Analysis of Sequential Data
MSE Module TSM_AnSeqDa
MSE Module TSM_AnSeqDa
Fichier Détails
| Cartes-fiches | 96 |
|---|---|
| Langue | Deutsch |
| Catégorie | Mathématiques |
| Niveau | Université |
| Crée / Actualisé | 17.01.2021 / 08.09.2023 |
| Lien de web |
https://card2brain.ch/box/20210117_tsmanseqda
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| Intégrer |
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What are the parameter restrictions for ets models?
What are the different steps in automatic forecasting?
Which ets models can lead to numerical difficulties?
How do you interpret the parameters (alpha, beta, gamma, and phi) of a ETS model?
What is the ets() function in R about?
- Automatically chooses a model by default using the AIC, AICc or BIC
- Can handle any combination of trend, seasonality and damping
- Ensures the parameters are admissible ( equivalent to invertible)
- Produces an object of class "ets"
Exercise shown in lecture 5:
An exponential smoothing model with trend has parameters alpha = 0.0001, beta = 0.0001, with initial states l0 = 1; b0 = 1. Let us assume that the first observation of the time series has time index 1.
- Which is approximately the fitted value for time t=8? Discuss how you reach your conclusion, showing the relevant formulae.
- Compute exactly the fitted values for the first two time instants of the time instants of the time series, assuming the first two observations of the time series to be y=[1.5;2.2].
- How could you change the parameters of the model, in order to obtain a nive predictor?
How is stationarity defined and what is it important for?
- A stationary series is
- roughly horizontal
- constant variance
- no patterns predictable in th elong-term (for instance no seasonality)
- Necessaty for arima models
Is the following time series plot stationary?
No
Is the following time series plot stationary?
No
Is the following plot stationary?
No
Is the following plot stationary?
No
Is the following plot stationary?
It is kind of regular. But the problem is that the peaks between the peaks are not constant and therefore we can not apply seasonal differencies.
So no
How can you identify non-stationary time series (arima models need stationarity)?
- Time plot
- The ACF of stationary data drops to zero relatively quickly
- The ACF of non-stationary data decreases slowly
- For non-stationary data, the value of r1 is often large and positive
What is differencing about?
- Used when arima models are applied to forecast the time series
- Differencing helps to stailize the mean
- the differenced series is the change between each observation in the original series
- y't = yt - yt-1
- The differenced series will have only T-1 values since it is not possible to calculate a difference y'1 for the first observation
Is the random walk stationary?
If we simulate many random walks, the average value of the simulatoin at time t is 0, while the spread of the simulations increase with t -> variance of random walk is non-stationary
What is the difference between first- and second-order differencing?
Occasionally the first-order differenced data will not appear stationary and it may be necessary to difference the data a second time.
