# Tagged Questions

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

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### 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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### Advance Methods of Understanding Significance of Customer Behaviors

I currently own a couple of websites and lately I've been implementing some feature changes - I've noticed some changes in website traffic and I was wondering what some of the more sophisticated ways ...
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### 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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### Tuning an exponential moving average to a moving window mean?

The alpha parameter of an exponential moving average defines the smoothing that the average applies to a time series. In a similar way, the window size of a moving window mean also defines the ...
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### How to convert hourly data into a time seris in R [migrated]

I have hourly data arranged by date and the dput is given below: ...
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### 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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### 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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### 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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### 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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### 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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### Holt Winters with exogenous regressors in R

I need to forecast using HoltWinters with regression parameters using R. But I found there is not any option of xreg in ...
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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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### '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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### 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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### 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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### Forecasting time series one step ahead - with and without taking into account trend

In the Exponential Smoothing chapter of Hyndman and AthanaÂ­sopouÂ­los's online book 'Forecasting: principles and practice', the authors first introduce simple exponential smoothing and then Holt's ...
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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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### 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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### Usage of AIC for comparing models [duplicate]

Can AIC be used to compare a model with exponential smoothing with linear regressions?
719 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### measuring accuracy in one step forecast(using auto.arima() and ets() in R

Iâ€™m working on workersâ€™ 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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### 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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### 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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### 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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### 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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### 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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### 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 ...