views

Anomaly detection using exponential weighted moving average

I would like to detect anomaly using exponential weighted moving average. I don't have series of data points. All I have is EMA(t-1) and the data point of the current time(t) DP(t). From these data, ...
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2answers
38 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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32 views

When to use Exponential Smoothing vs ARIMA?

I have recently been refreshing my forecasting knowledge while working on some monthly forecasts at work and reading Rob Hyndman's book but the one place I am struggling is when to use an exponential ...
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1answer
272 views

Interpretation of level, trend and seasonal indices in Holt-Winters exponential smoothing

I am trying to learn Holt-Winters exponential smoothing. In the algorithm there are three indices involved (level, trend, ...
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16 views

Detect increase/decrease events on time series

Given a time series, I have to detect two types of events: 1) "medium" decrease 2) "high" increase Event detection should be "fast enough". I used quotation marks as I'd like to set different ...
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1answer
58 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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8 views

Linear regression (best fit line) on moving averages vs raw data?

I have a series of sets of data over a period of time, with the amount of data available being quite variable between sets. One has points for almost every day but is really quite noisy; another has ...
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1answer
263 views

How 'good' are Holt-Winters forecasts with unusual alpha, beta and gamma values?

I'm using this python script for Holt-Winters forecasting (https://gist.github.com/andrequeiroz/5888967) that I believe chooses values of alpha, gamma and beta via RMSE optimisation. Sometimes the ...
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1answer
24 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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59 views

Time Series ETS model out-of-sample one-step-ahead forecasts. Weird Results

EDIT Secondary Question: Does using one-step ahead predictions even make sense, logically, for anomaly detection? I tried introducing anomalies manually and it seems the one-step-ahead timeseries ...
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12 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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1answer
1k views

Holt-Winters exponential smoothing formula

I am trying to implement Holt-Winters exponential smoothing in Java program (I understand that R and Python have implementations of these algorithms, but I can't use those due to other reasons, so ...
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2answers
27 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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13 views

Forecasting time series one step ahead - with and without taking into account trend

In the Exponential Smoothing chapter of Hyndman and Athana­sopou­los's online book 'Forecasting: principles and practice', the authors first introduce simple exponential smoothing and then Holt's ...
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4 views

Leadtime Analysis

I need to know which statistical method to use to analyze past leadtime data. My goal is to find a more "realistic" leadtime than plugging in an arbitrary number, such as 18 weeks. The data I am ...
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43 views

Understand Exponential Moving Averages in Matlab

I'm unable to manually replicate the exponential moving average values that I see when using MATLAB's tsmovavg function. There seems to be some ambiguity online ...
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13 views

Usage of AIC for comparing models [duplicate]

Can AIC be used to compare a model with exponential smoothing with linear regressions?
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1answer
644 views

Standard Deviation of an Exponentially-weighted Mean

I wrote a simple function in Python to calculate the exponentially weighted mean: ...
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2answers
362 views

Problem with proof - why exponentially smoothed time series is biased

I'm working through the proof why the exponential smoothing is a biased estimator of a linear trend. The book is trying to describe the expected value of an exponentially smoothed time series. It's ...
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1answer
36 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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1answer
52 views

Why do my weights have to equal one?

I'm currently learning the very basics of exponential smoothing. As follows: The book first presents the following model: $$\sum{\theta^tY_{T-1}}$$ It then claims that the sum of all weights add ...
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1answer
216 views

How to choose automatically between Auto.ARIMA, ETS and STL in R

I'm working on a sales forecasting package which should be easy to use for the end user. Given a time series with historical sales data I would like to automatically select one of the three forecasts: ...
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1answer
30 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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20 views

Upper and lower limits for ets()

In the following function ets(x, lower=c(rep(0.0001,3), 0.8), upper=c(rep(0.9999,3),0.98)) How does one interpret the upper and lower limits for the ...
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110 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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1answer
74 views

Efficient automated prediction for a 1000 growing, big data sets. How to?

I have daily data points of the number of sales, but I am not looking at historic data only. My system delivers a new data point every day and in the evening I want to predict the number of sales ...
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39 views

How to find out and quantify rate of change of trend in time series?

I have a temperature data which has approximately exponential trend how can I find the temperature at which temperature is approximately constant. Is there any way to quantify the same?
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14 views

How to calculate initial states in ets function when we refit model to new data set?

usfit<-ets(usnetelec[1:45],model="AAN") test<-ets(usnetelec[46:55],model=usfit) s1 <- usfit$states[45,] s2 <- test$states[1,] How can we calculate ...
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44 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
50 views

How can I calculate the PI of (simple) exponential smoothing?

I would like to calculate the prediction intervals of exponential smoothing. In R there is a function (ses in a forecast package) which calculates the point forecast and also the prediction intervals. ...
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159 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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134 views

measuring accuracy in one step forecast(using auto.arima() and ets() in R

I’m working on workers’ remittances data (quarterly) for Bangladesh. The data span is from 1980 quarter 1 to 2014 quarter 4. My objective is to do univariate time series forecasting with ...
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1answer
50 views

simple exponential smoothing - Ljung-Box test - residual

While reading this page on time series (http://a-little-book-of-r-for-time-series.readthedocs.org/en/latest/src/timeseries.html), I found this sentence: The Ljung-Box test showed that there is ...
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1answer
115 views

Best way to deal with forecasting with noisy data?

I have a bunch of sales data. It is from distributors of 2000 different items, who service big companies and large distributors to a number of small independent stores. They sell some items which do ...
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84 views

Using a stationary data set with exponential smoothing

I am doing time series forecasting and running Holts Method with several variations.(exponential, damped, simple) ...
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2answers
155 views

Confusing Holt-Winters parameters

I have got a model for forecasting using holt-winters. However the parameters confuse me... The parameters show that there is no trend or seasonality even though there is definite trend and ...
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0answers
229 views

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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1answer
101 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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28 views

Which time series model to use?

Hi I have a large data set of objects, each containing a list of the same attributes. The data is arranged in a time series so that the value for an attribute for an object is indexed by its time. ...
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88 views

EWMA or Moving Average when Estimating Trend in Seasonal Data

What is generally the best practice when estimating trend (non-seasonal component) in seasonal data? Centred Moving Average as suggested by MatLab docs Averaged EWMA (backwards & forwards) as ...
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1answer
145 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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1answer
543 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 ...
3
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1answer
130 views

Holt-Winters Forecasting - Why do we use most recent estimate for all projections going forward?

Ive been doing some research on using the Holt-Winters method for forecasting and understand all but one aspect. Why do we use the most recent estimate for the base and trend components for all ...
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68 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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5answers
410 views

Is it always required to achieve stationarity before performing any time-series analysis?

For example, I know that for ARIMA models stationarity needs to be achieved. What about Exponential Smoothing? Is it also required?
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1answer
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Holt-Winters and Abnormal termination in LNSRCH

I try to fit data with Holt-Winters function in R. Nevertheless, i am getting the following message: ...
2
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1answer
231 views

Forecasting with two or more causal factors using the Holt-Winters method (in R)

Is there something similar to the Holt-Winters forecasting method in R, which can be used to model two or more explanatory factors?