# 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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### Errors and residuals in simple exponential smoothing (state space form) in FPP textbook

I am reading Hyndman & Athanasopoulos "Forecasting: Principles and Practice" 2nd edition (FPP2). (I am aware that 3rd edition exists.) In the chapter about exponential smoothing, section ...
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### Heteroscedasticity

I am trying to build a regression model to explain variations in mortgage volumes using variations in different mortgage rates. To account for the drastic change in macroeconomic environment: from ...
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### Is Brown's double exponential smoothing a special case of Holt's exponential smoothing?

I am currently reading the book "Forecasting with Exponential Smoothing: The State Space Approach". On the bottom of page 14, it says that “In the special case where $\alpha=\beta^*$, Holt’s ...
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### Derivation of Double (Brown) Exponential Smoothing

I am learning the double (Brown) exponential smoothing. Comparing to the simple exponential smoothing, the Brown exponential smoothing smooths the output sequence $Y_t$ twice, such that \begin{align} ...
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### I cannot replicate the slope for an ETS model with alpha = 0.5 and beta =0.5 using the model's formula. Misunderstanding or a bug?

When I fit an "AAN" ETS model with alpha and beta both equal to 0.5, the level is correct as per the Level equation, but the slope as independently calculated by the Trend equation is not. I ...
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### ETS (error, trend, seasonal) formulation

Does someone know if there is (clever) way to formulate mathematically all the following models below: in a unique (system) of equations?
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### Problem with ets function diagnostic for model with trend and seasonality

I have been meaning to fit an exponential smoothing model to a monthly series that looks like the one below: When I decompose the series it is almost evident that we have seasonality and also there ...
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### What to do when model fails Ljung-Box test?

I have been learning time-series forecasting recently and I am trying to understand the procedure. I would like to find the best model for a daily time series, so far I tried exponential smoothing ...
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### Estimating average of a random variable with lower variance is faster to converge than a variable with higher variance?

I have a fallowing problem: I have to estimate average of 2 random variables $X$ and $Y$ based on average of two other. Where the $X$ and $Y$ are some $n$ by $n$ matrices. $$X = 0.5\cdot(A+B)$$  Y ...
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### Hyperparameters of Exponential Smoothing

I have a large number of time series to forecast on which I would like to evaluate the potential of Exponential Smoothing. However, I am faced with a problem of parameter selection: I dont know how to ...
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### Appropriate forecasting methods for only 20 observations [duplicate]

I am trying to forecast the regional GDP growth of our region in the next five years, I only have 20 observations in my data which is yearly, what forecasting model is appropriate? I tried ARIMA in r ...
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### Differentiating data before exponential smoothing?

I know that to perform exponential smoothing you don't have to make your time series stationary, but I seem to get better results when I do it. Do you know anything about it?
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### (How) Can you combine moving average and exponential smoothing filters to get smoother trends?

Goal: Have a machine perform smoothing on time series data set to have a smooth looking trend. The correctness of the trend is balanced by being optimal i.e., minimize the MSE (Mean Standard Error). ...
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### Point Estimates using forecast in R for Multi-Step TS Forecast -- Sometimes Same/Sometimes Not -- Why?

I am using the simple forecast(data, h = 6) function in R - as I work through Hyndman's 'Forecasting: Principles and Practice" textbook - which returns forecasts from the ETS algorithm. I'm not ...
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### Why does the exponential moving average equation divide with 1+(1-⍺)+...?

I am trying to understand an exponential moving average, reading its Wikipedia page: https://en.wikipedia.org/wiki/Moving_average#Weighted_moving_average In the middle of the explanation, the page ...
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